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authorNorbert Preining <norbert@preining.info>2023-01-12 03:01:29 +0000
committerNorbert Preining <norbert@preining.info>2023-01-12 03:01:29 +0000
commit6a7900c93acc16d1bbd2f1e26286c7dd7387e6c0 (patch)
tree76196287351cba68a51934c49468bf1a7846aa76 /macros
parentc1c19023b4b1d43cb874f84df5102b485853e672 (diff)
CTAN sync 202301120301
Diffstat (limited to 'macros')
-rw-r--r--macros/latex/contrib/diffcoeff/README.txt29
-rw-r--r--macros/latex/contrib/diffcoeff/diffcoeff-doc.def6
-rw-r--r--macros/latex/contrib/diffcoeff/diffcoeff.pdf11905
-rw-r--r--macros/latex/contrib/diffcoeff/diffcoeff.sty1051
-rw-r--r--macros/latex/contrib/diffcoeff/diffcoeff.tex4687
-rw-r--r--macros/latex/contrib/diffcoeff/diffcoeff4.pdf8756
-rw-r--r--macros/latex/contrib/diffcoeff/diffcoeff4.sty744
-rw-r--r--macros/latex/contrib/diffcoeff/diffcoeff4.tex2272
-rw-r--r--macros/latex/contrib/diffcoeff/diffcoeff5.def136
-rw-r--r--macros/latex/contrib/pythonimmediate/README4
-rw-r--r--macros/latex/contrib/pythonimmediate/pythonimmediate.pdfbin402484 -> 432126 bytes
-rw-r--r--macros/latex/contrib/pythonimmediate/pythonimmediate.sty157
-rw-r--r--macros/latex/contrib/pythonimmediate/pythonimmediate.tex92
-rwxr-xr-xmacros/latex/contrib/pythonimmediate/pythonimmediate_script_pytotex.py57
-rwxr-xr-xmacros/latex/contrib/pythonimmediate/pythonimmediate_script_textopy.py2295
-rw-r--r--macros/latex/contrib/sagetex/PKG-INFO19
-rw-r--r--macros/latex/contrib/sagetex/README.md10
-rw-r--r--macros/latex/contrib/sagetex/example.pdfbin276082 -> 277744 bytes
-rw-r--r--macros/latex/contrib/sagetex/py-and-sty.dtx14
-rw-r--r--macros/latex/contrib/sagetex/sagetex.dtx28
-rw-r--r--macros/latex/contrib/sagetex/sagetex.ins9
-rw-r--r--macros/latex/contrib/sagetex/sagetex.pdfbin497692 -> 501661 bytes
-rw-r--r--macros/latex/contrib/sagetex/scripts.dtx410
-rw-r--r--macros/latex/contrib/sagetex/setup.py11
-rw-r--r--macros/musixtex/README2
-rw-r--r--macros/musixtex/doc/musixdoc.pdfbin1434694 -> 1437432 bytes
-rw-r--r--macros/musixtex/doc/musixdoc/accidentals.tex5
-rw-r--r--macros/musixtex/doc/musixdoc/barlines.tex6
-rw-r--r--macros/musixtex/doc/musixdoc/extensions.tex62
-rw-r--r--macros/musixtex/doc/musixdoc/frontmatter.tex4
-rw-r--r--macros/musixtex/doc/musixdoc/miscellaneous.tex6
-rw-r--r--macros/musixtex/doc/musixdoc/settingup.tex14
-rw-r--r--macros/musixtex/dvips/psslurs.pro6
-rw-r--r--macros/musixtex/tex/musixmkm.tex54
-rw-r--r--macros/musixtex/tex/musixps.tex1
-rw-r--r--macros/musixtex/tex/musixtex.tex47
-rw-r--r--macros/musixtex/tex/musixthacc.tex49
-rw-r--r--macros/xetex/plain/unimath-plain-xetex/doc/unimath-plain-xetex-doc.pdfbin57374 -> 57390 bytes
-rw-r--r--macros/xetex/plain/unimath-plain-xetex/doc/unimath-plain-xetex-doc.tex2
-rw-r--r--macros/xetex/plain/unimath-plain-xetex/tex/unimath-plain-xetex.tex8
40 files changed, 23063 insertions, 9895 deletions
diff --git a/macros/latex/contrib/diffcoeff/README.txt b/macros/latex/contrib/diffcoeff/README.txt
index 79754f22e3..0122d5d56c 100644
--- a/macros/latex/contrib/diffcoeff/README.txt
+++ b/macros/latex/contrib/diffcoeff/README.txt
@@ -11,19 +11,26 @@ version. The latest version of this license is in
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-This is version 4.1 of diffcoeff.sty, and associated files,
-and requires the LaTeX3 bundles l3kernel and l3packages. The
-package eases the consistent writing of ordinary, partial
-and other derivatives of arbitrary order. Version 4.1 resolves
-an error arising from changes to xtemplate and some spacing
-issues in derivative denominators.
+Version 5.0 of diffcoeff introduces many interface incompat-
+ibilities with version 4. For that reason v5.0 and v4.2 are
+are packaged together. Version 4 can always be used to comp-
+ile an older document by using the trailing optional argument
+in the \usepackage statement, e.g., \usepackage{diffcoeff}[=v4]
+The aim in both versions is to ease the writing of differential
+coefficients (derivatives) and related quantities (jacobians,
+differentials). Both versions require xtemplate from the
+l3packages bundle. Version 5 also requires the mleftright
+package.
Manifest
%%%%%%%%
README.txt this document
-diffcoeff.sty LaTeX .sty file
-diffcoeff-doc.def definition file of variant forms
- to be placed with the .sty file
-diffcoeff.pdf documentation
-diffcoeff.tex LaTeX source of documentation
+diffcoeff.sty LaTeX .sty file (current version, v5.0)
+diffcoeff4.sty LaTeX .sty file (older version, v4.2)
+diffcoeff5.def definition file of variant forms in v5
+diffcoeff-doc.def definition file of variant forms in v4
+diffcoeff.pdf documentation for current version, v5
+diffcoeff.tex LaTeX source of documentation for v5.
+diffcoeff4.pdf documentation for older version, v4
+diffcoeff4.tex LaTeX source of documentation for v4
diff --git a/macros/latex/contrib/diffcoeff/diffcoeff-doc.def b/macros/latex/contrib/diffcoeff/diffcoeff-doc.def
index 884d41760b..879285dea0 100644
--- a/macros/latex/contrib/diffcoeff/diffcoeff-doc.def
+++ b/macros/latex/contrib/diffcoeff/diffcoeff-doc.def
@@ -114,4 +114,8 @@
left-delim = \left ( ,
right-delim = \right ),
subscr-nudge = -6 mu
- } \ No newline at end of file
+ }
+
+ %%%%%%%%%% differential %%%%%%%%%%
+ \diffdef { up }
+ { op-symbol = \mathrm{d} } \ No newline at end of file
diff --git a/macros/latex/contrib/diffcoeff/diffcoeff.pdf b/macros/latex/contrib/diffcoeff/diffcoeff.pdf
index 78a8eb2265..bdeb96b06a 100644
--- a/macros/latex/contrib/diffcoeff/diffcoeff.pdf
+++ b/macros/latex/contrib/diffcoeff/diffcoeff.pdf
@@ -1,3571 +1,5084 @@
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trailer
-<< /Size 743
-/Root 741 0 R
-/Info 742 0 R
-/ID [<818457CE2233F702C658A2D0C8DD2795> <818457CE2233F702C658A2D0C8DD2795>] >>
+<< /Size 1001
+/Root 999 0 R
+/Info 1000 0 R
+/ID [<2B2C6DC2C3D29EAE04593FA91ECE6D22> <2B2C6DC2C3D29EAE04593FA91ECE6D22>] >>
startxref
-744573
+795788
%%EOF
diff --git a/macros/latex/contrib/diffcoeff/diffcoeff.sty b/macros/latex/contrib/diffcoeff/diffcoeff.sty
index 4d2015a6b0..d7a541c78d 100644
--- a/macros/latex/contrib/diffcoeff/diffcoeff.sty
+++ b/macros/latex/contrib/diffcoeff/diffcoeff.sty
@@ -7,96 +7,163 @@
%
% Andrew Parsloe ajparsloe@gmail.com
%
-\RequirePackage{expl3}
-\RequirePackage{xparse,l3keys2e,xtemplate}
-\ProvidesExplPackage {diffcoeff} {2022/06/14} {4.1}
- {Write differential coefficients consistently and easily.}
-%
+\DeclareRelease{v4}{}{diffcoeff4.sty}
+\DeclareCurrentRelease{}{2023/01/02}
+
+\RequirePackage{xtemplate,mleftright}
+\ProvidesExplPackage {diffcoeff} {2023/01/02} {5.0}
+ {Write differential coefficients easily and consistently.}
\keys_define:nn { diffcoeff }
{
- ISO .bool_set:N = \l__diffcoeff_ISO_bool,
- spaced .int_set:N = \l__diffcoeff_spaced_int,
- spaced .default:n = 1,
- spaced .initial:n = 0,
- def-file .tl_gset:N = \g__diffcoeff_def_tl,
- def-file .initial:n = diffcoeff,
- def-file .default:n = diffcoeff
+ spaced .int_set:N = \l__diffcoeff_spaced_int,
+ spaced .default:n = 1,
+ spaced .initial:n = 0,
+ mleftright .bool_set:N = \l__diffcoeff_mLR_bool,
+ mleftright .default:n = true,
+ mleftright .initial:n = false,
+ def-file .tl_gset:N = \g__diffcoeff_def_tl,
+ DIF .clist_set:N = \l__diffcoeff_dif_clist
+ }
+\IfFormatAtLeastTF {2020-10-01} {}
+ { \RequirePackage { xparse } }
+\IfFormatAtLeastTF {2022-06-01}
+ { \ProcessKeyOptions [ diffcoeff ] }
+ {
+ \RequirePackage { l3keys2e }
+ \ProcessKeysOptions { diffcoeff }
}
-\ProcessKeysPackageOptions { diffcoeff }
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\cs_generate_variant:Nn \tl_if_eq:nnTF { nV }
-
-\tl_new:N \l__diffcoeff_oporder_tl
+\bool_if:NT \l__diffcoeff_mLR_bool
+ { \mleftright }
+%%%%%%%%%% messages %%%%%%%%%
+\cs_new:Npn \__diffcoeff_msg_autocalc:n #1
+ {
+ in~the~order~spec.~[#1]~\msg_line_context:.~Calculation~of~the~
+ total~order~of~differentiation~fails~in~this~case.~
+ Use~the~\tl_to_str:n { \difoverride }command~to~enter~the~total~order.~
+ \msg_see_documentation_text:n {diffcoeff}
+ }
+\cs_new:Npn \__diffcoeff_msg_style:nnn #1#2#3
+ {
+ The~style~specified~in~the~current~instance,~#1,~
+ \msg_line_context:,~#3~Reverting~to~default~style~#2.
+ }
+\tl_const:Nn \c__diffcoeff_msg_vcon_tl
+ { Version~5~of~diffcoeff~does~not~support~the~use~of~ }
+\tl_const:Nn \c__diffcoeff_msg_revert_tl
+ { Or~revert~to~version~4~by~appending~[=v4]~to~the~preamble~call;~
+ for~example,~\tl_to_str:n{\usepackage}{diffcoeff}[=v4] }
+\msg_new:nnn { diffcoeff } { file-not-found } { File~#1.def~not~found. }
+\msg_new:nnn { diffcoeff } { order-spec-general }
+ { #3~followed~by~#2~\__diffcoeff_msg_autocalc:n { #1 } }
+\msg_new:nnn { diffcoeff } { unknown-style }
+ { \__diffcoeff_msg_style:nnn {#1} {#2} { is~unknown. } }
+\msg_new:nnn { diffcoeff } { wrong-style }
+ { \__diffcoeff_msg_style:nnn {#1} {#2} { conflicts~with~its~template. } }
+\msg_new:nnn { diffcoeff } { version-conflict }
+ {
+ \c__diffcoeff_msg_vcon_tl #1~\msg_line_context:.~\tl_to_str:n { #2 }
+ \msg_see_documentation_text:n {diffcoeff}~\c__diffcoeff_msg_revert_tl
+ }
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\bool_new:N \l__diffcoeff_multitok_bool
+\bool_new:N \l__diffcoeff_append_bool
+\bool_new:N \l__diffcoeff_op_left_bool
+\bool_new:N \l__diffcoeff_dl_bool
+\bool_new:N \l__diffcoeff_exponent_bool
+\tl_new:N \l__diffcoeff_override_tl
+\tl_new:N \l__diffcoeff_frac_tl
\tl_new:N \l__diffcoeff_derivand_tl
-\tl_new:N \l__diffcoeff_type_tl
-\tl_new:N \l__diffcoeff_tot_order_tl
+\tl_new:N \l__diffcoeff_instance_tl
+\tl_new:N \l__diffcoeff_ord_tl
+\tl_new:N \l__diffcoeff_var_tl
+\tl_new:N \l__diffcoeff_tot_ord_tl
+\tl_new:N \l__diffcoeff_vph_tl
+\tl_new:N \l__diffcoeff_exponent_tl
\tl_new:N \l__diffcoeff_curr_num_tl
\tl_new:N \l__diffcoeff_curr_var_tl
\tl_new:N \l__diffcoeff_paren_tl
-
-\tl_const:Nn \c__diffcoeff_digits_tl { 1234567890 }
-
-\seq_new:N \l__diffcoeff_orders_seq
+\seq_new:N \l__diffcoeff_ords_seq
\seq_new:N \l__diffcoeff_vars_seq
-\seq_new:N \l__diffcoeff_denom_seq
\seq_new:N \l__diffcoeff_paren_seq
-
-\prop_new:N \l__diffcoeff_vars_prop
-
-\bool_new:N \l__diffcoeff_op_left_bool
-\bool_new:N \l__diffcoeff_single_var_bool
-\bool_new:N \l__diffcoeff_opwrap_bool
-\bool_new:N \l__diffcoeff_integ_bool
-\bool_new:N \l__diffcoeff_spaced_bool
-\bool_new:N \l__diffcoeff_altsep_bool
-
-\int_new:N \l__diffcoeff_vars_int
-\int_new:N \l__diffcoeff_format_int
+\int_new:N \l__diffcoeff_group_int
+\int_new:N \l__diffcoeff_style_int
\int_new:N \l__diffcoeff_curr_tok_int
\int_new:N \l__diffcoeff_curr_state_int
\int_new:N \l__diffcoeff_nos_int
\int_new:N \l__diffcoeff_parenvar_int
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\DeclareObjectType { derivative } { 3 }
-
-% defaults: ordinary deriv. values
-\DeclareTemplateInterface { derivative } { DERIV } { 3 }
+\prop_new:N \l__diffcoeff_vars_prop
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\DeclareObjectType { diffcoeff } { 5 }
+% #1 append boolean; #2 order spec(clist); #3 derivand(tl);
+% #4 diff variables(clist); #5 pt of eval(tl)
+\DeclareTemplateInterface { diffcoeff } { DIF } { 5 }
{
- op-symbol : tokenlist = d ,
+ style-group : choice { f, s, c, j, l } = f,
+ style : choice { frac, tfrac, dfrac,
+ /, auto, big, Big, bigg, Bigg,
+ _, dl
+ } = frac ,
+ slash-tok : tokenlist = / ,
+ slash-sep : tokenlist = 0 mu,
+ derivand-sep : tokenlist = 3 mu plus 1 mu minus 2 mu,
+ op-symbol : tokenlist = \mathrm{d},
op-symbol-alt : tokenlist = \KeyValue { op-symbol },
- op-order-sep : muskip = 1 mu ,
- derivand-sep : muskip = 3 mu plus 1 mu minus 2 mu,
+ op-order-nudge : tokenlist = 0 mu ,
+ var-sup-nudge : tokenlist = 1 mu ,
+ multi-term-sep : tokenlist = 2 mu plus 1 mu minus 1 mu,
+ term-sep-adjust : tokenlist = -1 mu,
long-var-wrap : choice { dv, d(v), (dv) }
- = d(v) ,
- denom-term-sep : muskip = 2 mu ,
- term-sep-adjust : muskip = -1 mu ,
- left-delim : tokenlist = \left . ,
- right-delim : tokenlist = \right |,
- elbowroom : muskip = 0 mu ,
- subscr-nudge : muskip = 0 mu ,
- *-derivand-sep : muskip = \KeyValue { derivand-sep },
- *-op-left : boolean = false ,
- *-italic-nudge : muskip = 3 mu ,
- /-derivand-sep : muskip = \KeyValue { derivand-sep },
- /-denom-term-sep : muskip = 1 mu ,
- /-left-delim : tokenlist = ( ,
- /-right-delim : tokenlist = ) ,
- /-elbowroom : muskip = 0 mu ,
- /-subscr-nudge : muskip = 0 mu ,
- */-derivand-sep : muskip = \KeyValue { /-derivand-sep },
- */-op-wrap : boolean = true
- }
-% #1 order spec(seqvar); #2 order override(tlvar)
-% #3 derivand(tlvar); #4 denominator(seqvar)
-% #5 subscript(tlvar)
-\DeclareTemplateCode { derivative } { DERIV } { 3 }
+ = d(v) ,
+ lvwrap-Ldelim : tokenlist = \mleft (,
+ lvwrap-Rdelim : tokenlist = \mright ),
+ lvwrap-sup-nudge : tokenlist = -2 mu,
+ outer-Ldelim : tokenlist = \left ( ,
+ outer-Rdelim : tokenlist = \right ),
+ elbowroom : tokenlist = 0 mu ,
+ sub-nudge : tokenlist = -5 mu,
+ op-sub-nudge : tokenlist = 0 mu ,
+ *derivand-sep : tokenlist = \KeyValue { derivand-sep },
+ *op-set-left : boolean = false,
+ *italic-nudge : tokenlist = 0 mu ,
+ *inner-wrap : boolean = false,
+ *inner-Ldelim : tokenlist = (,
+ *inner-Rdelim : tokenlist = ),
+ *outer-Ldelim : tokenlist = \bigl [,
+ *outer-Rdelim : tokenlist = \bigr ],
+ *sub-nudge : tokenlist = 0 mu
+ }
+\DeclareTemplateCode { diffcoeff } { DIF } { 5 }
{
- op-symbol = \l__diffcoeff_op_tl,
- op-symbol-alt = \l__diffcoeff_op_alt_tl,
- op-order-sep = \l__diffcoeff_oporder_muskip,
- derivand-sep = \l__diffcoeff_derivsep_muskip,
+ style-group = {
+ f = \int_set:Nn \l__diffcoeff_group_int { 0 },
+ s = \int_set:Nn \l__diffcoeff_group_int { 1 },
+ c = \int_set:Nn \l__diffcoeff_group_int { 2 },
+ j = \int_set:Nn \l__diffcoeff_group_int { 3 },
+ l = \int_set:Nn \l__diffcoeff_group_int { 4 }
+ },
+ style = {
+ frac = \__diffcoeff_style:nn { 0 } {},
+ tfrac = \__diffcoeff_style:nn { 1 } {},
+ dfrac = \__diffcoeff_style:nn { 2 } {},
+ / = \__diffcoeff_style:nn { 3 } {},
+ auto = \__diffcoeff_style:nn { 4 } {},
+ big = \__diffcoeff_style:nn { 5 } { big },
+ Big = \__diffcoeff_style:nn { 5 } { Big },
+ bigg = \__diffcoeff_style:nn { 5 } { bigg },
+ Bigg = \__diffcoeff_style:nn { 5 } { Bigg },
+ _ = \__diffcoeff_style:nn { 6 } {},
+ dl = \__diffcoeff_style:nn { 7 } {},
+ unknown = \__diffcoeff_style:nn { 9 } {}
+ },
+ slash-tok = \l__diffcoeff_slashtok_tl,
+ slash-sep = \l__diffcoeff_slashsep_tl,
+ derivand-sep = \l__diffcoeff_derivsep_tl,
+ op-symbol = \l__diffcoeff_opi_tl,
+ op-symbol-alt = \l__diffcoeff_opii_tl,
+ op-order-nudge = \l__diffcoeff_opordsep_tl,
+ var-sup-nudge = \l__diffcoeff_varsupnudge_tl,
+ multi-term-sep = \l__diffcoeff_termsep_tl,
+ term-sep-adjust = \l__diffcoeff_sep_adj_tl,
long-var-wrap = {
dv = \cs_set_eq:NN \__diffcoeff_wrap_longvars:nn
\__diffcoeff_wrap_longvars_dv:nn,
@@ -105,307 +172,164 @@
(dv) = \cs_set_eq:NN \__diffcoeff_wrap_longvars:nn
\__diffcoeff_wrap_longvars_dvii:nn,
unknown = \cs_set_eq:NN \__diffcoeff_wrap_longvars:nn
- \__diffcoeff_wrap_longvars_dvi:nn
+ \__diffcoeff_wrap_longvars_dvi:nn
},
- denom-term-sep = \l__diffcoeff_varsep_muskip,
- term-sep-adjust = \l__diffcoeff_sep_adj_muskip,
- left-delim = \l__diffcoeff_ldelim_tl,
- right-delim = \l__diffcoeff_rdelim_tl,
- elbowroom = \l__diffcoeff_elbowrm_muskip ,
- subscr-nudge = \l__diffcoeff_subnudge_muskip,
- *-derivand-sep = \l__diffcoeff_derivsepi_muskip,
- *-op-left = \l__diffcoeff_op_left_bool,
- *-italic-nudge = \l__diffcoeff_opnudge_muskip,
- /-derivand-sep = \l__diffcoeff_derivsepii_muskip,
- /-denom-term-sep = \l_tmpb_muskip,
- /-left-delim = \l__diffcoeff_ldelimi_tl,
- /-right-delim = \l__diffcoeff_rdelimi_tl,
- /-elbowroom = \l_tmpc_muskip,
- /-subscr-nudge = \l_tmpd_muskip,
- */-derivand-sep = \l__diffcoeff_derivsepiii_muskip,
- */-op-wrap = \l__diffcoeff_opwrap_bool
+ lvwrap-Ldelim = \l__diffcoeff_lvw_ldelim_tl,
+ lvwrap-Rdelim = \l__diffcoeff_lvw_rdelim_tl,
+ lvwrap-sup-nudge = \l__diffcoeff_lvsupnudge_tl,
+ outer-Ldelim = \l__diffcoeff_ldelim_tl,
+ outer-Rdelim = \l__diffcoeff_rdelim_tl,
+ elbowroom = \l__diffcoeff_elbowrm_tl ,
+ sub-nudge = \l__diffcoeff_subnudge_tl,
+ op-sub-nudge = \l__diffcoeff_opsubnudge_tl,
+ *derivand-sep = \l__diffcoeff_derivsepi_tl,
+ *op-set-left = \l__diffcoeff_op_left_bool,
+ *italic-nudge = \l__diffcoeff_opleftnudge_tl,
+ *inner-wrap = \l__diffcoeff_innerwrap_bool,
+ *inner-Ldelim = \l__diffcoeff_lopwrap_tl,
+ *inner-Rdelim = \l__diffcoeff_ropwrap_tl,
+ *outer-Ldelim = \l__diffcoeff_ldelimapp_tl,
+ *outer-Rdelim = \l__diffcoeff_rdelimapp_tl,
+ *sub-nudge = \l__diffcoeff_subnudgeapp_tl
}
{
\AssignTemplateKeys
-
- \bool_if:NF\l__diffcoeff_integ_bool
- {
- \int_compare:nNnT { \l__diffcoeff_format_int } > { 1 }
- { \__diffcoeff_slash_vals: }
- \__diffcoeff_build:nnn { #1 } { #2 } { #3 }
- }
+ \__diffcoeff_check_style:nn
+ { \l__diffcoeff_group_int } { \l__diffcoeff_style_int }
+ \__diffcoeff_append:n { #1 }
+ \exp_args:Nx \__diffcoeff_orders:nn { \clist_count:n {#4} } { #2 }
+ \__diffcoeff_override:N \l__diffcoeff_override_tl
+ \__diffcoeff_derivand:n { #3 }
+ \__diffcoeff_build:nn { #4 } { #5 }
}
%%%%%%%%%%
-\cs_new:Npn \__diffcoeff_slash_vals:
- {
- \muskip_set:Nn \l__diffcoeff_varsep_muskip \l_tmpb_muskip
- \muskip_set:Nn \l__diffcoeff_elbowrm_muskip \l_tmpc_muskip
- \muskip_set:Nn \l__diffcoeff_subnudge_muskip \l_tmpd_muskip
- \tl_set:NV \l__diffcoeff_ldelim_tl \l__diffcoeff_ldelimi_tl
- \tl_set:NV \l__diffcoeff_rdelim_tl \l__diffcoeff_rdelimi_tl
- }
-% #1 diff'and; #2 vars clist; #3 trailing arg
-\cs_new:Npn \__diffcoeff_build:nnn #1#2#3
+\cs_new_protected:Npn \__diffcoeff_style:nn #1#2
{
- \tl_set:Nn \l__diffcoeff_derivand_tl { #1 }
- \seq_set_from_clist:Nn \l__diffcoeff_vars_seq { #2 }
- \bool_if:nT
- {
- !\l__diffcoeff_opwrap_bool &&
- \int_compare_p:nNn { \l__diffcoeff_format_int } > { 1 }
- }
- { \int_set:Nn \l__diffcoeff_format_int { 4 } }
- \__diffcoeff_spaced:n { \l__diffcoeff_spaced_int }
- \bool_if:nTF
- {
- ( \l__diffcoeff_altsep_bool && !\l__diffcoeff_spaced_bool )
- || ( !\l__diffcoeff_altsep_bool && \l__diffcoeff_spaced_bool )
- }
- { \__diffcoeff_derivsep: }
- { \tl_put_left:Nn \l__diffcoeff_derivand_tl { \mskip 0 mu } }
- \tl_if_novalue:nF { #3 }
- { \l__diffcoeff_ldelim_tl \mskip \l__diffcoeff_elbowrm_muskip }
- \bool_if:NTF \l__diffcoeff_single_var_bool
+ \int_set:Nn \l__diffcoeff_style_int { #1 }
+ \tl_set:Nn \l__diffcoeff_frac_tl { \prg_do_nothing: }
+ \int_case:nn { #1 }
{
- \tl_set:Nx \l_tmpa_tl { \seq_use:Nn \l__diffcoeff_vars_seq { , } }
- \__diffcoeff_single:NNN \l__diffcoeff_tot_order_tl \l__diffcoeff_derivand_tl \l_tmpa_tl
- }
- {
- \int_zero:N \l_tmpa_int
- \seq_mapthread_function:NNN \l__diffcoeff_orders_seq
- \l__diffcoeff_vars_seq \__diffcoeff_map_orders:nn
- \__diffcoeff_mixed:NNN \l__diffcoeff_tot_order_tl
- \l__diffcoeff_derivand_tl \l__diffcoeff_denom_seq
- }
- \tl_if_novalue:nF { #3 }
- {
- \mskip \l__diffcoeff_elbowrm_muskip \l__diffcoeff_rdelim_tl
- \tl_if_empty:nF { #3 }
- {
- \c_math_subscript_token
- { \mskip \l__diffcoeff_subnudge_muskip { #3 } }
+ { 0 } { \tl_set:Nn \l__diffcoeff_frac_tl { \frac } }
+ { 1 } { \tl_set:Nn \l__diffcoeff_frac_tl { \tfrac } }
+ { 2 } { \tl_set:Nn \l__diffcoeff_frac_tl { \dfrac } }
+ { 3 } { \tl_set:Nn \l__diffcoeff_frac_tl { \difstfrac } }
+ { 4 } { \tl_set:Nn \l__diffcoeff_frac_tl { \difsafrac } }
+ { 5 } { \tl_set:Nn \l__diffcoeff_frac_tl { \difsbfrac[#2] } }
+ { 6 } { \tl_set:Nn \l__diffcoeff_frac_tl {} }
+ { 7 } { \bool_set_true:N \l__diffcoeff_dl_bool }
+ { 9 }
+ {
+ \msg_error:nnxx { diffcoeff } { unknown-style }
+ { \l__diffcoeff_instance_tl }
+ { \__diffcoeff_style_group:n { \l__diffcoeff_group_int } }
}
}
}
-%%%%%%%%%%%%%%%%%%%%
-\cs_new_protected:Npn \__diffcoeff_spaced:n #1
- {
- \int_case:nn { \int_sign:n { #1 } }
- {
- { 1 } { \bool_set_true:N \l__diffcoeff_spaced_bool }
- { 0 } { \bool_set_false:N \l__diffcoeff_spaced_bool }
- { -1 }
- {
- \int_compare:nNnTF { 1 } <
- { \tl_count:N \l__diffcoeff_derivand_tl }
- { \bool_set_true:N \l__diffcoeff_spaced_bool }
- { \bool_set_false:N \l__diffcoeff_spaced_bool }
- }
- }
- }
-\cs_new_protected:Npn \__diffcoeff_derivsep:
- {
- \tl_put_left:Nx \l__diffcoeff_derivand_tl
- {
- \int_case:nn { \l__diffcoeff_format_int }
- {
- { 0 } { \mskip \l__diffcoeff_derivsep_muskip }
- { 1 } { \mskip \l__diffcoeff_derivsepi_muskip }
- { 2 } { \mskip \l__diffcoeff_derivsepii_muskip }
- { 3 } { \mskip \l__diffcoeff_derivsepiii_muskip }
- { 4 } { \mskip \l__diffcoeff_derivsepiii_muskip }
- }
+% #1 group int; #2 style int
+\cs_new_protected:Npn \__diffcoeff_check_style:nn #1#2
+ {
+ \bool_if:nF
+ {
+ ( \int_compare_p:nNn { \int_div_truncate:nn {#2} {3} } = { #1 }
+ && \int_compare_p:nNn { #1 } < { 3 } ) % f,s,c
+ || ( \int_compare_p:nNn { \int_div_truncate:nn {#2} {2} } < { #1 }
+ && \int_compare_p:nNn { #1 } = { 3 } ) % j
+ || \int_compare_p:nNn { #1 + #2 } = { 11 } % l
}
- }
-\cs_new:Npn \__diffcoeff_wrap_longvars_dv:nn #1#2
- { \l__diffcoeff_op_alt_tl { {}#2 }^{ #1 } }
-\cs_new:Npn \__diffcoeff_wrap_longvars_dvi:nn #1#2
- { \l__diffcoeff_op_alt_tl { {}(#2) }^{ #1 } }
-\cs_new:Npn \__diffcoeff_wrap_longvars_dvii:nn #1#2
- { (\l__diffcoeff_op_alt_tl { {}#2) }^{ #1 } }
-% (ptl) form denom #1 from orders seq & #2 from vars seq
-\cs_new_protected:Npn \__diffcoeff_map_orders:nn #1#2
- {
- \tl_if_eq:nnTF { #1 } { 1 }
- { \seq_put_right:Nn \l__diffcoeff_denom_seq { \l__diffcoeff_op_alt_tl { #2 } } }
{
- \int_compare:nNnTF { \tl_count:n { #2 } } = { 1 }
+ \msg_warning:nnxx { diffcoeff } { wrong-style }
+ { \l__diffcoeff_instance_tl }
+ { \__diffcoeff_style_group:n { #1 } }
+ \int_compare:nNnTF { #1 } = { 3 }
+ { \__diffcoeff_style:nn { 0 } {} }
{
- \seq_put_right:Nn \l__diffcoeff_denom_seq
- { \l__diffcoeff_op_alt_tl { #2 }^{ #1 } }
- }
- {
- \seq_put_right:Nn \l__diffcoeff_denom_seq
- { \__diffcoeff_wrap_longvars:nn { #1\vphantom{)} } { #2 } }
+ \int_compare:nNnTF { #1 } = { 4 }
+ { \__diffcoeff_style:nn { 7 } {} }
+ { \__diffcoeff_style:nn { 3*#1 } {} }
}
}
- }
-% #1 order(tlvar) ; #2 diff'iand(tlvar); #3 denom(tlvar)
-\cs_new:Npn \__diffcoeff_single:NNN #1#2#3
- {
- \__diffcoeff_numer:N { #1 }
- \__diffcoeff_form_deriv:NNn
- \l__diffcoeff_oporder_tl
- \l__diffcoeff_derivand_tl
- { \__diffcoeff_denom_single:NN #1 #3 }
- }
-% #1 total order; #2 derivand; #3 denom seq
-\cs_new_protected:Npn \__diffcoeff_mixed:NNN #1#2#3
- {
- \__diffcoeff_numer:N #1
- \__diffcoeff_form_deriv:NNn
- \l__diffcoeff_oporder_tl
- \l__diffcoeff_derivand_tl
- { \__diffcoeff_denom_sep:N #3 }
- }
-\cs_new:Npn \__diffcoeff_denom_sep:N #1
+ \bool_if:nT
+ { \int_compare_p:nNn { #1 } > { 0 } && \int_if_even_p:n { #1 } }
+ { \tl_set_eq:NN \l__diffcoeff_opii_tl \l__diffcoeff_opi_tl }
+ \int_compare:nNnF { #1 } = { 1 }
+ { \bool_set_false:N \l__diffcoeff_innerwrap_bool }
+ }
+\cs_new:Npn \__diffcoeff_style_group:n #1
+ { \clist_item:nn { frac, /, _, frac, dl } { #1 + 1 } }
+\cs_new:Npn \__diffcoeff_style_aux:n #1
{
- \int_zero:N \l_tmpa_int
- \seq_map_inline:Nn #1
- {
- \int_incr:N \l_tmpa_int ##1
- \int_compare:nNnT { \l_tmpa_int } < { \l__diffcoeff_vars_int }
- {
- \seq_pop:NN \l__diffcoeff_orders_seq \l_tmpa_tl
- \str_if_eq:VnTF \l_tmpa_tl { 1 }
- { \mskip \l__diffcoeff_varsep_muskip }
- {
- \mskip \muskip_eval:n { \l__diffcoeff_varsep_muskip +
- \l__diffcoeff_sep_adj_muskip }
- }
- }
+ \int_compare:nNnTF { #1 } = { 3 } { { 0 } {} }
+ {
+ \int_compare:nNnTF { #1 } = { 4 } { { 7 } {} }
+ { { 3*#1 } {} }
}
}
-% #1(tl) total order
-\cs_new_protected:Npn \__diffcoeff_numer:N #1
- {
- \bool_if:NTF \l__diffcoeff_op_left_bool
+%%%%%%%%% append? (& wrap slash diff operator?)
+\cs_new_protected:Npn \__diffcoeff_append:n #1
+ {
+ \bool_if:nTF
+ { #1 || \int_compare_p:nNn { \l__diffcoeff_group_int } = {2} }
{
- \tl_set:Nn \l__diffcoeff_oporder_tl
- { \mskip \l__diffcoeff_opnudge_muskip }
+ \bool_set_true:N \l__diffcoeff_append_bool
+ \bool_if:NT \l__diffcoeff_innerwrap_bool
+ { \tl_put_right:Nn \l__diffcoeff_frac_tl { * } }
}
- { \tl_clear:N \l__diffcoeff_oporder_tl }
- \tl_put_right:No \l__diffcoeff_oporder_tl \l__diffcoeff_op_tl
- \exp_args:NnV \tl_if_eq:nnF { 1 } #1
+ { \bool_set_false:N \l__diffcoeff_append_bool }
+ }
+%%%%%%%%%
+% #1(int) no. of vars; #2(clist) orders spec
+\cs_new_protected:Npn \__diffcoeff_orders:nn #1#2
+ {
+ \bool_if:NTF \l__diffcoeff_exponent_bool
{
- \tl_put_right:Nn \l__diffcoeff_oporder_tl
- { \mskip \l__diffcoeff_oporder_muskip ^ { #1 } }
+ \exp_args:NNx \seq_set_from_clist:Nn \l__diffcoeff_ords_seq
+ { \prg_replicate:nn { #1 } { \l__diffcoeff_exponent_tl, } }
}
- \bool_if:NT \l__diffcoeff_op_left_bool
- { \tl_put_right:Nn \l__diffcoeff_oporder_tl { \hfill } }
- }
-% #1 order; #2 var
-\cs_new_protected:Npn \__diffcoeff_denom_single:NN #1#2
- {
- \tl_if_eq:nVTF { 1 } #1
- { \l__diffcoeff_op_alt_tl {}#2 }
{
- \int_compare:nNnTF { \tl_count:N #2 } = { 1 }
- { \l__diffcoeff_op_alt_tl {}#2^{ #1 } }
- { \__diffcoeff_wrap_longvars:nn { #1\vphantom) } { #2 } }
+ \seq_set_from_clist:Nn \l__diffcoeff_ords_seq { #2 }
+ \exp_args:Nnx\__diffcoeff_adj_ords_seq:nn { #1 }
+ { \seq_count:N \l__diffcoeff_ords_seq }
}
+ \tl_set:Nx \l__diffcoeff_vph_tl {\seq_use:Nn\l__diffcoeff_ords_seq {} }
}
-% #1 op+order; #2 diff'iand; #3 denom
-% 0 frac; 1 frac append; 2 slash ; 3 ( slash ) append; 4 slash append
-\cs_new:Npn \__diffcoeff_form_deriv:NNn #1#2#3
+\cs_new_protected:Npn \__diffcoeff_adj_ords_seq:nn #1#2
{
- \int_case:nn { \l__diffcoeff_format_int }
- {
- { 0 } { \frac { #1 #2 } { #3 } }
- { 1 } { \frac { #1 } { #3 } #2 }
- { 2 } { #1 #2 / #3 }
- { 3 } { ( #1 / #3 ) #2 }
- { 4 } { #1 / #3 #2 }
+ \int_compare:nNnTF { #1 } < { #2 }
+ { % truncate
+ \int_step_inline:nn { #2 - #1 }
+ { \seq_pop_right:NN \l__diffcoeff_ords_seq \l_tmpa_tl }
+ }
+ { % pad
+ \int_step_inline:nnnn { 1 + #2 } { 1 } { #1 }
+ { \seq_put_right:Nn \l__diffcoeff_ords_seq { 1 } }
}
}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% differential
-% #1 variant; #2 = space in mu before d (0--9)
-% note \group_end placement for \vec{x} etc
-\NewDocumentCommand \dl { d.. t- m }
- {
- \group_begin:
- \bool_set_true:N \l__diffcoeff_integ_bool
- \bool_set_true:N \l__diffcoeff_single_var_bool
- \seq_set_from_clist:Nn \l__diffcoeff_orders_seq { 1 }
- \tl_set:Nn \l__diffcoeff_tot_order_tl { 1 }
- \IfValueTF { #1 }
- { \tl_set:Nn \l__diffcoeff_type_tl { .#1 } }
- { \tl_set:Nn \l__diffcoeff_type_tl { } }
- \UseInstance { derivative } { ord\l__diffcoeff_type_tl }
- \l__diffcoeff_orders_seq \l__diffcoeff_tot_order_tl
- \c_empty_tl \c_empty_seq \c_empty_tl
- \tl_if_in:NnTF \c__diffcoeff_digits_tl { #3 }
- { \mskip \IfBooleanT #2 { - }#3 mu \l__diffcoeff_op_tl \group_end: }
- { \l__diffcoeff_op_tl \group_end: {} #3 }
- }
-\NewDocumentCommand \negmu {} { \mskip -1 mu }
-\NewDocumentCommand \nilmu {} { \mskip 0 mu }
-\NewDocumentCommand \onemu {} { \mskip 1 mu }
-\NewDocumentCommand \twomu {} { \mskip 2 mu }
-% derivative
-% #1(tl) = name of variant; #2(*)= append diff'iand boolean
-% #3(clist) = orders of diff. in each var.; #4(tl) = order override
-% #5(bool) spacing switch; #6(tl) = diff'iand; #7( / ) = slash boolean
-% #8(clist) = vars of diff.; #9(tl) = pt of eval./vars held const
-\NewDocumentCommand \diff { d.. s O{1} o t! >{\TrimSpaces} m t/ m !o }
+\cs_new_protected:Npn \__diffcoeff_override:N #1
{
- \group_begin:
- \IfBooleanTF #5
- { \bool_set_true:N \l__diffcoeff_altsep_bool }
- { \bool_set_false:N \l__diffcoeff_altsep_bool }
- \seq_set_from_clist:Nn \l__diffcoeff_orders_seq { #3 }
- \int_set:Nn \l_tmpb_int { \seq_count:N \l__diffcoeff_orders_seq }
- \int_set:Nn \l__diffcoeff_vars_int { \clist_count:n { #8 } }
- \int_compare:nNnTF { \l__diffcoeff_vars_int } = { 1 }
- { \bool_set_true:N \l__diffcoeff_single_var_bool }
- {
- \int_compare:nNnTF { \l__diffcoeff_vars_int } < { \l_tmpb_int }
- {
- \msg_error:nnxxxx { diffcoeff } { numbers-conflict }
- { \int_use:N \l__diffcoeff_vars_int } { \int_use:N \l_tmpb_int }
- { \seq_use:Nn \l__diffcoeff_orders_seq { , } }
- { \clist_use:nn { #8 } { , } }
- }
- { % pad orders seq if nec.
- \int_step_inline:nnnn
- { 1 + \l_tmpb_int } { 1 } { \l__diffcoeff_vars_int }
- { \seq_put_right:Nn \l__diffcoeff_orders_seq { 1 } }
- }
- }
- % override/calc total order
- \IfValueTF { #4 }
- { \tl_set:Nn \l__diffcoeff_tot_order_tl { #4 } }
+ \tl_if_empty:NTF { #1 }
{
- \bool_if:NTF \l__diffcoeff_single_var_bool
- { \tl_set:Nn \l__diffcoeff_tot_order_tl { #3 } }
- {
- \__diffcoeff_calc_tot_order:NN \l__diffcoeff_orders_seq
- \l__diffcoeff_tot_order_tl
- }
+ \__diffcoeff_calc_tot_order:NN \l__diffcoeff_ords_seq
+ \l__diffcoeff_tot_ord_tl
}
- \IfValueTF { #1 }
- { \tl_set:Nn \l__diffcoeff_type_tl { .#1 } }
- { \tl_set:Nn \l__diffcoeff_type_tl { } }
- % append? slash?
- \int_zero:N \l__diffcoeff_format_int
- \IfBooleanT #2 { \int_incr:N \l__diffcoeff_format_int }
- \IfBooleanT #7 { \int_add:Nn \l__diffcoeff_format_int { 2 } }
- \UseInstance { derivative } { ord\l__diffcoeff_type_tl } {#6}{#8}{#9}
- \group_end:
- } % end of \diff
-%%%%%%%%%%%%%%%%%%%
-% #2(seq) expr in; #1(tlv) expr out
-\cs_new:Npn \__diffcoeff_calc_tot_order:NN #1 #2
+ { \tl_set:Nn \l__diffcoeff_tot_ord_tl { #1 } }
+ \seq_pop_right:NN \l__diffcoeff_ords_seq \l__diffcoeff_ord_tl
+ }
+%%%%%%%%%% calc. total order %%%%%%%%%%
+% #1(seq) expr in; #2(tl) expr out
+\cs_new_protected:Npn \__diffcoeff_calc_tot_order:NN #1 #2
{
\tl_clear:N \l__diffcoeff_nos_tl
- \exp_args:Nx\__diffcoeff_digest_expr:n { \seq_use:Nn #1 { + } }
+ \exp_args:Nx \__diffcoeff_digest_expr:n { \seq_use:Nn #1 { + } }
\prop_if_empty:NTF \l__diffcoeff_vars_prop
{ \tl_set:NV #2 \l__diffcoeff_nos_tl }
- { \__diffcoeff_evaluate:NN \l__diffcoeff_vars_prop #2 }
+ {
+ \int_compare:nNnT { \l__diffcoeff_nos_int } = { 0 }
+ { \tl_clear:N \l__diffcoeff_nos_tl }
+ \__diffcoeff_evaluate:NN \l__diffcoeff_vars_prop #2
+ }
}
-\cs_new:Npn \__diffcoeff_digest_expr:n #1
- {
+\cs_new_protected:Npn \__diffcoeff_digest_expr:n #1
+ {
\tl_set:Nn \l__diffcoeff_curr_num_tl { + }
\tl_set:Nn \l__diffcoeff_paren_tl { +1 }
\tl_set:Nn \l__diffcoeff_nos_tl { 0 }
@@ -419,13 +343,11 @@
}
\int_set:Nn \l__diffcoeff_nos_int { \l__diffcoeff_nos_tl }
\tl_set:Nx \l__diffcoeff_nos_tl { \int_use:N \l__diffcoeff_nos_int }
- \int_compare:nNnT { \l__diffcoeff_nos_int } = { 0 }
- { \tl_clear:N \l__diffcoeff_nos_tl }
}
% #1 curr tok (tl); #2 <== curr tok ndx (int)
\cs_new_protected:Npn \__diffcoeff_get_curr_ndx:nN #1#2
{
- \tl_if_in:NnTF \c__diffcoeff_digits_tl { #1 }
+ \tl_if_in:nnTF { 1234567890 } { #1 }
{ \int_set:Nn #2 { 1 } } % digit
{
\str_case:nnF { #1 }
@@ -461,7 +383,7 @@
{
{ 0 } % tok = s
{
- \tl_if_eq:nVTF { #1 } \l__diffcoeff_curr_num_tl
+ \str_if_eq:nVTF { #1 } \l__diffcoeff_curr_num_tl
{ \tl_set:Nn \l__diffcoeff_curr_num_tl { + } }
{ \tl_set:Nn \l__diffcoeff_curr_num_tl { - } }
}
@@ -497,11 +419,11 @@
{ 1 } % tok = d
{ \tl_put_right:Nn \l__diffcoeff_curr_num_tl { #1 } }
{ 2 } % tok = v
- {
- \tl_if_in:nnTF { ^ \times * / \div } { #1 }
- {
- \msg_error:nnxxx { diffcoeff } { order-specification }
- { \seq_use:Nn \l__diffcoeff_orders_seq { , } }
+ {
+ \tl_if_in:nnTF { ^ \times * / } { #1 }
+ {
+ \msg_error:nnxxx { diffcoeff } { order-spec-general }
+ { \seq_use:Nn \l__diffcoeff_ords_seq { , } }
{ #1 } { number }
}
{ \tl_set:Nn \l__diffcoeff_curr_var_tl { #1 } }
@@ -511,7 +433,7 @@
\seq_push:NV \l__diffcoeff_paren_seq \l__diffcoeff_paren_tl
\tl_put_left:Nn \l__diffcoeff_paren_tl { * }
\tl_put_left:NV \l__diffcoeff_paren_tl \l__diffcoeff_curr_num_tl
- \tl_set:Nn \l__diffcoeff_curr_num_tl { + }
+ \tl_set:Nn \l__diffcoeff_curr_num_tl { + }
\int_set:Nn #3 { 0 }
}
{ 4 } % tok = )
@@ -584,8 +506,8 @@
\int_set_eq:NN #2 #3
}
{
- \msg_error:nnxxx { diffcoeff } { order-specification }
- { \seq_use:Nn \l__diffcoeff_orders_seq { , } } { #1 } { ) }
+ \msg_error:nnxxx { diffcoeff } { order-spec-general }
+ { \seq_use:Nn \l__diffcoeff_ords_seq { , } } { #1 } { ) }
}
}
% #1 is var. (tlvar); #2 is num. (tlvar); #3 num. coeff. (tlvar)
@@ -598,7 +520,7 @@
}
% #1 (propv) key=var, val=coeff; #2 <= total order
\cs_new_protected:Npn \__diffcoeff_evaluate:NN #1#2
- {
+ {
\prop_map_inline:Nn #1 { \seq_put_left:Nn \l_tmpa_seq { ##1 } }
\seq_sort:Nn \l_tmpa_seq
{
@@ -610,15 +532,17 @@
\prop_pop:NnN #1 { ##1 } \l_tmpb_tl
\seq_put_right:Nx \l_tmpb_seq { \int_eval:n \l_tmpb_tl }
}
- \tl_clear:N \l_tmpa_tl
- \seq_mapthread_function:NNN \l_tmpa_seq \l_tmpb_seq
- \__diffcoeff_tot_order:nn
+ \tl_set:Nx \l_tmpa_tl
+ {
+ \seq_mapthread_function:NNN \l_tmpa_seq \l_tmpb_seq
+ \__diffcoeff_tot_order:nn
+ }
\exp_args:NV \tl_if_head_eq_charcode:nNTF \l_tmpa_tl +
{
\tl_set:Nx \l_tmpb_tl { \tl_tail:N \l_tmpa_tl }
\int_compare:nNnT { \l__diffcoeff_nos_int } > { 0 }
{ \tl_put_left:Nn \l__diffcoeff_nos_tl { + } }
- \tl_concat:NNN #2 \l_tmpb_tl \l__diffcoeff_nos_tl
+ \tl_concat:NNN #2 \l_tmpb_tl \l__diffcoeff_nos_tl
}
{
\int_compare:nNnTF { \l__diffcoeff_nos_int } > { 0 }
@@ -630,116 +554,367 @@
\cs_new:Npn \__diffcoeff_tot_order:nn #1#2
{
\int_compare:nNnTF { #2 } > { 0 }
+ { \int_compare:nNnTF { #2 } = { 1 } { +#1 } { +#2#1 } }
+ {
+ \int_compare:nNnT { #2 } < { 0 }
+ { \int_compare:nNnTF { #2 } = { -1 } { -#1 } { #2#1 } }
+ }
+ }
+%%%%%%%%% derivand
+\cs_new_protected:Npn \__diffcoeff_derivand:n #1
+ {
+ \tl_set:Nn \l__diffcoeff_derivand_tl { #1 }
+ \int_compare:nNnTF { \tl_count:N \l__diffcoeff_derivand_tl } > { 1 }
+ { \bool_set_true:N \l__diffcoeff_multitok_bool }
{
- \int_compare:nNnTF { #2 } = { 1 }
- { \tl_put_left:Nn \l_tmpa_tl { +#1 } }
- { \tl_put_left:Nn \l_tmpa_tl { +#2#1 } }
+ \str_if_eq:VnTF \l__diffcoeff_derivand_tl { ! }
+ { \msg_error:nnnn { diffcoeff } { version-conflict } { #1 } {} }
+ {
+ \str_if_eq:VnT \l__diffcoeff_derivand_tl { [ }
+ { \msg_error:nnnn { diffcoeff } { version-conflict } { the~
+ order-override~argument } { Use~\difoverride instead.~ } }
+ }
}
+ }
+%%%%%%%%% build #1 vars clist; #2 trailing arg
+\cs_new_protected:Npn \__diffcoeff_build:nn #1#2
+ {
+ \str_if_eq:nnT { #1 } { / }
+ {
+ \msg_error:nnnn { diffcoeff } { version-conflict } { / }
+ { Use~\difs or~\difsp instead.~ }
+ }
+ \seq_set_from_clist:Nn \l__diffcoeff_vars_seq { #1 }
+ \seq_pop_right:NN \l__diffcoeff_vars_seq \l__diffcoeff_var_tl
+ \tl_put_left:Nx \l__diffcoeff_derivand_tl
+ { \__diffcoeff_spaced:n { \l__diffcoeff_spaced_int } }
+ \tl_if_novalue:nF { #2 }
+ { \__diffcoeff_delim:N l \mskip \l__diffcoeff_elbowrm_tl }
+ \__diffcoeff_form_deriv:xNN
+ { \__diffcoeff_build_numer:Vn \l__diffcoeff_tot_ord_tl
+ { \l__diffcoeff_style_int } }
+ \__diffcoeff_build_denom:
+ \l__diffcoeff_derivand_tl
+ \tl_if_novalue:nF { #2 }
+ { \__diffcoeff_trailing_arg:n { #2 } }
+ }
+\cs_new:Npn \__diffcoeff_delim:N #1
+ {
+ \bool_if:nTF { \l__diffcoeff_innerwrap_bool && \l__diffcoeff_append_bool }
+ { \use:c { l__diffcoeff_#1 delimapp_tl } }
+ { \use:c { l__diffcoeff_#1 delim_tl } }
+ }
+\cs_new:Npn \__diffcoeff_subnudge:
+ {
+ \bool_if:nTF { \l__diffcoeff_innerwrap_bool && \l__diffcoeff_append_bool }
+ { \l__diffcoeff_subnudgeapp_tl } { \l__diffcoeff_subnudge_tl }
+ }
+\cs_new:Npn \__diffcoeff_trailing_arg:n #1
+ {
+ \mskip \l__diffcoeff_elbowrm_tl \__diffcoeff_delim:N r
+ \tl_if_empty:nF { #1 }
+ { \c_math_subscript_token { \mskip \__diffcoeff_subnudge: #1 } }
+ }
+\cs_new:Npn \__diffcoeff_spaced:n #1
+ {
+ \int_case:nn { \int_sign:n { #1 } }
{
- \int_compare:nNnT { #2 } < { 0 }
- {
- \int_compare:nNnTF { #2 } = { -1 }
- { \tl_put_right:Nn \l_tmpa_tl { -#1 } }
- { \tl_put_right:Nn \l_tmpa_tl { #2#1 } }
+ { 1 } { \__diffcoeff_derivsep: }
+ { 0 } { \mskip 0 mu }
+ {-1 }
+ {
+ \bool_lazy_or:nnT { \l__diffcoeff_multitok_bool }
+ { \int_compare_p:nNn { \l__diffcoeff_group_int } = { 2 } }
+ { \__diffcoeff_derivsep: }
}
+ }
+ }
+\cs_new:Npn \__diffcoeff_derivsep:
+ {
+ \bool_if:NTF \l__diffcoeff_append_bool
+ { \mskip \l__diffcoeff_derivsepi_tl }
+ { \mskip \l__diffcoeff_derivsep_tl }
+ }
+%%%%%%%%% numerator #1 total order tl #2 style int
+\cs_new:Npn \__diffcoeff_build_numer:nn #1#2
+ {
+ \int_compare:nNnF { #2 } > { 5 }
+ {
+ \bool_if:NT \l__diffcoeff_op_left_bool
+ { \mskip \l__diffcoeff_opleftnudge_tl }
+ \exp_not:o \l__diffcoeff_opi_tl
+ \str_if_eq:nnF {#1} {1}
+ { ^ { \mskip \l__diffcoeff_opordsep_tl \exp_not:o {#1} } }
+ \bool_if:NT \l__diffcoeff_op_left_bool
+ { \exp_not:o { \hfill } }
+ }
+ }
+\cs_generate_variant:Nn \__diffcoeff_build_numer:nn { V }
+%%%%%%%%%% denominator %%%%%%%%%
+\cs_new:Npn \__diffcoeff_build_denom:
+ {
+ \seq_mapthread_function:NNN \l__diffcoeff_ords_seq
+ \l__diffcoeff_vars_seq \__diffcoeff_build_denom_items:nn
+ \__diffcoeff_build_denom_item:VV \l__diffcoeff_ord_tl \l__diffcoeff_var_tl
+ \str_if_eq:VnF \l__diffcoeff_ord_tl { 1 }
+ {
+ \int_compare:nNnT { \l__diffcoeff_group_int } < { 2 }
+ { \mskip -\l__diffcoeff_sep_adj_tl}
}
}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% create new instances or edit existing ones
-% #1 = name; #2 = key-value list
-\NewDocumentCommand \diffdef { > { \TrimSpaces } m m }
+\cs_new:Npn \__diffcoeff_build_denom_items:nn#1#2
+ {
+ \__diffcoeff_build_denom_item:nn {#1} {#2}
+ \mskip \l__diffcoeff_termsep_tl
+ }
+% #1 order #2 var
+\cs_new:Npn \__diffcoeff_build_denom_item:nn #1#2
+ {
+ \int_compare:nNnTF { \l__diffcoeff_style_int } = { 6 }
+ { \__diffcoeff_build_denom_difc:onn \l__diffcoeff_vph_tl {#1}{#2} }
+ { \__diffcoeff_build_denom_dif:nn {#1} {#2} }
+ }
+\cs_generate_variant:Nn \__diffcoeff_build_denom_item:nn { VV }
+% #1 vphantom orders #2 order #3 var
+\cs_new:Npn \__diffcoeff_build_denom_difc:nnn #1#2#3
+ {
+ \exp_not:o \l__diffcoeff_opii_tl \c_math_subscript_token
+ { \mskip \l__diffcoeff_opsubnudge_tl {}#3 } ^
+ {
+ \mskip \l__diffcoeff_opordsep_tl \exp_not:o { \vphantom{#1} }
+ \str_if_eq:nnF { #2 } { 1 }
+ { \exp_not:o {#2} \mskip \l__diffcoeff_sep_adj_tl }
+ }
+ }
+\cs_generate_variant:Nn \__diffcoeff_build_denom_difc:nnn { o }
+% #1 order #2 var
+\cs_new:Npn \__diffcoeff_build_denom_dif:nn #1#2
{
- \tl_if_empty:nTF { #1 }
+ \str_if_eq:nnTF { #1 } { 1 }
+ { \exp_not:o { \l__diffcoeff_opii_tl #2 } }
{
- \EditTemplateDefaults { derivative }
- { DERIV } { #2 }
- \EditInstance { derivative } { ord } { #2 }
+ \int_compare:nNnTF { \tl_count:n { #2 } } = { 1 }
+ { \exp_not:o { \l__diffcoeff_opii_tl {}#2^
+ { \mskip \l__diffcoeff_varsupnudge_tl #1 } } }
+ { \__diffcoeff_wrap_longvars:nn { #1 } { #2 } }
+ \mskip \l__diffcoeff_sep_adj_tl
}
+ }
+\cs_new:Npn \__diffcoeff_wrap_longvars_dv:nn #1#2
+ { \exp_not:o { \l__diffcoeff_opii_tl {{}#2 }^
+ { \mskip \l__diffcoeff_varsupnudge_tl #1 } } }
+\cs_new:Npn \__diffcoeff_wrap_longvars_dvi:nn #1#2
+ {
+ \exp_not:o { \l__diffcoeff_opii_tl \l__diffcoeff_lvw_ldelim_tl #2
+ \l__diffcoeff_lvw_rdelim_tl^{ \mskip \l__diffcoeff_lvsupnudge_tl #1 } }
+ }
+\cs_new:Npn \__diffcoeff_wrap_longvars_dvii:nn #1#2
+ {
+ \exp_not:o { \l__diffcoeff_lvw_ldelim_tl \l__diffcoeff_opii_tl {}#2
+ \l__diffcoeff_lvw_rdelim_tl^{ \mskip \l__diffcoeff_lvsupnudge_tl #1 } }
+ }
+%%%%%%%%%%
+% #1 op+order; #2 denom; #3 diff'iand
+\cs_new:Npn \__diffcoeff_form_deriv:nNN #1#2#3
+ {
+ \bool_if:NTF \l__diffcoeff_append_bool
+ { \l__diffcoeff_frac_tl { #1 } { #2 } #3 }
+ { \l__diffcoeff_frac_tl { #1 #3 } { #2 } }
+ }
+\cs_generate_variant:Nn \__diffcoeff_form_deriv:nNN { x }
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\file_get:nnNT { diffcoeff.DIF } {} \l_tmpa_tl
+ { \exp_args:Nnno \EditTemplateDefaults { diffcoeff } { DIF } \l_tmpa_tl }
+\exp_args:Nnno \EditTemplateDefaults { diffcoeff } { DIF }
+ \l__diffcoeff_dif_clist
+% Child template with some restricted, some new defaults.
+% #1 object type #2 parent template #3 child template
+% #4 restricted defaults (key=value) #5 new defaults (key=value)
+\NewDocumentCommand \DeclareChildTemplate { m m m m m }
+ {
+ \DeclareRestrictedTemplate {#1} {#2} {#3} {}
+ \EditTemplateDefaults {#1} {#3} {#5}
+ \DeclareRestrictedTemplate {#1} {#3} {#3} {#4}
+ }
+% create new, edit existing templates/instances;
+% #1 edit defaults with (no *) or without (*) inheritance;
+% #2 id: f,s,c,fp, sp, cp, j,l; #3 name; #4 key-value list
+\NewDocumentCommand \difdef { >{ \TrimSpaces } m >{ \TrimSpaces } m m }
+ {
+ \clist_map_inline:nn { #1 }
{
- \IfInstanceExistTF { derivative } { ord.#1 }
- { \EditInstance { derivative } { ord.#1 } { #2 } }
+ \tl_if_empty:nTF { #2 }
{
- \DeclareInstance { derivative } { ord.#1 }
- { DERIV } { #2 }
+ \DeclareChildTemplate { diffcoeff }
+ { DIF\str_uppercase:n {##1} } { DIF\str_uppercase:n {##1} }
+ { style-group = \use_i:nn ##1 \c_empty_tl } { #3 }
+ \DeclareInstance { diffcoeff } { dif##1 }
+ { DIF\str_uppercase:n {##1} } {}
+ }
+ {
+ \IfInstanceExistTF { diffcoeff } { dif##1.#2 }
+ { \EditInstance { diffcoeff } { dif##1.#2 } { #3 } }
+ { \exp_args:Nnnx
+ \DeclareInstance { diffcoeff } { dif##1.#2 }
+ { DIF\str_uppercase:n {##1} } { #3 }
+ }
}
}
}
-% relic from version 1
-\NewDocumentCommand \diffset { o }
- { \msg_warning:nn { diffcoeff } { obsolete } }
-
-% ordinary & D
-\DeclareInstance { derivative } { ord } { DERIV } { }
-\bool_if:NTF \l__diffcoeff_ISO_bool
- {
- \diffdef { }
- {
- op-symbol = \mathrm{d},
- op-order-sep = 0 mu ,
- left-delim = \left ( ,
- right-delim = \right ) ,
- subscr-nudge = -6 mu
- }
- \diffdef { D } { op-symbol = \mathrm{D} }
+\DeclareDocumentCommand \diffdef { m m }
+ {
+ \msg_error:nnnn { diffcoeff } { version-conflict } { \diffdef~(two~
+ arguments) } { Use~\difdef~(three~arguments)~instead.~ }
}
- { \diffdef { D } { op-symbol = D } }
-
-% partial
-\diffdef { p }
+\DeclareChildTemplate { diffcoeff } { DIF } { DIFF }
+ { style-group = f } {}
+\DeclareChildTemplate { diffcoeff } { DIFF } { DIFFP }
+ { style-group = f }
+ {
+ op-symbol = \partial,
+ op-order-nudge = 1 mu,
+ *italic-nudge = 3 mu
+ }
+\DeclareChildTemplate { diffcoeff } { DIF } { DIFS }
+ { style-group = s }
{
- op-symbol = \partial ,
- left-delim = \left ( ,
- right-delim = \right ) ,
- subscr-nudge = -6 mu
+ style = /,
+ derivand-sep = 2 mu plus 1 mu minus 2 mu,
+ outer-Ldelim = (,
+ outer-Rdelim = ),
+ sub-nudge = 0 mu,
+ *inner-wrap = true
+ }
+\DeclareChildTemplate { diffcoeff } { DIFS } { DIFSP }
+ { style-group = s }
+ {
+ op-symbol = \partial,
+ op-order-nudge = 1 mu
}
-\NewDocumentCommand \diffp {} { \diff.p. }
-\NewDocumentCommand \dlp {} { \dl.p. }
-
-% delta
-\diffdef { delta }
+\DeclareChildTemplate { diffcoeff } { DIF } { DIFC }
+ { style-group = c }
+ {
+ style = _ ,
+ derivand-sep = 1 mu plus 1 mu minus 1 mu ,
+ multi-term-sep = 1 mu ,
+ term-sep-adjust = 0 mu ,
+ outer-Ldelim = \bigl (,
+ outer-Rdelim = \bigr ),
+ sub-nudge = -2 mu
+ }
+\DeclareChildTemplate { diffcoeff } { DIFC } { DIFCP }
+ { style-group = c }
+ {
+ op-symbol = \partial,
+ op-order-nudge = 1 mu
+ }
+\DeclareInstance { diffcoeff } { diff } { DIFF } {}
+\DeclareInstance { diffcoeff } { diffp } { DIFFP } {}
+\DeclareInstance { diffcoeff } { difs } { DIFS } {}
+\DeclareInstance { diffcoeff } { difsp } { DIFSP } {}
+\DeclareInstance { diffcoeff } { difc } { DIFC } {}
+\DeclareInstance { diffcoeff } { difcp } { DIFCP } {}
+% jacobian
+\DeclareChildTemplate { diffcoeff } { DIF } { DIFJ }
+ { style-group = j }
{
- op-symbol = \delta ,
- op-order-sep = 0 mu
+ op-symbol = \partial,
+ outer-Ldelim = ,
+ outer-Rdelim =
}
-\diffdef { Delta }
- {
- op-symbol = \Delta ,
- op-order-sep = 0 mu
+\DeclareInstance { diffcoeff } { difj } { DIFJ } {}
+% differential
+\DeclareChildTemplate { diffcoeff } { DIF } { DIFL }
+ { style-group = l }
+ {
+ style = dl ,
+ derivand-sep = 0 mu,
+ long-var-wrap = dv ,
+ outer-Ldelim = {\,},
+ outer-Rdelim =
}
-% for compatibility with version 1
-\NewDocumentCommand \Diff { } { \diff.D. }
-\NewDocumentCommand \diffd { } { \diff.delta. }
-\NewDocumentCommand \Diffd { } { \diff.Delta. }
+\DeclareInstance { diffcoeff } { difl } { DIFL } {}
-% user-defined
-\file_if_exist:nT { \g__diffcoeff_def_tl.def }
+\file_if_exist:nTF { \g__diffcoeff_def_tl.def }
{ \file_input:n { \g__diffcoeff_def_tl.def } }
-%%%%%%%%%%%%%%%%%%%%
-% Jacobian
-\NewDocumentCommand \jacob { m t/ m }
- {
- \group_begin:
- \IfBooleanTF #2
- { \partial(#1) / \partial(#3) }
- { \frac{ \partial(#1) } { \partial(#3) } }
- \group_end:
+ {
+ \tl_if_empty:NF \g__diffcoeff_def_tl
+ { \msg_note:nnx { diffcoeff } { file-not-found }
+ { \g__diffcoeff_def_tl } }
}
-%%%%%%%%%%%%%%%%%%%%
-% messages
-\msg_new:nnn { diffcoeff } { order-specification }
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\NewDocumentCommand \negmu {} { \mskip -1 mu }
+\NewDocumentCommand \nilmu {} { \mskip 0 mu }
+\NewDocumentCommand \onemu {} { \mskip 1 mu }
+\NewDocumentCommand \twomu {} { \mskip 2 mu }
+\NewDocumentCommand \difstfrac { s m m }
+ { \__diffcoeff_slashfracs:Nnnn #1 { #2 } { #3 } {} }
+\NewDocumentCommand \difsbfrac { o s m m }
+ { \__diffcoeff_slashfracs:Nnnn #2 { #3 } { #4 } { \use:c{#1} } }
+\NewDocumentCommand \difsafrac { s m m }
+ { \__diffcoeff_slashfracs:Nnnn #1 { \left. #2\vphantom{#3} }
+ { #3\right.} { \middle } }
+\cs_new:Npn \__diffcoeff_slashfracs:Nnnn #1#2#3#4
{
- #3~followed~by~#2~in~the~order~specification~[#1]~\msg_line_context:.~
- Diffcoeff~cannot~calculate~the~overall~order~of~differentiation~in~
- this~case.~Use~the~order-override~option~to~enter~the~overall~order.
+ \bool_if:NT #1 { \l__diffcoeff_lopwrap_tl }
+ #2 \mskip \l__diffcoeff_slashsep_tl
+ #4 \l__diffcoeff_slashtok_tl
+ \mskip \l__diffcoeff_slashsep_tl #3
+ \bool_if:NT #1 { \l__diffcoeff_ropwrap_tl }
+ }
+% derivatives
+% #1(tl) variant name; #2(*) append boolean; #3(*) switch #5#6 order;
+% #4(clist) diff. orders; #5(tl) = derivand; #6(clist) = diff. vars;
+% #7(tl) = pt of eval./vars held const
+\clist_map_inline:nn { f,s,c, fp, sp, cp }
+ {
+ \exp_args:Nc \NewDocumentCommand {dif#1}
+ { >{\TrimSpaces} D..{} s s O{1} >{\TrimSpaces} m m !o }
+ {
+ \IfBooleanTF ##3
+ { \__diffcoeff_inputs:nnnnnnn {#1}
+ {##1} {##2} {##4} {##6} {##5} {##7} }
+ { \__diffcoeff_inputs:nnnnnnn {#1}
+ {##1} {##2} {##4} {##5} {##6} {##7} }
+ }
}
-\msg_new:nnn { diffcoeff } { obsolete }
- {
- Obsolete~command:~\diffset is~superseded~by~the~\diffdef\
- command.~\msg_see_documentation_text:n { diffcoeff }
+\cs_new_protected:Npn \__diffcoeff_inputs:nnnnnnn #1#2#3#4#5#6#7
+ {
+ \group_begin:
+ \tl_set:Nx \l__diffcoeff_instance_tl
+ { dif#1 \tl_if_empty:nF { #2 } { .#2 } }
+ \UseInstance { diffcoeff } { \l__diffcoeff_instance_tl }
+ {#3} {#4} {#5} {#6} {#7}
+ \group_end:
}
-\msg_new:nnn { diffcoeff } { numbers-conflict }
+\NewDocumentCommand \difoverride { >{\TrimSpaces} m }
+ { \tl_set:Nn \l__diffcoeff_override_tl { #1 } }
+% Jacobian
+\NewDocumentCommand \jacob { >{\TrimSpaces} D..{} m m }
{
- #2~orders~of~differentiation~specified~for~#1~variables;~
- orders~[#3]\ (\msg_line_context:)~for~variables~#4.
+ \group_begin:
+ \int_zero:N \l__diffcoeff_spaced_int
+ \tl_set:Nx \l__diffcoeff_instance_tl
+ { difj \tl_if_empty:nF { #1 } { .#1 } }
+ \UseInstance { diffcoeff } { \l__diffcoeff_instance_tl }
+ { \c_false_bool } {}
+ { \l__diffcoeff_lvw_ldelim_tl #2 \l__diffcoeff_lvw_rdelim_tl }
+ { {\l__diffcoeff_lvw_ldelim_tl #3\l__diffcoeff_lvw_rdelim_tl } } {}
+ \group_end:
+ }
+% differential; #1 variant ; #2 ord(s); #3 vars; #4 exponent
+\NewDocumentCommand \dl { >{ \TrimSpaces } D..{} O{1} m e{^} }
+ {
+ \group_begin:
+ \tl_set:Nx \l__diffcoeff_instance_tl
+ { difl \tl_if_empty:nF { #1 } { .#1 } }
+ \difoverride {}
+ \tl_set:Nn \l__diffcoeff_exponent_tl { #4 }
+ \tl_if_novalue:nTF {#4}
+ { \bool_set_false:N \l__diffcoeff_exponent_bool }
+ { \bool_set_true:N \l__diffcoeff_exponent_bool }
+ \UseInstance { diffcoeff } { \l__diffcoeff_instance_tl }
+ {\c_false_bool} {#2} {} {#3} {}
+ \group_end:
}
% end of file diffcoeff.sty \ No newline at end of file
diff --git a/macros/latex/contrib/diffcoeff/diffcoeff.tex b/macros/latex/contrib/diffcoeff/diffcoeff.tex
index b37af90a43..973f074511 100644
--- a/macros/latex/contrib/diffcoeff/diffcoeff.tex
+++ b/macros/latex/contrib/diffcoeff/diffcoeff.tex
@@ -1,21 +1,26 @@
%% LyX 2.4.0-alpha3 created this file. For more info, see https://www.lyx.org/.
%% Do not edit unless you really know what you are doing.
-\documentclass[english]{article}
+\documentclass[english]{report}
\usepackage{lmodern}
\renewcommand{\sfdefault}{lmss}
\renewcommand{\ttdefault}{lmtt}
\usepackage[T1]{fontenc}
\usepackage{textcomp}
\usepackage[latin9]{inputenc}
+\setcounter{secnumdepth}{3}
+\setcounter{tocdepth}{3}
\synctex=-1
\usepackage{color}
+\definecolor{shadecolor}{rgb}{1, 0.667969, 0.5}
\usepackage{babel}
+\usepackage{cprotect}
\usepackage{wrapfig}
\usepackage{booktabs}
-\usepackage{calc}
+\usepackage{framed}
\usepackage{url}
\usepackage{amsmath}
\usepackage{amssymb}
+\usepackage{stmaryrd}
\usepackage{esint}
\usepackage[unicode=true,pdfusetitle,
bookmarks=true,bookmarksnumbered=true,bookmarksopen=true,bookmarksopenlevel=2,
@@ -33,721 +38,1095 @@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Textclass specific LaTeX commands.
\newenvironment{centred}%
- {\begin{center}\baselineskip=13pt\parskip=1pt}{\end{center}}
+ {\begin{center}\baselineskip=13pt\parskip=1pt }{\end{center}}
\newenvironment{example}%
{\begin{center}\ttfamily}{\end{center}}
-\newenvironment{lyxcode}
- {\par\begin{list}{}{
- \setlength{\rightmargin}{\leftmargin}
- \setlength{\listparindent}{0pt}% needed for AMS classes
- \raggedright
- \setlength{\itemsep}{0pt}
- \setlength{\parsep}{0pt}
- \normalfont\ttfamily}%
- \item[]}
- {\end{list}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% User specified LaTeX commands.
-\usepackage{babel}
-\usepackage[def-file=diffcoeff-doc]{diffcoeff}
-
+\usepackage[def-file=diffcoeff5,spaced=-1]{diffcoeff}
+
+% nabla in numer, d in denom
+\difdef { f, s } { n }
+ {
+ op-symbol = \nabla,
+ op-symbol-alt = \mathrm{d}
+ }
+% no sub nudge (a sea of white space)
+\difdef { fp } { wsp }
+ { sub-nudge = 0 mu }
+% align op left; no italic nudge
+\difdef { f } { left0 }
+ {
+ *op-set-left = true,
+ *italic-nudge = 0 mu
+ }
+% align op left; italic nudge
+\difdef { fp } { left }
+ {
+ op-symbol = \partial,
+ op-order-nudge = 1 mu,
+ *op-set-left = true,
+ *italic-nudge = 3 mu
+ }
+% partial variant of \diff
+\difdef { f } { p }
+ {
+ op-symbol = \partial,
+ op-order-nudge = 1 mu
+ }
+% partial, 3mu sep of terms
+\difdef { fp, sp } { 3mu }
+ { multi-term-sep = 3 mu }
+% D jacobian
+\difdef { j } { D }
+ { op-symbol = D }
+% square bracket jabobian
+\difdef { j } { [ }
+ {
+ lvwrap-Ldelim = \onemu\mleft [,
+ lvwrap-Rdelim = \mright ]
+ }
+% mimicking the \Braket command
+% of the braket package
+\difdef{ s }{ bk }
+ {
+ slash-tok = ,
+ op-symbol = ,
+ multi-term-sep = 3mu\middle|\mskip3mu ,
+ outer-Ldelim=\left\langle ,
+ outer-Rdelim=\right\rangle
+ }
+\NewDocumentCommand \Braket { m }
+ {
+ \difoverride {\negmu}
+ \difs.bk.{}{#1}[]
+ }
+
+\ifdefined\showcaptionsetup
+ % Caption package is used. Advise subfig not to load it again.
+ \PassOptionsToPackage{caption=false}{subfig}
+\fi
+\usepackage{subfig}
\makeatother
\begin{document}
\title{\texttt{diffcoeff}~\\
a \LaTeX{} package to ease\texttt{ }the~\\
writing of differential coefficients \\
- Version 4.1}
+ Version 5.0}
\author{Andrew Parsloe\\
{\small (ajparsloe@gmail.com)}}
\maketitle
\begin{abstract}
-\noindent This package eases the consistent writing of ordinary, partial
-and other derivatives of arbitrary (algebraic or numeric) order. For
-mixed partial derivatives, the total order of differentiation is calculated
-by the package. Optional arguments allow for points of evaluation
-(ordinary derivatives), or variables held constant (partial derivatives),
-and the placement of the differentiand in numerator or appended. The
-package uses \texttt{xtemplate}, allowing systematic fine-tuning of
-the display and generation and use of variant forms, including derivatives
-built from $D$, $\Delta$ or $\delta$. A command for differentials
-ensures the $\dl x$ (or $\dl.up.x$) used in integrals is consistent
-with the form used in derivatives.
+\noindent \verb`diffcoeff` is a \LaTeX{} package to ease the writing
+of ordinary, partial and other derivatives of arbitrary algebraic
+or numeric order. For mixed partial derivatives, the total order of
+differentiation is calculated by the package. Optional arguments allow
+for points of evaluation (ordinary derivatives), or variables held
+constant (partial derivatives), and the placement of the differentiand
+in numerator or appended. Besides $\diff yx$, forms like $\difs yx$
+and $\difcp yx$ are also available, as well as derivatives built
+from $D$, $\Delta$, $\delta$, and configurable jacobians and differentials.
+Other notations like line elements ($\dl.+.{x,y,z}^{2}$) and bra-kets
+are easily produced.
+
+Version 5 of \verb`diffcoeff` more fully embraces the configurability
+offered by \verb`xtemplate` than earlier versions. Some incompatibilities
+have arisen, but all is not lost: version 4 is still available with
+the command
+
+\verb`\usepackage[<options>]{diffcoeff}[=v4]`
\end{abstract}
-\tableofcontents{}
-
-\section{Introduction}
-
-The \LaTeX{} package \texttt{diffcoeff.sty} is written in the expl3
-language of \LaTeX 3\texttt{ }and requires the bundles \texttt{l3kernel}
-which is now part of standard \LaTeX{} (since early 2020) and \texttt{l3packages}
-(the latter for the \texttt{xparse}, \texttt{l3keys2e} and especially
-\texttt{xtemplate} packages\texttt{)}. The package is invoked in the
-usual way by entering
-\begin{lyxcode}
-\textbackslash usepackage\{diffcoeff\}
-\end{lyxcode}
-in the preamble of your document.
-
-\subsubsection*{Note on terminology}
-
-I refer throughout to the quantity or function being differentiated
-as the \emph{differentiand} or \emph{derivand }(in line with \emph{integrand},
-\emph{operand}, etc.).
+\noindent\begin{minipage}[t]{1\columnwidth}%
+\begin{shaded}%
+
+\subsubsection*{For users of version 4}
+
+The \verb`\diff` and \verb`\diffp` commands of version 4 of \verb`diffcoeff`
+remain, but lack the `spacing switch' \verb`!` (which on reflection
+was a mistake) and, more noticeably, the `slash switch' \verb`/`.
+Slash-fraction derivatives are now created with the \verb`\difs`
+and \verb`\difsp` commands. New commands \verb`\difc` and \verb`\difcp`
+produce derivatives in `compact notation' like $\difc yx$ and $\difcp yx$.
+To avoid cluttering formulas with a second square-bracket delimited
+optional argument before the differentiand, the order-override option
+has been replaced by a new command \verb`\difoverride`. The order
+of differentiand and variable(s) of differentiation can now be reversed,
+when the differentiand is appended, by using a second star, e.g.,
+\verb`\diffp**`. The two-argument \verb`\diffdef` command of earlier
+versions has been replaced by the three-argument command \verb`\difdef`,
+the additional argument determining which one or more of the \verb`f`,
+\verb`s`, \verb`c`, \verb`fp`, \verb`sp` or \verb`cp` forms the
+defined variant applies to. The differential command \verb`\dl` has
+been rewritten and is now fully template-configurable (allowing easy
+writing of line elements like $\dl.+.{x,y,z}^{2}$), and the jacobian
+command \verb`\jacob` is also configurable. Indeed version 5 of \verb`diffcoeff`
+more fully embraces the configurability offered by the \verb`xtemplate`
+package than previous versions, bringing other notations -- like
+those of the \verb`braket` package -- within its compass.
+
+\subsubsection*{ISO defaults}
+
+Unlike the default set-up in version 4, the defaults in version 5
+of \verb`diffcoeff` are chosen to reflect ISO recommendations; see
+the standard ISO 80000-2. In particular this means upright `d's
+and subscripted parentheses enclosing a derivative to indicate a point
+of evaluation. This document is written with those defaults. For those
+(like the author) who prefer math-italic `d's and a subscripted
+vertical rule to indicate a point of evaluation, the means of creating
+`variant forms' or changing the defaults is readily available; see
+§§\ref{sec:Variant-forms}, \ref{sec:ChangingDefaults}.\end{shaded}%
+\end{minipage}
-\subsubsection*{New in version 4.0}
+\tableofcontents{}
-(See §\ref{sec:Version-comparison} for a comparison of versions.)
-Version 4.0
+\chapter{Introduction}
+
+\verb`diffcoeff.sty` is written in the \verb`expl3` language of
+\LaTeX 3, now part of standard \LaTeX{} since February 2020. A \LaTeX{}
+distribution from or later than that date is assumed. The package
+also requires the packages \verb`xtemplate` (part of the \verb`l3packages`
+bundle) and \verb`mleftright`. The package is loaded in the usual
+way by entering
+\begin{verbatim}
+ \usepackage{diffcoeff}
+\end{verbatim}
+in the preamble of your document or, if package options are being
+used,\footnote{Angle brackets indicate possible user input (\emph{without} the angle
+brackets).}
+\begin{verbatim}
+ \usepackage[<options>]{diffcoeff}
+\end{verbatim}
+The interface of \verb`diffcoeff` with version 5 has changed from
+earlier versions. If you want the familiar behaviour of version 4,
+add to these commands a trailing optional argument like this,
+\begin{verbatim}
+ \usepackage[<options>]{diffcoeff}[=v4]
+\end{verbatim}
+(with no space after the `=' sign!). Of course you will not get
+the new features of version 5. Working with version 4 is described
+in the document \verb`diffcoeff4.pdf`.
+
+\section{Package options}
+
+\label{sec:Package-options}There are four package options, which
+are entered in a comma-separated list in the optional argument of
+the \verb`\usepackage` command. The \emph{second} and \emph{fourth}
+are new with version 5 of \verb`diffcoeff`.
\begin{enumerate}
-\item enables the insertion of a small space before the differentiand, either
-as the default behaviour (package option \verb`spaced`) or at explicit
-request (argument \verb`!` of the \verb`\diff` command); see §\ref{subsec:Spacing-before-derivand};
-\item prevents the ligature $df$ that marred previous versions; this is
-now rendered $\dl f$;
-\item offers the document command \verb`\dlp` for the \emph{partial} differential;
-see §\ref{subsec:Partial-differential};
-\item no longer accepts \emph{the braced form} of the\emph{ }trailing optional
-argument specifying a point of evaluation or (for partial derivatives)
-variables held constant. This was a relic from version 1 of \texttt{diffcoeff},
-and has been deprecated since version 2.
-\end{enumerate}
-
-\subsubsection*{New in version 4.1}
+\item The first package option is the \verb`spaced` option which takes
+three values:
\begin{enumerate}
-\item changes the code handling the \verb`long-var-wrap` setting to avoid
-a problem with a change in \verb`xtemplate` (see \url{https://tex.stackexchange.com/questions/646976/error-with-package-diffcoeff})\footnote{Based on a suggestion from \noun{Joseph Wright}.};
-\item prevents (hitherto overlooked) ligatures in the \emph{denominators}
-of differential coefficients.
+\item \verb`spaced=1` inserts a small space before the differentiand; this
+is the default so that entering \verb`spaced` is equivalent to \verb`spaced=1`;
+\item \verb`spaced=0` inserts no space before the differentiand; \verb`diffcoeff`
+is initialized to \verb`spaced=0` so that if the spaced option is
+not used \verb`spaced=0` is assumed;
+\item \verb`spaced=-1` inserts a small space before the differentiand \emph{if
+it contains more than one token}, and no space otherwise. The present
+document uses \verb`spaced=-1`.
\end{enumerate}
-
-\subsection{Package options}
-
-\label{subsec:Package-options}There are three package options, which
-are entered in a comma-separated list in the optional argument of
-the \texttt{\textbackslash usepackage} command.
-\begin{enumerate}
-\item The first is a switch, \texttt{ISO}, which turns on formatting conforming
-to ISO recommendations, principally upright `d's:
-\begin{lyxcode}
-\textbackslash usepackage{[}ISO{]}\{diffcoeff\}
-\end{lyxcode}
-The full effect of this option is disscussed in §\ref{sec:Changing-defaults}.
-\item The second is another switch, \texttt{spaced}, and \emph{is new with
-version 4 }of \texttt{diffcoeff}. This switch ensures a small space
-is inserted before the differentiand:
-\begin{lyxcode}
-\textbackslash usepackage{[}spaced{]}\{diffcoeff\}
-\end{lyxcode}
-This is discussed in §\ref{subsec:Spacing-before-derivand}.
-\item The third requires a filename \texttt{<filename>} for a file \texttt{<filename>.def}
-containing definitions of variant forms of derivative:
-\begin{lyxcode}
-\textbackslash usepackage{[}def-file=<filename>{]}\{diffcoeff\}
-\end{lyxcode}
-This is discussed in §\ref{subsec:The-.def-file}. For the present
-document, the call is
-\begin{lyxcode}
-\textbackslash usepackage{[}def-file=diffcoeff-doc{]}\{diffcoeff\}
-\end{lyxcode}
+This option is discussed in §\ref{subsec:Spacing-before-derivand}.
+\item For the second package option, by entering \verb`mleftright` in the
+options list the command \verb`\mleftright` is automatically inserted
+in the preamble. The effect is to change all occurrences of \verb`\left`,
+\verb`\right` in the document to \verb`\mleft`, \verb`\mright`
+so that the spacing around scalable delimiters modified by \verb`\left`,
+\verb`\right` is reduced; see the box below and §\ref{subsec:mleftright}.
+The present document does not use this package option.
+\item The third package option requires the \verb`<filename>` of a file
+with extension \verb`.def`, \verb`<filename>.def`, containing definitions
+of variant forms (see §\ref{sec:Variant-forms}) of derivative:
+\begin{verbatim}
+ \usepackage[def-file=<filename>]{diffcoeff}
+\end{verbatim}
+This is discussed in §\ref{subsec:The-.def-file}. The present document
+uses the package option \verb`def-file=diffcoeff5`.
+\item The fourth package option \verb`DIF` is a comma list of \emph{key=value}
+statements amending the built-in defaults for the `grandparent'
+template \verb`DIF`; see §\ref{subsec:Changing-DIF-defaults}. The
+present document does not use this package option.
\end{enumerate}
+\noindent\begin{minipage}[t]{1\columnwidth}%
+\begin{shaded}%
+To see the effect of the \verb`mleftright` package, consider the
+expression
+\begin{centred}
+\verb`\[ \ln \left(\frac xy\right),\quad\sin\left(x^2\right). \]`
+$\Longrightarrow$ \[ \ln \left(\frac xy\right),\quad\sin\left(x^2\right). \]
+\end{centred}
+in which there is significant whitespace before and after the parentheses.
+The package \verb`mleftright` enables this whitespace to be reduced
+by using \verb`\mleft`, \verb`\mright` in place of \verb`\left`,
+\verb`\right`:
+\begin{centred}
+\verb`\[ \ln \mleft(\frac xy\mright),\quad\sin\mleft(x^2\mright). \]`
+$\Longrightarrow$ \[ \ln \mleft(\frac xy\mright),\quad\sin\mleft(x^2\mright). \]
+\end{centred}
+\end{shaded}%
+\end{minipage}
-\section{A Rogues' Gallery of derivatives}
-
-\label{sec:Rogues'-gallery}Browsing through texts on statistical
-mechanics, relativity and classical mechanics I find the following
-choice examples of derivatives `disporting every which way'.
+\noindent %
+\noindent\begin{minipage}[t]{1\columnwidth}%
+\begin{shaded}%
+If you put \verb`\mleftright` in the preamble, which is what the
+\verb`mleftright` package option does, then all occurrences of \verb`\left`,
+\verb`\right` in the document will be affected. \verb`\left`, \verb`\right`
+can be restored to their normal behaviour by the command \verb`\mleftrightrestore`.
+Rather than use \verb`\mleft`, \verb`\mright` explicitly, as in
+the example, the same effect can be obtained by using \verb`\left`,
+\verb`\right` and preceding the expression with the command \verb`\mleftright`:
+\begin{verbatim}
+ \mleftright
+ \[ \ln \left(\frac xy\right),\quad\sin \left(x^2\right). \]
+ \mleftrightrestore
+\end{verbatim}
+$\Longrightarrow$ \mleftright
+ \[ \ln \left(\frac xy\right),\quad\sin \left(x^2\right). \]
+ \mleftrightrestore \end{shaded}%
+\end{minipage}\medskip{}
+For the present document, the call is
+\begin{verbatim}
+ \usepackage[def-file=diffcoeff5,spaced=-1]{diffcoeff}
+\end{verbatim}
-Multi-character variables of differentiation un-parenthesized:
+\section{A Rogues' Gallery of derivatives}
+\label{sec:Rogues'-gallery}Browsing through some (rather old) calculus
+textbooks and texts on statistical mechanics, relativity and classical
+mechanics I find the following choice examples of derivatives `disporting
+every which way'.
+\begin{itemize}
+\item Multi-character variables of differentiation un-parenthesized:
\begin{equation}
-\diffp{\frac{\psi}{\Theta}}{\frac{1}{\Theta}},\quad\diffp{E/T}{1/T},\quad\diffp{\ln f}{\ln x_{0}},\quad\diffp\psi{a_{i},\frac{1}{\Theta}},\quad\diffp{\mathcal{L}}{\eta_{,i}^{(r)}}.\label{eq:eg1}
-\end{equation}
-Multi-character variables of differentiation parenthesized:
-\begin{equation}
-\diffp H{\displaystyle \diffp S{q_{k}}[]},\quad\diffp\varepsilon{(1/\Theta)}.\label{eq:eg2}
+\diffp{\frac{\psi}{\Theta}}{\frac{1}{\Theta}},\quad\diffp{E/T}{1/T},\quad\diff{\ln f}{\ln x_{0}},\quad\diffp\psi{a_{i},\frac{1}{\Theta}},\quad\diffp{\mathcal{L}}{\eta_{,i}^{(r)}}.\label{eq:eg1}
\end{equation}
-Higher-order derivatives where the parentheses do not or sometimes
-do include the operator:
+\item Multi-character variables of differentiation parenthesized in \emph{higher-order}
+derivatives, where the parentheses do not or (sometimes) do include
+the operator:
\begin{equation}
-\diffp[2]q{\frac{1}{\Theta}},\quad\diffp[2]q{1/\Theta},\quad\diffp[2]\varepsilon{a_{i}},\quad\diff.wrapall.[2]{\phi^{i}(x^{i})}{x^{i}}.\label{eq:eg3}
+\diffp[2]q{\frac{1}{\Theta}},\quad\diffp[2]q{1/\Theta},\quad\diffp[2]\varepsilon{a_{i}},\quad\diff.(dv).[2]{\phi^{i}(x^{i})}{x^{i}}.\label{eq:eg3}
\end{equation}
-Should the $d$ or $\partial$ be included within the parentheses,
+Should the $\mathrm{d}$ or $\partial$ be included within the parentheses,
as in the last of (\ref{eq:eg3}), or not, as in the others? Logic
says `yes'; practice suggests (generally) `no'.
-
-Indicating a point of evaluation is similarly varied:
+\item Indicating a point of evaluation is similarly varied:
\begin{equation}
-\diff.pvrule.\phi\varepsilon[\varepsilon=\varepsilon_{0}],\quad\diff.pvrule.[2]\phi\varepsilon[\varepsilon=\varepsilon_{0}],\quad\diff.psqbra.{b^{\beta}}{a^{\alpha}}[b=0],\quad\diff.paren.uv[v=0].\label{eq:eg4}
+\diffp.|.\phi\varepsilon[\varepsilon=\varepsilon_{0}],\quad\diff.|.[2]\phi\varepsilon[\varepsilon=\varepsilon_{0}],\quad\diffp.].{b^{\beta}}{a^{\alpha}}[b=0],\quad\diff uv[v=0].\label{eq:eg4}
\end{equation}
ISO 80000-2 (item 2.11.13) favours the last of these -- parentheses
-- for ordinary derivatives. Presumably, partial derivatives should
follow suit, although parentheses are also used to indicate variables
held constant:
\begin{equation}
-\diffp*{\frac{P}{T}}U[V],\quad\diffp S{N_{2}}[U,V,N_{1}],\quad\diffp S/T[V].\label{eq:eg5}
+\diffp*{\frac{P}{T}}U[V],\quad\diffp S{N_{2}}[U,V,N_{1}],\quad\difsp ST[V]\,.\label{eq:eg5}
\end{equation}
-
-Other symbols besides $d$ and $\partial$ are used to denote derivative-like
-quantities. From introductory calculus and from classical mechanics
-and thermodynamics come $\delta$ and $\Delta$, from fluid mechanics
-comes $D$:
+\item Other symbols besides $\mathrm{d}$ and $\partial$ are used to denote
+derivative-like quantities. From introductory calculus and from classical
+mechanics and thermodynamics come $\delta$ and $\Delta$, from fluid
+mechanics comes $\mathrm{D}$:
\begin{equation}
-\diff.delta.yx,\quad\diff.D.\rho t,\quad\diff.pDelta.UT[V],\quad\diff.Delta.U/T,\quad\diff.delta.{\mathcal{L}}{\eta^{(r)}}.\label{eq:eg6}
+\diff.gd.yx,\quad\diff.D'.\rho t,\quad\diff.gD.UT[V],\quad\difs.gD.UT,\quad\diff.gd.{\mathcal{L}}{\eta^{(r)}}.\label{eq:eg6}
\end{equation}
-
-There are those, like the International Organization for Standardization
-(ISO), who stipulate (or prefer) an upright `d' for their derivatives:
+\item There are those, like the International Organization for Standardization
+(ISO), who stipulate (or prefer) an upright $\mathrm{d}$ for their
+derivatives, and there are those (like the author, through sixty years
+of habit) who prefer a math-italic $d$:
\begin{equation}
-\diff.up.yx.\label{eq:eg11}
+\diff yx,\qquad\diff.d'.yx,\label{eq:eg11}
\end{equation}
-When the differentiand is too big or awkward to sit in the numerator
-and is appended to the operator, the $d$ or $\partial$ in the numerator
-is generally centred -- but not always. In texts prior to the age
-of computerised typesetting one will sometimes find the symbol pushed
-to the \emph{left}:
+and of course also in slash-fraction form $\difs yx$, $\difs.d'.yx$.
+Subscripted forms of derivative are also used -- for example, $\difcp Fx$,
+or in the discussion of differential equations one sometimes comes
+across expressions like
+\[
+\difc.bD.[2]y{x}+2\difc.bD.y{x}-4=0.
+\]
+\item When the differentiand is too big or awkward to sit in the numerator
+and is appended to the operator, the $\mathrm{d}$ or $\partial$
+in the numerator is generally centred -- but not always. In texts
+prior to the age of computerised typesetting one will sometimes find
+the symbol pushed to the \emph{left}:
\begin{equation}
-\diff.pleft.*{\diffp{x^{i^{*}}}{x^{k^{*}}}{}}{x^{l^{*}}},\quad\diff.left.*{\left(\frac{m\mathbf{q}_{x}}{\sqrt{1-q^{2}}}\right)}{t}.\label{eq:eg12}
+\diffp.left.*{\diffp.left.{x^{i^{*}}}{x^{k^{*}}}}{x^{l^{*}}},\quad\diff.left0.*{\left(\frac{m\mathbf{q}_{x}}{\sqrt{1-q^{2}}}\right)}{t}.\label{eq:eg12}
\end{equation}
-The observant will note an italic adjustment with the first expression,
-so that the $\partial$ in the numerator and the $\partial$ in the
-denominator line up in a slanting column, but no such adjustment for
-the $d$-s in the second derivative.
-
-Then there is the case when the operator in the numerator differs
+The keen-eyed will note an italic adjustment with the first expression,
+so that the $\partial$s in the numerators are indented a little (to
+line up -- more or less -- in a slanting column with the $\partial$s
+in the denominators).
+\item Then there is the case when the operator in the numerator differs
from that in the denominator. For instance, in tensor calculus acceleration
is sometimes written
\[
-\diff.nabla.{v^{i}}t=\diff{v^{i}}t+\Gamma_{k\hphantom{i}h}^{\hphantom{k}i}v^{h}\diff{y^{k}}t
+\diff.n.{v^{i}}t=\diff{v^{i}}t+\Gamma_{k\hphantom{i}h}^{\hphantom{k}i}v^{h}\diff{y^{k}}t
\]
where $\nabla v^{i}$ is the `absolute differential' of the velocity
$v^{i}$.
+\end{itemize}
+The \verb`diffcoeff` package has the generative power to cope with
+all these variations -- see §\ref{sec:Variant-forms} -- although
+it is unlikely an author should need to call on this capacity to anything
+like the extent required for this Rogues' Gallery.
+
+\chapter{Syntax and use}
+
+\verb`diffcoeff` aims to ease the writing of derivatives (sometimes
+also called differential coefficients). There are long-established
+shorthands available in a few cases: $\dot{x}$ and $\ddot{x}$ for
+the time derivatives of a function $x$ of time $t$; $y'$ and $y''$
+for the derivatives of a function $y$ (usually) of $x$. But mostly
+derivatives are expressed in fraction form and require more keystrokes
+to compose. It is here that \verb`diffcoeff` is aimed. It uses three
+pairs of commands: \verb`\diff` and \verb`\diffp` to write (upright)
+fraction forms of ordinary and partial derivatives like $\diff yx$,
+$\diffp yx$, generally intended for display-style environments; \verb`\difs`
+and \verb`\difsp` for slash-fraction forms of ordinary and partial
+derivatives like $\difs yx$, $\difsp yx$, generally intended for
+text-style environments; and \verb`\difc` and \verb`\difcp` to write
+compact forms of ordinary and partial derivatives like $\difc yx$
+and $\difcp yx$. (Of these, the `s' forms replace the slash argument
+for the \verb`\diff`, \verb`\diffp` commands in version 4 of \verb`diffcoeff`,
+and the `c' form is new to version 5.\cprotect\footnote{Suggested by a question on \TeX{} StackExchange: \url{https://tex.stackexchange.com/questions/652223/write-a-derivative-operator-without-denominator-using-diffcoef/652298#652298}})
+
+\subsubsection*{Note}
-Version 2 or later of the \texttt{diffcoeff} package has the generative
-power to cope with all these variations -- see §\ref{sec:Changing-defaults}
--- although it is unlikely an author should need to call on this
-capacity to anything like the extent required for this Rogues' Gallery.
-
-Finally and new with version 4 of \texttt{diffcoeff}, is the ability
-to insert space before the differentiand, something that had to be
-done explicitly by the user before. One way of thinking of a derivative
-is as an operator $\diff{}x$ applied to a function $F(x)$ producing
-another function $F'(x)$, a \emph{derived }function, the derivative.
-Although the original function is included in the numerator of the
-differential coefficient, a small space between the $d$ and $F$
-feels natural to separate the thing operated on from the thing operating:
-\[
-F'(x)=\diff!{F(x)}x.
-\]
-\texttt{diffcoeff} can now produce such spaced derivatives, either
-as the default behaviour or at explicit request; see §\ref{subsec:Spacing-before-derivand}.
-
-\newpage{}
+I refer throughout to the quantity or function being differentiated
+as the \emph{differentiand} or \emph{derivand }(in line with \emph{integrand},
+\emph{operand}, etc.) and shall sometimes use \verb`\difx` (resp.
+\verb`\difxp`) to make general statements about any or all of \verb`\diff`,
+\verb`\difs` or \verb`\difc` (resp.\verb`\diffp`, \verb`\difsp`,
+\verb`\difcp`).
+
+\section{Syntax}
+
+All commands, \verb`\difx`, \verb`\difxp`, share the same syntax.
+With options present the syntax is
+\begin{verbatim}
+ \difx.name.*[order-spec]{differentiand}
+ {variable(s)}[pt of eval]
+
+ \difx.name.**[order-spec]{variable(s)}
+ {differentiand}[pt of eval]
+\end{verbatim}
+The syntax is identical for \verb`\difxp`. The seven arguments have
+the following meanings:
+\begin{itemize}
+\item \verb`name` (optional) A dot-delimited name to distinguish a variant
+form (non-default form) of derivative; not discussed further until
+§\ref{chap:Templates-defaults-variants} below, and specifically,
+§\ref{sec:Variant-forms}.
+\item \verb`*` (optional) The presence of a star (asterisk) signals: \emph{append}
+the differentiand; its absence means the differentiand appears in
+the numerator of an upright- or slash-fraction form derivative; no
+effect for compact-form derivatives unless (see next) a second \verb`*`
+is present; see §\ref{subsec:Appending-the-differentiand}.
+\item \verb`*` (optional) The presence of a \emph{second} star signals
+that the argument specifying the variable(s) of differentiation comes
+\emph{before} the argument specifying the differentiand; this is sometimes
+convenient when a complicated or lengthy differentiand is appended;
+see §\ref{subsec:Transposing-the-argument}.
+\item \verb`order-spec` (optional) The order of differentiation when differentiating
+in a single variable, or a comma list of orders of differentiation
+for a mixed partial derivative; see §\ref{subsec:Higher-order-derivatives}
+and §\ref{subsec:Mixed-partial-derivatives}.
+\item \verb`differentiand` (mandatory) The function being differentiated.
+\item \verb`variable(s)` (mandatory) The variable of differentiation or
+a comma list of variables of differentiation (for a mixed partial
+derivative).
+\item \verb`pt of eval` (optional) Point of evaluation or, for partial
+derivatives, variable or variables held constant; \emph{no space}
+before the left square bracket; see §\ref{subsec:Point-of-evaluation}.
+\end{itemize}
-\section{Ordinary derivatives \protect\label{sec:Ordinary-derivatives}}
+\section{General use}
-Writing\textbf{ }\texttt{\textbackslash diff\{y\}\{x\}} will produce
-$\diff{y}{x}$ in text style (i.e., placed between \texttt{\textbackslash (
-\textbackslash )} or \texttt{\$ \$}) or
+\label{sec:General-use}Writing \verb`\diff{y}{x}` will produce $\diff{y}{x}$
+in an inline math environment (i.e., placed between \verb`\( \)`
+or \verb`$ $`) or
\[
\diff{y}{x}
\]
-in display style (i.e., placed between \texttt{\textbackslash{[}
-\textbackslash{]}} ). In fact \texttt{\textbackslash diff yx} (omitting
-the braces) will produce these results, with a saving on keystrokes.
-The braces are needed only when an argument -- the differentiand
-or the variable of differentiation -- is multi-token.
+in display style (placed, for instance, between {\ttfamily\verb`\[ \]`}
+). In fact \verb`\diff yx` (omitting the braces) will produce these
+results, with a saving on keystrokes. The braces are needed only when
+an argument -- the variable of differentiation, or the differentiand
+-- is multi-token:
+\begin{centred}
+\verb`\[ \diff{\ln x}x \]` $\Longrightarrow$ \[ \diff{\ln x}x\]
+\end{centred}
\begin{itemize}
-\item If you want upright `$\mathrm{d}$'s as default, as ISO 80000-2 recommends,
-rather than the math-italic `$d$'s used here, this can easily be
-done with the package option \texttt{ISO}; see §\ref{sec:Changing-defaults}
-on changing default settings.
+\item If you want math-italic `$\mathrm{d}$'s as default, see §\ref{sec:ChangingDefaults}
+on changing default settings. As noted earlier, upright `d's conform
+to the standard ISO 80000-2 and are used in this document.
\end{itemize}
For inclusion in a line of text you might prefer to use a slash-fraction
-form of derivative. That is achieved by inserting a slash, `/', between
-numerator and denominator arguments: \texttt{\textbackslash diff\{\textbackslash ln
-x\}/x} produces $\diff{\ln x}/x$. Braces are required for the numerator
-in this case since it contains more than one token.
+form of derivative. That is achieved with the \verb`\difs` command:
+\verb`$ \difs yx $` produces $ \difs yx $. If you want still more
+compactness, you can use the \verb`\difc` (`c' for \emph{compact})
+command: \verb`$ \difc yx $` produces the form $ \difc yx $.
+
+Partial derivatives follow the same pattern as ordinary derivatives.
+The commands this time are \texttt{\textbackslash}\verb`diffp`,
+\verb`\difsp` and \verb`\difcp` for (upright) fraction, slash fraction
+and compact forms of partial derivative. Thus \verb`\diffp{F}{x}`,
+or \verb`\diffp Fx` with a saving on keystrokes, produce $\diffp Fx$
+in text style and
+\[
+\diffp{F}{x}
+\]
+in display style. (As for \verb`\diff`, the omission of braces is
+possible when dealing with a single-token differentiand or differentiation
+variable.) For inline use, \verb`\difsp Fx`, displays as $\difsp Fx$
+and \verb`\difcp` displays as $\difcp Fx$. Given that \verb`\partial`
+takes 8 keystrokes to type, all forms\emph{ }economise on keystrokes.
\subsection{Spacing before the differentiand}
\label{subsec:Spacing-before-derivand}There are (at least) two different
-ways in which we think of derivatives.\footnote{I thank \noun{Hans Schülein} for first raising this issue with me
-and for subsequent thoughtful comments. } We are all familiar with the argument presented in elementary calculus
-books where a curve is shown, and a point on the curve through which
-a chord has been drawn. The chord is a side -- the hypotenuse --
-of a small right-angled triangle, the other sides having lengths $\delta x$
-and $\delta y$ and being parallel to the coordinate axes. The slope
-of the chord is $\diffd yx$. By drawing smaller and smaller chords
-through the point, the ratio $\diffd yx$ approaches the slope of
-the tangent to the curve at the point. We write
+ways in which we think of derivatives. We are all familiar with the
+argument presented in elementary calculus books where a curve is shown,
+and also a point on the curve through which a chord has been drawn.
+The chord is the hypotenuse of a small right-angled triangle, the
+other sides having lengths $\delta x$ and $\delta y$ and being parallel
+to the coordinate axes. The slope of the chord is $\diff.gd.yx$.
+By drawing smaller and smaller chords through the point, the ratio
+$\diff.gd.yx$ approaches the slope of the tangent to the curve at
+the point. We write
\[
\diff yx
\]
-for the limit of $\diffd yx$. It is natural to think of $\dl y$
-and $\dl x$ as tiny lengths, like $\delta y$ and $\delta x$, in
-which case it would be quite wrong to insert space between the $d$
-and the $y$ (let alone the $d$ and the $x$). $dy$ is a single
-object, called a differential, and we write expressions like
-\begin{centred}
-\verb`\[ dy=\diff yx dx \]` $\Longrightarrow$
+for the limit of $\diff.gd.yx$. It is natural following this line
+of argument to think of $\dl y$ and $\dl x$ as tiny lengths, like
+$\delta y$ and $\delta x$, in which case it would be quite wrong
+to insert space between the $\mathrm{d}$ and the $y$ (let alone
+the $\mathrm{d}$ and the $x$). $\dl y$ is a single object, called
+a differential, and we write expressions like
\[
\dl y=\diff yx\dl x
\]
-\end{centred}
-and justly call the `fraction' in this expression a differential
-coefficient.
+and justly call the fraction in this expression a \emph{differential
+coefficient}.
But there is another way of viewing differentiation: as a process
-producing (or \emph{deriving}) one function, $f'(x)$, from another,
-$f(x)$. Here the sense is of applying $\diff{}x$ to $f(x)$. Although
-we include $f(x)$ in the numerator it is not attached to the $d$
-and should be separated from it by a small space:
-\begin{centred}
-\verb`\[ f'(x)=\diff!{f(x)}x \]` $\Longrightarrow$
+producing (or \emph{deriving}) one function, $y'(x)$, from another,
+$y(x)$. Here the sense is of applying $\diff{}x$ to a quite separate
+object, the function $y(x)$. Although we include $y(x)$ in the numerator
+it is distinct from the $d$ and should be separated from it by a
+small space:\footnote{I thank \noun{Hans Schülein} for first raising this issue with me
+and for subsequent thoughtful comments.}
\[
-f'(x)=\diff!{f(x)}x.
+y'(x)=\diff{y(x)}x.
\]
-\end{centred}
-Here the `fraction' on the right is another name for the derived
-function $f'$ and is justly called the derivative of $f$. As you
-can see a small space has been inserted between the $d$ and the $f$
-in the numerator. By default the space is \texttt{3 mu} but with the
-ability to stretch by \texttt{1 mu} or shrink by\texttt{ 2 mu}{\ttfamily\footnote{In \TeX -speak, \texttt{3mu plus 1mu minus 2mu}. }}
-as \TeX{} adjusts lines to fit on the page. (A `mu' is a `math unit'
-and is one eighteenth of a quad.) To achieve this result I have inserted
-an exclamation mark \verb`!` before the braces delimiting the differentiand.
+Here the fraction on the right is another name for the derived function
+$y'$ and is justly called the \emph{derivative} of $y$. As you can
+see a small space has been inserted between the $\mathrm{d}$ and
+the $y$ in the numerator. By default the space is \verb`3 mu` but
+with the ability to stretch by \verb`1 mu` or shrink by\texttt{ }\verb`2 mu`
+--\texttt{ }\verb`3 mu plus 1 mu minus 2 mu`\texttt{ }in \TeX -speak\footnote{Or even \texttt{3muplus1muminus2mu}.}
+-- as \TeX{} adjusts lines to fit on the page. (A `mu' is a `math
+unit' and is one eighteenth of a quad.) The size of the space inserted
+by default can be easily changed; see §\ref{sec:Variant-forms} and
+§\ref{sec:ChangingDefaults}.
\begin{itemize}
-\item You may want all or most of your derivatives to have this space and
-therefore will not want to be inserting exclamation marks in every
-\texttt{\textbackslash diff} command. The \texttt{spaced} package
-option switches the default behaviour to spaced derivatives (in which
-case the \texttt{!} switch now creates an \emph{un-spaced} derivative).
-The size of the space inserted by default can be easily changed; see
-§\ref{sec:Changing-defaults}.
+\item You may want all or most of your derivatives to have this space before
+the derivand. The \verb`spaced=1` package option switches this behaviour
+on. However, I have used the \verb`spaced=-1` option for the present
+document which inserts space only if the derivand contains \emph{more
+than one token}. Thus \verb`y(x)` will have space inserted before
+it, but \verb`y` alone will not. This (I think) maintains the distinction
+between a differential coefficient, thought of as a ratio of tiny
+lengths, and a derivative, thought of as an operator applied to a
+function. \verb`spaced=0` inserts no space before the derivand.
+\item In version 4 of \verb`diffcoeff` an argument was added to the \verb`\diff`
+command to manually introduce a space (the \verb`!` switch) before
+the differentiand. This was a mistake and has been removed. If you
+wish to adjust the spacing, there are plenty of (short) commands in
+\LaTeX{} and \verb`diffcoeff` to do the job; see immediately below,
+§\ref{subsec:Spacing-commands}.
\end{itemize}
-The present document uses the un-spaced default. For backwards compatibility
-(and perhaps because the author has done this for the last 60 years),
-this is the \textquoteleft out-of-the-box\textquoteright{} default
-that \texttt{diffcoeff} uses. Authors should make a habit of using
-one form predominantly. (There is also the possibility which I haven't
-emphasized of spacing multi-token differentiands and leaving single-token
-differentiands unspaced; see §\ref{subsec:A-final-flourish}.)
-
-Slash-form derivatives also allow space before the differentiand.
-By default this has the same value as applied to the fraction form
-of derivative (but can be changed; see §\ref{sec:Changing-defaults}):
-\begin{centred}
-\verb`$ \diff!{\ln\sin x}/x $` $\Longrightarrow$ $ \diff!{\ln\sin x}/x$.
-\end{centred}
-The \verb`\diff` command has other optional arguments (e.g. to specify
-the order of differentiation) but always the exclamation mark, if
-used, immediately precedes the differentiand. It is the positioning
-of the differentiand that it affects after all and its placement immediately
-before that argument seems natural.
-
-\subsubsection{Ligatures: }
-
-Prior to v.4 of \texttt{diffcoeff}, \texttt{\textbackslash diff fx}
-produced the tight pairing evident in
-\[
-\frac{df}{dx}.
-\]
-This was a bug. From version 4.0 of \texttt{diffcoeff}, such ligatures
-are prevented: \verb`\[ \diff fx \]` $\Longrightarrow$ \[ \diff fx.\]
+Slash-form derivatives also allow space before the derivand. By default
+this is \verb`2 mu plus 1 mu minus 2 mu`, slightly reduced from the
+fraction-form value to avoid visually detaching the initial `d'
+operator from the derivative as a whole. The value can be changed;
+see §\ref{sec:Variant-forms} and §\ref{sec:ChangingDefaults}. For
+the present document, with \verb`spaced=-1`, multi-token derivands
+have the space inserted, single-token derivands do not:
+\begin{centred}
+\verb`$ \difs{\ln\sin x}x, \quad \difs st $` $\Longrightarrow$ $ \difs{\ln\sin x}x, \quad \difs st $.
+\end{centred}
+For \emph{compact-form} derivatives the space before the derivand
+is \emph{always} inserted, irrespective of the setting of the \verb`spaced`
+package option, since the subscript precludes the entire symbol ever
+being viewed as a differential -- it is always an operator operating
+on a function. The inserted space, \verb`1 mu plus 1 mu minus 1 mu`
+by default, can be changed should you wish; see §\ref{sec:Variant-forms}
+and §\ref{sec:ChangingDefaults}:
+\begin{centred}
+\verb`$ \difc{\ln\sin x}x, \quad \difc st $` $\Longrightarrow$ $ \difc{\ln\sin x}x, \quad \difc st $.
+\end{centred}
+(The space is less for compact forms since the subscript already provides
+some visual separation.) The \verb`spaced` package option has the
+same effects on partial derivatives. Thus with \verb`spaced=1` or
+\verb`spaced=-1`, \verb`3 mu plus 1 mu minus 2 mu` of space is inserted
+before the differentiand \verb`F(x,y)` in the first member of the
+following example, space of \verb`2 mu plus 1 mu minus 2 mu` in the
+second, and space of \verb`1 mu plus 1 mu minus 1 mu` in the third:
+\begin{centred}
+\verb`\[ \diffp{F(x,y)}x,\;\difsp{F(x,y)}x,\;\difcp{F(x,y)x, \]`
+\end{centred}
+$\Longrightarrow$ \[ \diffp{F(x,y)}x,\;\difsp{F(x,y)}x,\;\difcp{F(x,y)}x. \]
+
+\noindent But for single-token differentiands in this document the
+space is not inserted for upright and slash-form derivatives:
+\begin{centred}
+\verb`\[ \diffp Fx,\quad \difsp Fx. \]` $\Longrightarrow$ \[ \diffp Fx,\quad \difsp Fx. \]
+\end{centred}
+If you always want the space present, use \verb`spaced=1`; if you
+never want the space for upright- or slash-form derivatives, or wish
+to insert such space always `by hand', use \verb`spaced=0`.
\subsubsection{Spacing commands}
-\label{subsec:Spacing-commands}The \texttt{diffcoeff} package also
-offers four simple spacing commands to fine-tune the display of derivatives
-and of other quantities. These are
+\label{subsec:Spacing-commands}\LaTeX{} has its own explicit spacing
+commands. In particular \verb`\,` which is \verb`3 mu` (a thin space)
+and \verb`\!` which is \verb`-3 mu` (a negative thin space) are
+convenient in math mode. The \verb`diffcoeff` package adds four simple
+spacing commands to `fill in (most of) the gap' between these two.
+These are
\begin{description}
-\item [{\texttt{\textbackslash negmu}}] insert spacing of $-1$ mu
-\item [{\texttt{\textbackslash nilmu}}] insert spacing of $0$ mu (cf.
-use of an empty brace pair \texttt{\textbf{\{\}}} )
-\item [{\texttt{\textbackslash onemu}}] insert spacing of $1$ mu
-\item [{\texttt{\textbackslash twomu}}] insert spacing of $2$ mu
+\item [{\texttt{\textbackslash negmu}}] insert spacing of \verb`-1 mu`;
+\item [{\texttt{\textbackslash nilmu}}] insert spacing of \verb`0 mu`
+(cf. use of an empty brace pair \texttt{\textbf{\{\}}} );
+\item [{\texttt{\textbackslash onemu}}] insert spacing of \verb`1 mu`;
+\item [{\texttt{\textbackslash twomu}}] insert spacing of \verb`2 mu`.
\end{description}
+It is also worth recalling here the reduced spacing around scalable
+delimiters that results from using \verb`\mleft`, \verb`\mright`
+in place of \verb`\left`, \verb`\right`; see §\ref{sec:Package-options}
+for the \verb`mleftright` package option, and the example at §\ref{subsec:mleftright}.
-\subsection{Appending the differentiand: \texttt{\textbackslash diff{*}}}
+\subsection{Higher order derivatives}
-Some differentiands are too big or awkward to be placed neatly in
-the numerator of a derivative and it is natural to append them to
-a preceding differential operator. One way to do this is to leave
-the numerator argument empty in the \texttt{\textbackslash diff}
-command and follow the command with the differentiand. A better way
-is to star the \texttt{\textbackslash diff} command. This tells \texttt{diffcoeff}
-to append the differentiand. Thus suppose the differentiand is a polynomial,
-say $ax^{2}+bx+c$. Add a star (an asterisk) to the \texttt{\textbackslash diff}
-command:
+\label{subsec:Higher-order-derivatives}An optional argument allows
+the order of differentiation to be specified. The order need not be
+a number; an algebraic order of differentiation is perfectly acceptable
+as is a mix of the two:
\begin{centred}
-\verb`\[ \diff*{(ax^2+bx+c)}x \]` $\Longrightarrow$ \[\diff*{(ax^{2}+bx+c)}x\]
+\verb`\[ \diff[2]yx, \quad \diff[n+1]yx. \]` $\Longrightarrow$ \[ \diff[2]yx, \quad \diff[n+1]yx. \]
\end{centred}
-With the \texttt{!} switch or \texttt{spaced} package option, additional
-space (by default \texttt{3mu plus 1mu minus 2mu}) is inserted between
-the operator and the differentiand:
+As mentioned, the braces can be and have been omitted around the $x$
+and $y$ since they are single tokens. The square brackets around
+the optional order-of-differentiation argument are essential. In slash
+form,
\begin{centred}
-\verb`\[ \diff*!{(ax^2+bx+c)}x \]` $\Longrightarrow$ \[\diff*!{(ax^{2}+bx+c)}x.\]
+\verb`$ \difs[2]yx, \quad \difs[n+1]yx $` $\Longrightarrow$ $ \difs[2]yx, \quad \difs[n+1]yx, $
\end{centred}
-A virtue of using an asterisk to append the differentiand is that
-if one isn't sure whether a differentiand should be appended or not,
-it is an easy matter to simply insert or delete the asterisk to compare
-the results. For example, a second derivative is an iterated derivative
--- one in which a derivative forms the differentiand of another derivative:
+the latter of which is a bit of an eyesore. In compact form,
\begin{centred}
-\verb`\[ \diff[2]yx = \diff*{\diff yx}x \]` $\Longrightarrow$ \[ \diff[2]yx=\diff*{\diff yx}x \]
+\verb`$ \difc[2]yx,\quad\difc[n+1]yx $` $\Longrightarrow$ $\difc[2]yx,\quad\difc[n+1]yx$.
\end{centred}
-\noindent which is more elegant to my eye than
+Note that entering \verb`1` as the optional argument has no effect:
\begin{centred}
-\noindent \verb`\[ \diff[2]yx = \diff!{\diff yx}x \]` $\Longrightarrow$
-\[ \diff[2]yx=\diff!{\diff yx}x \]
+\verb`$ \diff[1]yx,\;\difs[1]yx,\;\difc[1]yx $` $\Longrightarrow$
+$\diff[1]yx,\;\difs[1]yx,\;\difc[1]yx $.
\end{centred}
-\noindent although whether the \emph{meaning} is clearer is moot.\emph{
-}It is easy to switch between the two forms on the right, simply by
-inserting or removing the asterisk.
-
-In slash style with the star option, the polynomial example becomes
+For partial derivatives when differentiating in only one variable
+the pattern is the same:
\begin{centred}
-\verb`\[ \diff*{(ax^2+bx+c)}/x \]` $\Longrightarrow$ \[ \diff*{(ax^2+bx+c)}/x \]
+\verb`\[ \diffp[2]yx, \quad \diffp[n+1]yx. \]` $\Longrightarrow$
+\[ \diffp[2]yx, \quad \diffp[n+1]yx. \]
\end{centred}
-\noindent where the parentheses around the differential operator are
-automatically inserted by \texttt{diffcoeff}. Like other elements
-of automatic formatting, this is user-adjustable; see §\ref{sec:Changing-defaults}.
-
-With the \texttt{!} switch or \texttt{spaced} package option, this
-becomes
+For the slash forms,
+\begin{centred}
+\verb`$ \difsp[2]yx,\quad \difsp[n+1]yx $` $\Longrightarrow$ $ \difsp[2]yx,\quad \difsp[n+1]yx. $
+\end{centred}
+and in compact form,
\begin{centred}
-\verb`\[ \diff*!{(ax^2+bx+c)}/x \]` $\Longrightarrow$ \[ \diff*!{(ax^2+bx+c)}/x \]
+\verb`$ \difcp[2]yx,\quad \difcp[n+1]yx $` $\Longrightarrow$ $ \difcp[2]yx,\quad \difcp[n+1]yx. $
\end{centred}
+For partial differentiation in more than one variable -- so-called
+\emph{mixed} partial derivatives -- see §\ref{subsec:Mixed-partial-derivatives}.
-\subsection{Point of evaluation\protect\label{subsec:Point-of-evaluation}}
+\subsection{Appending the differentiand}
-If you want to specify a point at which the derivative is evaluated,
-append a final optional argument. Note that there \emph{must be no
-space} before the left square bracket of the argument:\footnote{In v.1 of \texttt{diffcoeff}, this was brace-delimited. From v.2,
-square-brackets have been used and braces deprecated. From v.4, braces
-are no longer accepted.}
+\label{subsec:Appending-the-differentiand}Some differentiands are
+too big or awkward to be placed neatly in the numerator of a derivative
+and it is natural to \emph{append} them to a preceding differential
+operator. One could leave the numerator argument empty in the \verb`\diff`
+or \verb`\diffp` command and follow the command with the differentiand,
+but \verb`diffcoeff` offers a better way: star the \verb`\diff`
+or \verb`\diffp` command. This tells \verb`diffcoeff` to append
+the differentiand. Thus suppose the differentiand is a polynomial,
+say $ax^{2}+bx+c$. Add a star (an asterisk) to the \verb`\diff`
+command:
\begin{centred}
-\verb`\[ \diff[2]yx[0] \]` $\Longrightarrow\quad{\displaystyle \diff[2]yx[0]}$
+\verb`\[ \diff*{(ax^2+bx+c)}x \]` $\Longrightarrow$ \[\diff*{(ax^{2}+bx+c)}x.\]
\end{centred}
-\noindent If a space does slip in before the final optional argument,
-it will not cause a \LaTeX{} error. Instead, the argument will be treated
-as a square-bracketed mathematical expression following the derivative,
-and typeset as such.
-\begin{itemize}
-\item If you prefer to use subscripted \emph{parentheses} around the derivative
-to indicate a point of evaluation -- as ISO 80000-2 recommends --
-then this can easily be done; see §\ref{sec:Changing-defaults} on
-changing default settings. Or, more simply, use the \texttt{ISO} package
-option.
-\end{itemize}
-Because the slash form spreads the derivative out horizontally, parentheses
-are preferred here to indicate a point of evaluation:
+Or, for a partial derivative, one might want to indicate in the differentiand
+all the variables on which it depends:
\begin{centred}
-\verb`$ \diff{\ln sin x}/{sin x}[x=\pi/6] $` $\Longrightarrow$ $ \diff{\ln\sin x}/{\sin x}[x=\pi/6] $.
+\verb`\[ \diffp*[2]{\Phi(x,y,z)}x \]` $\Longrightarrow$ \[ \diffp*[2]{\Phi(x,y,z)}x. \]
\end{centred}
-\noindent A vertical rule (or `pipe') can easily become too remote
-from the opening $d$ of the differential coefficient: $\diff.svrule.{\ln\sin x}/{\sin x}[x=\pi/6]$;
-parentheses tie the whole cluster of symbols together.
-
-\subsubsection{Superscripts}
+A virtue of using an asterisk to append the differentiand is that
+if one isn't sure whether a differentiand should be appended or not,
+it is an easy matter to simply insert or delete the asterisk to compare
+the results.
-It is easy to add a superscript to a derivative to indicate evaluation
-at two points and the difference between the values:
+For instance, a second derivative is an iterated derivative -- one
+in which a derivative forms the differentiand of another . Thus
\begin{centred}
-\verb`\[ \diff {\sin x}x[0]^{\pi/2} \]` ${\displaystyle \Longrightarrow}$
-\[ \diff{\sin x}x[0]^{\pi/2} \]
+\verb`\[ \diff[2]yx = \diff*{\diff yx}x \]` $\Longrightarrow$ \[ \diff[2]yx=\diff*{\diff yx}x .\]
\end{centred}
-\noindent If you want only the superscript, no subscript, include
-the final optional argument but leave it empty. Thus, for a particle
-of mass $m$ moving along a line, distance $x$ at time $t$, the
-kinetic energy is:
+\noindent This result is more elegant to my eye than what results
+when removing the asterisk,
\begin{centred}
-\noindent \verb`$ \tfrac 12 m \diff x/t[]^2 $` $\Longrightarrow$
-$\tfrac{1}{2}m\diff x/t[]^{2}$.
+\noindent \verb`\[ \diff[2]yx = \diff{\diff yx}x \]` $\Longrightarrow$
+\[ \diff[2]yx=\diff{\diff yx}x ,\]
\end{centred}
+\noindent although whether the \emph{meaning} is clearer is moot.
+
+Since the differentiand is appended \emph{by default} in compact-form
+derivatives, starring such a derivative has no effect other than when
+a second asterisk is used to transpose the order of arguments.
-\subsection{Order of differentiation}
+\subsubsection{Transposing the argument order}
-An optional first argument allows the order of differentiation to
-be specified. The order need not be a number; an algebraic order of
-differentiation is perfectly acceptable as is a mix of the two:
+\label{subsec:Transposing-the-argument}If a \emph{second} asterisk
+follows the first, the order of the arguments specifying the differentiand
+on the one hand and variable or variables of differentiation on the
+other are reversed. Thus it is clearer to the eye to write
\begin{centred}
-\verb`\[ \diff[2]yx \]` $\Longrightarrow$ \[ \diff[2]yx,\]\verb`\[ \diff[n+1]yx \]`
-$\Longrightarrow$ \[ \diff[n+1]yx.\]
+\verb`\[ \diff**x{(ax^2+bxy+cy^2)} \]` $\Longrightarrow$ \[\diff**x{(ax^2+bxy+cy^2)}\]
\end{centred}
-As mentioned, the braces can be and have been omitted around the $x$
-and $y$; the square brackets around the optional argument, the order
-of differentiation, are essential. For a first-order derivative, no
-optional argument is needed and entering \texttt{1} as the optional
-argument has no effect:
+than \verb`\[ \diff*{(ax^2+bxy+cy^2)}x \]`, where the eye has to
+search for the variable of differentiation. This is especially the
+case if the differentiand contains more than one variable and commands
+like \verb`\frac` or \verb`\sqrt` requiring braced arguments:
+\begin{centred}
+\verb`\[ \diffp**x{\frac1{\sqrt{x^2-y^2}}} \]` $\Longrightarrow$
+\[ \diffp**x{\frac1{\sqrt{x^2-y^2}}} \]
+\end{centred}
+For compact-form derivatives the initial, appending asterisk is always
+implicitly present. However, it must be \emph{explicitly} present
+for the second asterisk to take effect:
\begin{centred}
-\verb`$ \diff[1]yx $` $\Longrightarrow$$\diff[1]yx$.
+\verb`\[ \difcp yx,\quad \difcp*yx,\quad \difcp**yx \]` $\Longrightarrow$
+\[ \difcp yx,\quad \difcp*yx,\quad \difcp**yx \]
\end{centred}
-In slash style, \texttt{\$\textbackslash diff{[}2{]}y/x\$} produces
-$\diff[2]y/x$, and \texttt{\$\textbackslash diff{[}n+1{]}y/x\$}
-produces $\diff[n+1]y/x$.
-\subsection{Multi-character variables of differentiation}
+\subsubsection{Operator parenthesizing}
-Differentiating a function of a function may involve a multi-character
-differentiation variable. For instance, to differentiate $\ln\sin x$
-in $x$ means forming the product
+In slash style with the star option, the polynomial example becomes
\begin{centred}
-\verb`\[ \diff!{\ln\sin x}{\sin x}\diff{\sin x}x \]` $\Longrightarrow$
-\[\diff!{\ln\sin x}{\sin x}\diff{\sin x}x.\]
+\verb`$ \difs*{(ax^2+bx+c)}x $` $\Longrightarrow$ $ \difs*{(ax^2+bx+c)}x $
\end{centred}
-\noindent (Although I am mainly using un-spaced differentiands in
-this document, a space before the differentiand in the first of these
-derivatives -- the \verb`!` switch -- improves the appearance of
-the expression to my eye.)
-
-Forming the \emph{second} derivative of $\ln\sin x$ will now involve
-forming (among other quantities)
+\noindent where parentheses have been automatically inserted around
+the differential operator. Similarly, for slash-style partial derivatives,
\begin{centred}
-\noindent \verb`\[\diff[2]{\ln\sin x}{\sin x}\]` $\Longrightarrow$
-\[\diff[2]{\ln\sin x}{\sin x}\]
+\verb`\( \difsp*[n]{f(x)}x \)` $\Longrightarrow$ \( \difsp*[n]{f(x)}x \)
\end{centred}
-\noindent Parentheses have been inserted automatically by \texttt{diffcoeff}
-around $\sin x$ in the denominator to avoid any visual hint that
-we are differentiating in the sine of $x^{2}$.
+\noindent parentheses are again inserted automatically around the
+differential operator. Like other elements of automatic formatting,
+this behaviour is user-adjustable; see §§\ref{sec:Variant-forms},
+\ref{sec:ChangingDefaults}.
-The question is: are the parentheses in the right place? Logically,
-no. They should include the $d$: $(d\sin x)^{2}$ -- it is the differential
-$d\sin x$ that is of the second order. But as the examples in the
-Rogues' Gallery show -- see particularly (\ref{eq:eg3}) -- the
-inclination seems to be to do otherwise. This may be because one wants,
-in any case, to parenthesise the variable. A second, outer pair of
-parentheses then seems too fussy and detracts from comprehending the
-symbol `at a glance':
-\[
-\diff.wrapall.[2]{f(x)}{(1/x)}.
-\]
+\subsection{Point of evaluation/variables held constant}
-Customary but illogical notations are familiar in mathematics --
-think of the position of the superscripts in an identity like $\sin^{2}\theta+\cos^{2}\theta=1$.
-But, like other features of the derivative, the manner of this wrapping
-in parentheses of long variables for \emph{higher order} derivatives
-is customisable; see §\ref{sec:Changing-defaults}.
-
-For first order derivatives, parenthesising does not occur. If you
-want the variable of differentiation to be parenthesised, you need
-to insert them yourself:
+\label{subsec:Point-of-evaluation}If you want to specify a point
+at which a derivative is evaluated, append a final optional argument:
\begin{centred}
-\verb`\[\diff {f(x)}{1/x}, \quad \diff {f(x)}{(1/x)}.\]` $\Longrightarrow$
-\[ \diff {f(x)}{1/x}, \quad\diff {f(x)}{(1/x)}.\]
+\verb`\[ \diff[2]yx[0] \]` $\Longrightarrow$ \[ \diff[2]yx[0] \]
\end{centred}
-
-\section{Partial derivatives\protect\label{sec:Partial-derivatives}}
-
-\noindent Partial derivatives follow the same pattern as ordinary
-derivatives, with some extensions. The command this time is \texttt{\textbackslash diffp}.
-Thus \texttt{\textbackslash diffp\{F\}\{x\}}, or, with a saving on
-keystrokes,\texttt{ \textbackslash diffp Fx}, produces $\diffp Fx$
-in text style and
+\noindent Note that there must be \emph{no space} before the left
+square bracket of the trailing argument, otherwise it will be treated
+as part of the wider mathematical expression of which the derivative
+is part and typeset as such. (This should not cause a \LaTeX{} error.)
+\begin{itemize}
+\item If you prefer to use subscripted \emph{square} brackets
\[
-\diffp{F}{x}
+\diffp.].{F(x,y)}x[(0,0)]
\]
-in display style. (As for \texttt{\textbackslash diff}, the omission
-of braces is possible when the differentiand or the differentiation
-variable are single tokens.) As for \texttt{\textbackslash diff},
-there is a slash form, generally preferred for inline use, \texttt{\textbackslash diffp
-F/x}, displaying as $\diffp F/x$. Given that \texttt{\textbackslash partial}
-takes 8 keystrokes to type, the slash form \emph{does }economise on
-keystrokes for a partial derivative.
-
-With either the \verb`spaced` package option (see §\ref{subsec:Package-options})
-or the \verb`!` switch a space, defaulting to \verb`3 mu` with some
-stretch and shrink, can be inserted before the differentiand: \verb`\[ \diffp!{F(x,y)}x \]`
-$\Longrightarrow$ \[ \diffp!{F(x,y)}x. \]
-
-\noindent (But note that if the \verb`spaced` package option is used,
-the \verb`!` switch \emph{removes} any extra space.)
-
-Again an optional argument allows the specification of the order of
-differentiation which may be numeric or algebraic or a mix of the
-two:
-\begin{centred}
-\verb`\[ \diffp[3]F/x , \quad \diffp[n]F/x \]` $\Longrightarrow$
-\[\diffp[3]F/x , \quad \diffp[n]F/x\] \verb`\[ \diffp[n+1]Fx. \]`
-$\Longrightarrow$ \[ \diffp[n+1]Fx. \]
-\end{centred}
-
-\subsection{Variables held constant}
-
-In a subject like thermodynamics, there is a need to indicate which
-variables are held constant when the differentiation occurs. To show
-this, append a final square-bracketed optional argument and ensure
-that it follows \emph{immediately} on the preceding mandatory argument.
-A space here will detach the argument from the derivative and result
-in it being treated as a mathematical expression following the derivative.
-Thus to differentiate the entropy $S$ in temperature $T$ while holding
-the volume $V$ constant, write
-\begin{centred}
-\verb`\[ \diffp ST[V] \]` $\Longrightarrow$ \[ \diffp ST[V]. \]
-\end{centred}
-\noindent In slash form the same expression looks like
-\begin{centred}
-\noindent \verb`$ \diffp S/T[V] $` $\Longrightarrow$ $ \diffp S/T[V] $.
-\end{centred}
-This use of a parenthesised, subscripted form to indicate a variable
-or variables held constant, leaves open the question: how do we represent
-a point of evaluation? ISO 80000-2 makes no recommendation for \emph{partial}
-derivatives; presumably we follow the same practice as their recommendation
-for ordinary derivatives:
-\begin{example}
-\verb`\[ \diffp {F(x,y)}x[(0,0)] \]` $\Longrightarrow$ \[ \diffp {F(x,y)}x[(0,0)] \]
-\end{example}
-
-However, you may prefer (as many do) to use a vertical rule for this
-purpose:
+or a subscripted vertical rule after the derivative
\[
-\diff.pvrule.{F(x,y)}x[(0,0)]
+\diffp.|.{F(x,y}x[(0,0)]
\]
-Making this possibility available is discussed in §\ref{sec:Changing-defaults}.
-
-An empty final argument produces a parenthesised derivative with no
-subscript,
+to indicate a point of evaluation, then this can easily be done; see
+specifically §\ref{subsec:variantPoint-of-evaluation} (or §\ref{sec:ChangingDefaults}
+on changing default settings). Parentheses are the ISO recommendation;
+see ISO 80000-2.
+\end{itemize}
+Because the slash form spreads the derivative out horizontally, parentheses
+are the natural way in this case to indicate a point of evaluation:
\begin{centred}
-\verb`\[ \diffp yx[] \]` ${\displaystyle \Longrightarrow}$ \[ \diffp yx[] \]
+\verb`$ \difs{\ln sin x}{sin x}[x=\pi/3] $` $\Longrightarrow$ $ \difs{\ln\sin x}{\sin x}[x=\pi/3]$.
\end{centred}
-\noindent which can be useful sometimes. An instance is the writing
-of Lagrange's equations of motion in analytic mechanics:
+\noindent A vertical rule can easily become too remote from the opening
+$\mathrm{d}$ of the differential coefficient: $\difs.|.{\ln\sin x}{\sin x}[x=\pi/3]$.
+Parentheses tie the whole cluster of symbols together.
+
+One reason to query the ISO preference for subscripted parentheses
+to indicate a point of evaluation is that subscripted parentheses
+are used with partial derivatives to indicate variables held constant.
+This occurs frequently in thermodynamics for example. In the following
+well-known relation in thermodynamics, the differentiands are appended
+and the trailing argument is used to indicate the variables held constant:
\begin{centred}
-\noindent \verb`\[ \diffp L{q_k}-\diff*{\diffp L{\dot{q}_k}[]}t = 0 \]`
-$\Longrightarrow$ \[ \diffp L{q_k}-\diff*{\diffp L{\dot{q}_k}[]}t = 0. \]
+\verb`\[ \diffp*{\frac PT}U[V] = \diffp*{\frac 1T}V[U] \]` $\Longrightarrow$
+\[ \diffp*{\frac PT}U[V] = \diffp*{\frac 1T}V[U]. \]
\end{centred}
+\noindent This is much easier to write than building the expressions
+`by hand', starting with \verb`\left(` and finishing with \verb`_U`.
-\subsubsection{Text-style derivatives}
+\subsubsection{Superscripts}
-The \texttt{diffcoeff} package assumes that derivatives formed as
-`numerator over denominator' will be used in display-style expressions,
-and that the slash form will be used for inline use (text style).
-This is the familiar practice in the literature. If one \emph{does}
-use the first form in an inline expression where a variable is held
-constant, say \texttt{\textbackslash diffp ST{[}V{]}} as here $\diffp ST[V]$,
-the result is unsatisfactory, the subscript too tight on the closing
-parenthesis and too much space between parentheses and derivative.
-The matter is easily resolved using `variant forms' -- see §\ref{subsec:Text-and-script-style}
-below -- giving, for our example, $\diff.ptxt.ST[V]$.
+It is easy to add a superscript to a derivative to indicate evaluation
+at two points and the difference between the values:
+\begin{centred}
+\verb`\[ \diff {\sin x}x[0]^{\!\!\pi/2} \]` ${\displaystyle \Longrightarrow}$
+\[ \diff{\sin x}x[0]^{\!\!\pi/2} \]
+\end{centred}
+but to my eye either square brackets or a vertical rule are clearer
+for this purpose (and do not involve nudging the subscript or superscript
+closer to the right delimiter); see §\ref{sec:Variant-forms}.
+
+\subsubsection{Empty trailing argument}
+
+\noindent If the trailing argument is included but left empty it will,
+with the default set-up, wrap the derivative in parentheses but with
+no subscript. This fact can be exploited. Thus, for a particle of
+mass $m$ moving along a line, distance $x$ at time $t$, the kinetic
+energy is:
+\begin{centred}
+\noindent \verb`$ \tfrac 12 m \difs xt[]^2 $` $\Longrightarrow$
+$\tfrac{1}{2}m\difs xt[]^{2}$.
+\end{centred}
+Or, again exploiting the parentheses resulting from an empty trailing
+argument, Lagrange's equations of motion in analytic mechanics can
+be written,
+\begin{centred}
+\verb`\[ \diffp L{q_k}-\diff**t{ \diffp L{\dot{q}_k}[] } = 0 \]`
+$\Longrightarrow$\[\diffp L{q_k}-\diff**t{\diffp L{\dot{q}_k}[]} = 0. \]
+\end{centred}
+\noindent (See §\ref{subsec:Transposing-the-argument} for the double
+asterisk.) Like the author, you may feel that there is too much whitespace
+between $\diff{}t$ and the left parenthesis in this expression. One
+obvious remedy is to insert a negative thin space \verb`\!` before
+the second \verb`\diffp` command. Another is to use the package \verb`mleftright`.
+
+\subsubsection{Use of the package \texttt{mleftright}}
+
+\label{subsec:mleftright}The \verb`mleftright` package `tightens'
+the spacing around \verb`\left`, \verb`\right` delimiters. The user
+either by explicitly replaces \verb`\left`, \verb`\right` by \verb`\mleft`
+and \verb`\mright` or uses the command \verb`\mleftright` which
+effectively turns subsequent occurrences of \verb`\left`, \verb`\right`
+into \verb`\mleft`, \verb`\mright`; \verb`\mleftrightrestore` returns
+\verb`\left`, \verb`\right` to their original selves. This process
+can be `short-circuited' by using the \verb`diffcoeff` package
+option \verb`mleftright` that inserts \verb`\mleftright` in the
+preamble; see §\ref{sec:Package-options}.
+
+However, that package option is not used in this document. Nonetheless
+\verb`mleftright` is a required package of version 5 of \verb`diffcoeff`
+and its commands are available for use. Hence to reduce the whitespace
+I can write
+\begin{verbatim}
+ \mleftright
+ \[ \diffp L{q_k}-\diff**t{\diffp L{\dot{q}_k}[]} = 0. \]
+ \mleftrightrestore
+\end{verbatim}
+$\Longrightarrow$ \mleftright
+\[ \diffp L{q_k}-\diff**t{\diffp L{\dot{q}_k}[]} = 0. \]
+\mleftrightrestore
+
+\noindent which is better, but better still to my eye is to also add
+a negative thin space \verb`\!` before the second \verb`\diffp`
+command:
+\begin{verbatim}
+ \mleftright
+ \[ \diffp L{q_k}-\diff**t{ \!\diffp L{\dot{q}_k}[] } = 0 \]
+\end{verbatim}
+\noindent $\Longrightarrow$ \mleftright\[\diffp L{q_k}-\diff**t{\!\diffp L{\dot{q}_k}[]} = 0. \]
+
+\noindent The problem is that in addition to the space around \verb`\left`,
+\verb`\right` pairs (which is reduced by issuing the command \verb`\mleftright`),
+there is also the space inserted by \verb`diffcoeff` before a multi-token
+differentiand. The user should be aware of this, and may wish to define
+a `variant form' (see §\ref{sec:Variant-forms}) that introduces
+no space before an appended differentiand.
-\subsection{Appending the differentiand\protect\label{subsec:Partial-appending}}
+\subsection{Mixed partial derivatives}
-For a long or awkward differentiand, it is generally better to \emph{append}
-it to a preceding differential operator, rather than create a fractional
-form with the long expression in the numerator. As with ordinary derivatives,
-this is achieved by adding an asterisk to (i.e. by starring) the \texttt{\textbackslash diffp}
-command.
-\begin{centred}
-\verb`\[ \diffp*[2]{\Phi(x,y,z)}x \]` $\Longrightarrow$ \[ \diffp*[2]{\Phi(x,y,z)}x. \]
-\end{centred}
-With the \verb`spaced` package option, or with the \verb`!` switch
-if the package option is not used (which is the case for this document),
-one gets
+\label{subsec:Mixed-partial-derivatives}The new thing with partial
+derivatives, not present with ordinary derivatives, is so-called \emph{mixed}
+partial derivatives, where differentiation occurs in more than one
+variable. If each variable is differentiated only to the first order,
+then it is easy to specify the derivative. Suppose $F$ is a function
+of three variables, $x$, $y$ and $z$. Then
\begin{centred}
-\verb`\[ \diffp*[2]!{\Phi(x,y,z)}x \]` $\Longrightarrow$ \[ \diffp*[2]!{\Phi(x,y,z)}x \]
+\verb`\[ \diffp F{x,y,z},\quad\diffp{F(x,y,z)}{x,y,z}. \]` $\Longrightarrow$
+\[ \diffp F{x,y,z},\quad \diffp{F(x,y,z)}{x,y,z}. \]
\end{centred}
-which is an improvement (to my eye).
+(The \verb`spaced=-1` package option inserts space before the multi-token
+differentiand in the second of these.)
-Alternatively you could leave the first mandatory argument empty and
-manually append the differentiand, but by deleting or inserting an
-asterisk, it is easy to compare the two forms, differentiand-in-the-numerator,
-differentiand-appended, and see which is preferable.
+The variables of differentiation are listed in order in a comma list
+-- \verb`{x,y,z}` -- forming the second mandatory argument. The
+total order of differentiation (3 in this example) was inserted automatically.
+It did not need to be specified or calculated `by hand' -- \verb`diffcoeff`
+did the calculation.
-In slash form, parentheses are automatically inserted around the differential
-operator when the differentiand is appended,
+The slash form is
\begin{centred}
-\verb`\[ \diffp*[n]{f(x)}/x \]` $\Longrightarrow$ \[ \diffp*[n]{f(x)}/x, \]
+\verb`$ \difsp F{x,y,z} $` $\Longrightarrow$ $ \difsp F{x,y,z}$,
\end{centred}
-\noindent although this behaviour can be changed (§\ref{sec:Changing-defaults}
-again).
-
-If you wish to both append the differentiand \emph{and} indicate variables
-held constant, then the starred form is much the easier way to achieve
-this. Thus, to express a relation in thermodynamics,
+as expected, and the compact form is
\begin{centred}
-\verb`\[ \diffp*{\frac PT}U[V] = \diffp*{\frac 1T}V[U] \]` $\Longrightarrow$
-\[ \diffp*{\frac PT}U[V] = \diffp*{\frac 1T}V[U], \]
+\verb`$ \difcp F{x,y,z} $` $\Longrightarrow$ $ \difcp F{x,y,z}$.
\end{centred}
-\noindent where the starring automatically takes care of the parentheses
-and subscripts.
+One might wonder about even more compact notations like $\partial_{xyz}^{\onemu3}F$
+for this example but it becomes messy if different orders of differentiation
+are involved for different variables.
-\subsection{Iterated derivatives}
-
-Derivatives can be the differentiands of derivatives, as seen above
-when writing Lagrange's equations,
-\begin{centred}
-\noindent \verb`\[ \diffp L{q_k}-\diff*{\diffp L{\dot{q}_k}[]}t = 0 \]`
-$\Longrightarrow$ \[ \diffp L{q_k}-\diff*{\diffp L{\dot{q}_k}[]}t = 0. \]
-\end{centred}
-\noindent However, in versions of \texttt{diffcoeff} before version
-3.2, an ordinary derivative within a partial derivative rendered as
-a partial derivative. That is now corrected, the ordinary derivative
-rendering correctly:
+To differentiate variables to higher order, their orders need to be
+specified explicitly. To do so use a comma list for the optional argument:
\begin{centred}
-\verb`\[ \diffp*{\diff{x^\mu}{\lambda}}{x^\sigma} \]` $\Longrightarrow$
-\[ \diffp*{\diff{x^\mu}{\lambda}}{x^\sigma}. \]
+\verb`$ \difcp[2,3]F{x,y,z} $` $\Longrightarrow$ $ \difcp[2,3] F{x,y,z}$,
+
+\verb`\[ \diffp[2,3]F{x,y,z} \]` $\Longrightarrow$ \[ \diffp[2,3]F{x,y,z}. \]
\end{centred}
+\noindent Notice that the overall order of the derivative -- 6 --
+in the second of these is again automatically calculated and inserted
+as a superscript on the $\partial$ symbol in the numerator.
+
+In the example, the comma list of orders has only \emph{two} members,
+although there are \emph{three} variables. It is assumed that the
+orders given in the comma list apply in sequence to the variables,
+the first order to the first variable, the second to the second variable,
+and so on, and that any subsequent orders not listed in the optional
+argument are, by default, 1. Thus we need to specify only 2 and 3
+in the example; the order of differentiation of $z$ is 1 by default.
+But you \emph{cannot} use an order specification like \verb`[,,2]`;
+instead write {\ttfamily\verb`[1,1,2]`} (which is the natural
+thing to do in any case).\textbf{ }It is only the \emph{tail} of an
+order specification which can be omitted.
+
+In the other direction, if there are more orders of differentiation
+specified than there are variables, the list of orders is truncated
+to match the number of variables.
-\subsection{Mixed partial derivatives}
+\subsubsection{Algebraic orders of differentiation}
-The new thing with partial derivatives, not present with ordinary
-derivatives, is \emph{mixed} partial derivatives, where there is more
-than one variable of differentiation. If each variable is differentiated
-only to the first order, then it is easy to specify the derivative.
-Suppose $F$ is a function of three variables, $x$, $y$ and $z$.
-Then
+Orders of differentiation do not need to be numerical. They can also
+be algebraic:
+\begin{centred}
+\verb`\[ \diffp[2m-1,m+1,2]F{x,y,z} \]` $\Longrightarrow$ \[ \diffp[2m-1,m+1,2]F{x,y,z}\]
+\end{centred}
+The total order of differentiation is still calculated by \verb`diffcoeff`.
+Or again,
+\begin{centred}
+\verb`\[ \diffp[1,km+1,m+k-1]{F(x,y,z)}{x,y,z} \]` $\Longrightarrow$
+\[ \diffp[1,km+1,m+k-1]{F(x,y,z)}{x,y,z}. \]
+\end{centred}
+
+\subsubsection{Order-override command: \texttt{\textbackslash difoverride}}
+
+\noindent \label{subsec:Order-override-command}$m+k+km+1$ factorizes
+to $(k+1)(m+1)$ and you may prefer to express the total order of
+differentiation in this form. \verb`diffcoeff` is not a computer
+algebra system and does not do such factorizations but the \verb`\difoverride`
+command offers the means to use the factorized form as the total order
+of differentiation in the derivative. (The \verb`\difoverride` command
+replaces the order-override option of the \verb`\diff` command in
+version 4 of \verb`diffcoeff`. That option is no longer available.)
+\begin{verbatim}
+ \[
+ \difoverride{(k+1)(m+1)}
+ \diffp[1,km+1,m+k-1]{F(x,y,z)}{x,y,z}
+ \]
+\end{verbatim}
+$\Longrightarrow$ \[
+ \difoverride{(k+1)(m+1)}
+ \diffp[1,km+1,m+k-1]{F(x,y,z)}{x,y,z}
+ \]
+
+\verb`\difoverride` takes only one (mandatory) argument, the total
+order of differentiation, which it stores. When \verb`\difoverride`
+is non-empty, then the algorithm that calculates the total order is
+sidestepped. It does not get called at all. In this way one can present
+not only the total order in whatever manner one wishes but essentially
+arbitrary material as a superscript to the $\partial$ symbol in the
+numerator. (For compact-form derivatives, which do not use a total
+order of differentiation, the command is irrelevant.)
+
+Note that in the example \verb`\difoverride` has been used \emph{within
+}the math environment. This is good practice. It prevents the contents
+of \verb`\difoverride` erroneously overriding the orders of later
+derivatives:
+\begin{verbatim}
+ $ \difoverride{N} \difsp[m,n]f{x,y} $,\quad
+ $ \difsp[1,2]f{x,y} $.
+\end{verbatim}
+$\Longrightarrow$ $ \difoverride{N} \difsp[m,n]f{x,y} $,\quad
+ $ \difsp[1,2]f{x,y} $.
+
+\noindent There is no spillover here whereas by placing the override
+command outside the math environment the command reaches beyond the
+intended target. To cancel the overreach, I have used \verb`\difoverride`
+with an \emph{empty} argument, :
+\begin{verbatim}
+ \difoverride{K}
+ $ \difsp[m,n]f{x,y} $,\quad
+ $ \difsp[1,2]f{x,y} $,\quad
+ \difoverride{}
+ $ \difsp[1,2]f{x,y}$.
+\end{verbatim}
+$\Longrightarrow$ \difoverride{K} $ \difsp[m,n]f{x,y} $,\quad
+ $ \difsp[1,2]f{x,y} $,\quad
+ \difoverride{} $ \difsp[1,2]f{x,y}$.
+
+\noindent Clearly one should use the override command \emph{within}
+the math environment.
+
+\subsubsection{Parentheses}
+
+Auto-calculation of the total order accommodates the simple use of
+parentheses:
\begin{centred}
-\verb`\[ \diffp F{x,y,z} \]` $\Longrightarrow$ \[ \diffp F{x,y,z}, \]
+\verb`\[ \diffp[2m-(k+1),2(k+1)-m]{F(x,y,z)}{x,y,z} \]` $\Longrightarrow$
+\[ \diffp[2m-(k+1),2(k+1)-m]{F(x,y,z)}{x,y,z} \]
+\end{centred}
+This is an example of the use of \emph{dynamic} parentheses: the left
+parenthesis in each case is preceded by a number or a sign. In evaluating
+the total order \verb`diffcoeff` multiplies out the expression (or
+that is the effect).
+
+On the other hand, an order specification like \verb`[f(n+1),f(n-1)]`
+is an example of the use of \emph{static} parentheses where they are
+part of the familiar `function of' notation -- in this case a function
+$f$ of some variable, say $x$, evaluated at $x=n\pm1$. \verb`diffcoeff`
+\emph{always} interprets a left parenthesis preceded by something
+that is neither number nor sign in this way. It does not try to multiply
+out such expressions when calculating the total order.
+
+The following example combines both uses -- and includes a nested
+pair of (dynamic) parentheses:
+\begin{centred}
+\verb`\[\diffp[2(f(n)-(m-1)),5-(f(n)+m)]F{x,y}\]` $\Longrightarrow$
+\[\diffp[2(f(n)-(m-1)),5-(f(n)+m)]F{x,y}\]
+\end{centred}
+Where confusion arises is with specifications like \verb`[m(k-1)+1,m(k+1)-1]`
+where \verb`m` could be interpreted as either a function or a variable.
+As stated, \verb`diffcoeff` \emph{always} interprets a left parenthesis
+preceded by something that is not a number or a sign as signalling
+`function of'. Hence:
+\begin{centred}
+\verb`\[\diffp[m(k-1)+1,m(k+1)-1]F{x,y}\]` $\Longrightarrow$ \[\diffp[m(k-1)+1,m(k+1)-1]F{x,y}\]
+\end{centred}
+\noindent If, in fact, \verb`m` is intended as a \emph{variable}
+then the order-override command is there to rescue the situation:
+\begin{verbatim}
+ \[
+ \difoverride{2mk}
+ \diffp[m(k-1)+1,m(k+1)-1]F{x,y}
+ \]
+\end{verbatim}
+$\Longrightarrow$ \[
+ \difoverride { 2mk }
+ \diffp[m(k-1)+1,m(k+1)-1]F{x,y}
+ \]
-\verb`\[ \diffp !{F(x,y,z)}{x,y,z} \]` $\Longrightarrow$ \[ \diffp !{F(x,y,z)}{x,y,z}. \]
-\end{centred}
-In the second of these I have inserted space before the differentiand
-by using the \verb`!` switch. If the \verb`spaced` package option
-was being used, this would have been done automatically.
+\subsubsection{Error messages}
-The variables of differentiation are listed in order in a comma list
-forming the second mandatory argument. The total order of differentiation
-(3 in this example) is inserted automatically -- \texttt{diffcoeff}
-does the calculation. There is also a slash form:
-\begin{centred}
-\verb`$ \diffp F/{x,y,z} $` $\Longrightarrow$ $ \diffp F/{x,y,z}$.
-\end{centred}
-If we want to differentiate variables to higher order, then their
-orders need to be specified explicitly. To do so use a comma list
-for the optional argument:
-\begin{centred}
-\verb`\[ \diffp[2,3]F{x,y,z} \]` $\Longrightarrow$ \[ \diffp[2,3]F{x,y,z}. \]
-\end{centred}
-\noindent Notice that the overall order of the derivative -- 6 --
-is again automatically calculated and inserted as a superscript on
-the $\partial$ symbol in the numerator. In this example, the comma
-list of orders has only two members, even though there are three variables.
-It is assumed that the orders given in the comma list apply in sequence
-to the variables, the first order to the first variable, the second
-to the second variable, and so on, and that any subsequent orders
-not listed in the optional argument are, by default, 1. Thus we need
-to specify only 2 and 3 in the example; the order of differentiation
-of $z$ is 1 by default. But you \emph{cannot} use an order specification
-like \texttt{{[} , ,2{]}}. Instead write \texttt{{[}1,1,2{]}}.\textbf{
-}It is only the \emph{tail} of an order specification which can be
-omitted.
-
-\subsubsection{Minutiae of spacing (again)\protect\label{subsec:Minutiae-of-spacing}}
-
-In Chapter 18 of the \emph{The\TeX book}, Knuth suggests inserting
-a thin space, {\ttfamily\verb`\,`} (or {\ttfamily\verb`3 mu`}),
-between differentials in appropriate contexts, giving as an example
-$dx\,dy=r\,dr\,d\theta$. In the denominator of a derivative, however,
-that degree of extra spacing seems too great (to my eye), interfering
-with seeing the derivative `as a whole',
+The order-override command is also needed when calculation of the
+total order is beyond the abilities of \verb`diffcoeff`. The package
+is \emph{not} a computer algebra system. It can cope with order specifications
+where variables are followed by diverse arithmetic operators: \verb`n^2`,
+\verb`m\times n`, \verb`m/2` and the like cause no problems. But
+a \emph{number} can be followed \emph{only} by a sign or a variable
+or a left parenthesis. Anything beyond this will raise an error. For
+instance
+\begin{centred}
+\verb`\[ \diffp[2^k]F{x,y} \]`
+\end{centred}
+produces a message beginning `\texttt{! Package diffcoeff Error:}'
+and continuing,
+\begin{verbatim}
+ number followed by ^ in the order spec. [2^k,1] on
+ line xx. Calculation of the total order of
+ differentiation fails in this case. Use the
+ \difoverride command to enter the total order.
+ See the diffcoeff documentation for further
+ information.
+\end{verbatim}
+(The \verb`xx` will be replaced by a specific line number in each
+case. Line breaking may also differ from case to case.) To avoid such
+errors and enable compilation to proceed, use the override command:
+\begin{verbatim}
+ \[
+ \difoverride { 2^{n+1} }
+ \diffp[2^n+1,2^n-1]F{x,y}
+ \]
+\end{verbatim}
+$\Longrightarrow$ \[
+ \difoverride { 2^{n+1} }
+ \diffp[2^n+1,2^n-1]F{x,y}
+ \]
+
+There are limitations on what order specifications the \verb`diffcoeff`
+package can `digest', but in real life that is unlikely to be significant.
+Mixed partial derivatives are used far less often than the pure derivatives,
+and when they \emph{are} used it is nearly always to low numerical
+orders like 1 or 2. For those rare other cases, \verb`\difoverride`
+is always available.
+
+\subsubsection{Comma list of variables of differentiation}
+
+\label{subsec:Comma-list-of-vars}In tensor calculus differentiations
+are almost always in terms of super- or subscripted coordinates. In
+many other contexts this is the case too -- the reciprocal of the
+temperature in thermodynamics or generalized coordinates in analytical
+mechanics. This is why a comma list is used in \verb`diffcoeff` for
+specifying variables of differentiation for mixed partial derivatives.
+Although it would be nice to write the minimal \verb`{xy}` rather
+than \verb`{x,y}` when two variables $x$ and $y$ are involved,
+the extra writing is trivial and the comma list allows a simpler handling
+of multi-character variables. For instance in tensor calculus we get
+expressions like
+\begin{centred}
+\verb`\[ \diffp{A_i}{x^j,x^k} \]` $\Longrightarrow$ \[ \diffp{A_i}{x^j,x^k}. \]
+\end{centred}
+\noindent It is easier to write \verb`{x^j,x^k}` here than, say,
+\verb`{{x^j}{x^k}}` to distinguish the variables. It's also easier
+to read, particularly if the indices themselves get ornamented and
+need surrounding braces:
+\begin{centred}
+\verb`\[ \diffp{A_i}{x^{j'},x^{k'}} \]` $\Longrightarrow$ \[ \diffp{A_i}{ x^{j'},x^{k'} }. \]
+\end{centred}
+\noindent Compare that variable specification with \verb`{{x^{j'}}{x^{k'}}}`.
+Admittedly some extra whitespace would help here, but the point stands:
+the comma list requires fewer nested braces -- unless a variable
+of differentiation includes a comma, for then the comma needs to be
+enclosed in braces. There are plenty of instances of this out in the
+world (see, e.g., the last equation of (\ref{eq:eg1})) but it is
+overall a rare occurrence.
+
+\subsubsection{Spacing in the denominator}
+
+\label{subsec:Minutiae-of-spacing}In Chapter 18 of the \emph{The
+\TeX book}, Knuth suggests inserting a thin space, {\ttfamily\verb`\,`}
+(or {\ttfamily\verb`3 mu`}), between differentials in appropriate
+contexts, giving as an example $dx\,dy=r\,dr\,d\theta$. In the denominator
+of a derivative, however, that degree of extra spacing -- to my eye
+-- seems too great, interfering with seeing the derivative `as a
+whole',
\[
-\diff.pwide.F{x,y,z},
+\diffp.3mu.F{x,y,z},
\]
-especially for the slash-form of derivative: $\diff.pwide.F/{x,y,z}$.
-Some spacing is desirable, but less; by default \texttt{diffcoeff}
-inserts \verb`2 mu` between the differentials in the fraction form
-of derivative and \verb`1 mu`\texttt{ }in the slash form.
+especially for the slash-form of derivative: $\difsp.3mu.F{x,y,z}$.
+Some spacing is desirable, but less. By default \verb`diffcoeff`
+inserts \verb`2 mu` (with stretch and shrink) between the differentials:
+$\difsp F{x,y,z}$.
Should a differentiation occur to higher order and so a variable acquire
a superscript, an adjustment is made to the extra spacing. By default
@@ -758,1347 +1137,2071 @@ a superscript, an adjustment is made to the extra spacing. By default
\verb`2 mu` of spacing is inserted between the $\partial y$ and
$\partial z$, but because the superscript already provides some separation
between them, only \verb`1 mu` is inserted between $\partial x^{2}$
-and $\partial y$.
-
-The values used for the spacing and its adjustment in the presence
-of a superscript can be changed by the user; see §\ref{sec:Changing-defaults}.
-Some other minutiae of spacing are discussed below in §\ref{subsec:Comma-list-of-vars}
-when the variables themselves are super- or subscripted (as happens
-in tensor calculus, for instance).
+and $\partial y$. The values used for the spacing and its adjustment
+in the presence of a superscript can be changed by the user; see Chapter~\ref{chap:Templates-defaults-variants}.
-Note that the \verb`!` switch, if used, is inserted \emph{immediately
-before} the differentiand. It is the placement of the differentiand,
-after all, that it is affecting:
+When the variables themselves are super- or subscripted, as happens
+in tensor calculus, no automatic adjustment is made. Any fine-tuning
+must be done by the user using explicit spacing commands -- like
+\verb`\negmu` (a space of \verb`-1 mu`); see §\ref{subsec:Spacing-commands}:
\begin{centred}
-\verb`\[ \diffp[2]!F{x,y,z} \]` $\Longrightarrow$ \[ \diffp[2]!F{x,y,z}. \]
+\verb`\[ \diffp{A_i}{ x^j\negmu,x^k } \]` $\Longrightarrow$ \[ \diffp{A_i}{ x^j\negmu,x^k }.\]
\end{centred}
+\noindent The \verb`\negmu` decreases the spacing between the terms
+from the default \verb`2 mu` (with stretch and shrink) to \verb`1 mu`.
-\subsubsection{Algebraic orders of differentiation}
+\subsection{Multi-token variables: parenthesizing}
-Calculation of the overall order of differentiation still occurs even
-when some or all of the individual orders are algebraic variables
-rather than numbers. For example, differentiating in three variables
-to orders \texttt{1, m+1, m-1},
+Differentiating a function of a function may involve a multi-character
+differentiation variable. For instance, to differentiate $\ln\sin x$
+in $x$ means forming the product
\begin{centred}
-\verb`\[ \diffp[1,m+1,m-1]{F(x,y,z)}{x,y,z} \]` $\Longrightarrow$
-\[ \diffp[1,m+1,m-1]{F(x,y,z)}{x,y,z}. \]
+\verb`\[ \diff{\ln\sin x}{\sin x}\diff{\sin x}x \]` $\Longrightarrow$
+\[\diff{\ln\sin x}{\sin x}\diff{\sin x}x.\]
\end{centred}
-
-\subsubsection{Error messages}
-
-Should you specify \emph{more} orders in the comma list of the order
-specification than there are variables, compilation will fail and
-an error message will be sent to the terminal and \LaTeX{} log . For
-example, if on (say) line 53 of my document I specify \texttt{{[}1,m-1,m+1,2{]}}
-for the orders of differentiation but list only \texttt{\{x,y,z\}}
-for the variables, the message will be
-\begin{lyxcode}
-!~Package~diffcoeff~Error:~4~orders~of~differentiation~
-
-specified~for~3~variables;~orders~{[}1,m+1,m-1,2{]}
-
-(on~line~53)~for~variables~x,y,z.
-\end{lyxcode}
-Should you try using a \emph{number} raised to a power in an order
-specification, it will cause an error. For example, if on line 53
-(say) of my document I try to form \texttt{\textbackslash diffp{[}2\textasciicircum 2{]}f\{x,y,z\}}
-compilation will fail with the message
-\begin{lyxcode}
-!~Package~diffcoeff~Error:~number~followed~by~\textasciicircum ~in~the~
-
-order~specification~{[}2\textasciicircum n,1,1{]}~on~line~53.~Diffcoeff~
-
-cannot~calculate~the~overall~order~of~differentiation~
-
-in~this~case.~Use~the~order-override~option~to~enter~
-
-the~overall~order.
-\end{lyxcode}
-The order-overide option mentioned here is discussed next. Similarly,
-you cannot use multiplication (\texttt{\textbackslash times} or \texttt{{*}})\texttt{
-}or division (\texttt{/} or \texttt{\textbackslash div}) signs after
-\emph{numbers} in an order specification; only \texttt{+} or \texttt{-}
-or a left parenthesis (see below) are allowed.
-
-\subsubsection{The order-override option}
-
-\noindent Perhaps the differentiations are to orders \texttt{{[}2km,m-1,m+1{]}}:
-\begin{centred}
-\noindent \verb`\[ \diffp[2km,m-1,m+1]{F(x,y,z)}{x,y,z} \]` $\Longrightarrow$
-\[ \diffp[2km,m-1,m+1]{F(x,y,z)}{x,y,z}. \]
-\end{centred}
-\noindent Here the overall order is presented as \texttt{2km+2m}.
-You might prefer this to be presented as \texttt{2m(k+1)}. Although
-\texttt{diffcoeff} takes some steps to present the overall order appropriately,
-it is not a computer algebra system and does not factorise expressions.
-If you want to present the order in a manner distinct from that presented
-by \texttt{diffcoeff}, use the \emph{order-override option}.
-
-This is a second optional argument immediately following the order
-specification. For our last example, filling the override option with
-\texttt{2m(k+1)} gives the desired result:
-\begin{centred}
-\verb`\[ \diffp[2km,m-1,m+1][2m(k+1)]{F(x,y,z)}{x,y,z} \]` $\Longrightarrow$
-\[ \diffp[2km,m-1,m+1][2m(k+1)]{F(x,y,z)}{x,y,z}. \]
-\end{centred}
-\noindent As another example, left to its own devices, \texttt{diffcoeff}
-produces
-\begin{centred}
-\noindent \verb`\[ \diffp[m/2+n/2,m/2,n/2]F{x,y,z} \]` $\Longrightarrow$
-\[ \diffp[m/2+n/2,m/2,n/2]F{x,y,z}, \]
-\end{centred}
-\noindent whereas we would like the total order to be presented as
-$m+n$. Using the override option,
-\begin{centred}
-\noindent \verb`\[ \diffp[m/2+n/2,m/2,n/2][m+n]F{x,y,z} \]` $\Longrightarrow$
-\[ \diffp[m/2+n/2,m/2,n/2][m+n]F{x,y,z}. \]
-\end{centred}
-The order-override option does exactly that: overrides the presentation
-of the calculated order with the manually given one. In fact the calculation
-algorithm does not get called at all when the override option is used
-so that one can in this way present the total order in whatever manner
-one wishes or, indeed, add essentially arbitrary material as a superscript
-to the $\partial$ symbol in the numerator.
-
-\subsubsection{Comma list of variables of differentiation\protect\label{subsec:Comma-list-of-vars}}
-
-In tensor calculus the differentiations are almost always in terms
-of super- or subscripted coordinates. In many other contexts this
-is the case too -- the reciprocal of the temperature in thermodynamics
-or generalized coordinates in analytical mechanics. This is why a
-comma list is used in \texttt{diffcoeff} for specifying variables
-of differentiation for mixed partial derivatives. Although it would
-be nice to write the minimal \texttt{\{xy\}} rather than \texttt{\{x,y}\}
-when two variables $x$ and $y$ are involved, the extra writing is
-trivial and the comma list allows a simpler handling of multi-character
-variables. For instance in tensor calculus we get expressions like
-\begin{centred}
-\verb`\[ \diffp{A_i}{ x^j,x^k } \]` $\Longrightarrow$ \[ \diffp{A_i}{ x^j,x^k }. \]
-\end{centred}
-\noindent It is easier to write \texttt{\{x\textasciicircum j,x\textasciicircum k\}}
-here than, say, \texttt{\{\{x\textasciicircum j\}\{x\textasciicircum k\}\}}
-to distinguish the variables. It does mean that should the variable
-of differentiation include a comma then that comma needs to be enclosed
-in braces. There are plenty of instances of this out in the world
-(see, e.g., the last equation of (\ref{eq:eg1})) but it is overall
-a rare occurrence.
-
-\paragraph*{Minutiae of spacing (yet again):}
-
-In §\ref{subsec:Minutiae-of-spacing} above, I discussed a slight
-reduction in the space inserted between the terms occurring in the
-denominator of a mixed partial derivative when a higher order differentiation
-is involved. The superscript appearing on a differentiation variable
-in that case \emph{of itself} introduced a spacing adjustment between
-the terms. But the present discussion involves only first order differentiations
-and no such reduction is automatically made by \texttt{diffcoeff}.
-However it is still possible to explicitly make such an adjustment
-with the \texttt{\textbackslash negmu} command introduced earlier
-(§\ref{subsec:Spacing-commands}), which inserts \texttt{-1 mu} of
-spacing. For our example, in
-\begin{centred}
-\verb`\[ \diffp{A_i}{ x^j\negmu,x^k } \]` $\Longrightarrow$ \[ \diffp{A_i}{ x^j\negmu,x^k } \]
-\end{centred}
-\noindent the \texttt{\textbackslash negmu} decreases the spacing
-between the terms from the default \verb`2 mu` to \verb`1 mu`.
-
-\subsubsection{Overkill territory}
-
-Two previous examples illustrate limitations of the algorithm that
-calculates the overall order of differentiation: \texttt{2m/2+2n/2}
-is not simplified to \texttt{m+n} and \texttt{2km+2m} is not factorised
-to \texttt{2m(k+1)}. But there is much that the algorithm \emph{can}
-handle -- for instance, the simple use of parentheses:
+Forming the \emph{second} derivative of $\ln\sin x$ will now involve
+forming, among other quantities,
\begin{centred}
-\verb`\[ \diffp[2m-(k+1),2(k+1)-m]{F(x,y,z)}{x,y,z} \]` $\Longrightarrow$
-\[ \diffp[2m-(k+1),2(k+1)-m]{F(x,y,z)}{x,y,z}. \]
+\noindent \verb`\[\diff[2]{\ln\sin x}{\sin x}\]` $\Longrightarrow$
+\[\diff[2]{\ln\sin x}{\sin x}\]
\end{centred}
+\noindent Parentheses have been inserted automatically by \verb`diffcoeff`
+around $\sin x$ in the denominator to avoid any visual hint that
+we are differentiating in the sine of $x^{2}$.
-\paragraph*{Dynamic use of parentheses}
-
-\noindent For parenthetic expressions to be evaluated as in this example
--- the \emph{dynamic} use of parentheses -- the left parenthesis
-must be preceded at most by a sign or a number; the right parenthesis
-must be followed at most by a sign.
-
-If a right parenthesis is followed by a \emph{variable}, say by \texttt{m}
-as in the order spec. \texttt{{[}(2n+1)m,(2n-1)m{]}}, it will throw
-an error and halt compilation. A message will be sent to the terminal
-and the \LaTeX{} log like the following (which assumes the order spec.
-was on line 53 of the document):
-\begin{lyxcode}
-!~Package~diffcoeff~Error:~)~followed~by~m~in~the~
-
-order~specification~{[}(2n+1)m,(2n-1)m{]}~on~line~53.~
-
-Diffcoeff~cannot~calculate~the~overall~order~of~
-
-differentiation~in~this~case.~Use~the~order-override~
-
-option~to~enter~the~overall~order.
-\end{lyxcode}
-This is a limitation on the dynamic use of parentheses -- but they
-\emph{can} be nested.
+\emph{That} is the problem: with a long (multi-character) variable,
+the superscript in a higher order derivative may look as if it applies
+to only part -- the last character -- of a multi-character variable.
+To solve that problem, \verb`diffcoeff` inserts parentheses around
+the variable -- for \emph{higher-order} derivatives, but not for
+first-order derivatives where the problem does not arise. You may
+prefer \verb`diffcoeff` not to parenthesize by default. Changing
+the default setting is easily accomplished; see §\ref{sec:ChangingDefaults}.
-\paragraph*{Static use of parentheses}
+And if you do want parentheses, are they in the right place? Logically,
+no. They should include the $d$: $(d\sin x)^{2}$ -- it is the differential
+$d\sin x$ that is of the second order. But as the examples in the
+Rogues' Gallery show -- see particularly (\ref{eq:eg3}) -- the
+inclination seems to be to do otherwise. This may be because one wants
+in any case to parenthesise the variable to show that the `d' symbol
+attaches to the whole variable and not just its \emph{first} character.
+A second, outer pair of parentheses then seems too fussy and detracts
+from comprehending the symbol `at a glance':
+\[
+\diff.(dv).[2]{f(x)}{(x/k)}.
+\]
+Customary but illogical notations are familiar in mathematics --
+think of the position of the superscripts in an identity like $\sin^{2}\theta+\cos^{2}\theta=1$.
+In any case, the manner of this wrapping in parentheses -- if any
+-- of long variables for \emph{higher order} derivatives is customisable
+(§\ref{sec:ChangingDefaults}).
-If a left parenthesis is preceded by a \emph{variable} (i.e., not
-a sign or a number) this signals to \texttt{diffcoeff} the \emph{static}
-use of parentheses, something like $f(k)$, `function of $k$'.
-No attempt is made to evaluate what is between them and they are treated
-simply as an extension of the variable. For example,
+For first order derivatives parenthesising does not occur automatically.
+If you want the variable of differentiation to be parenthesised, you
+need to do it yourself:
\begin{centred}
-\verb`\[ \diffp[f(k+1)+1,f(k-1)-1]{F(x,y)}{x,y} \]` $\Longrightarrow$
-\[ \diffp[f(k+1)+1,f(k-1)-1]{F(x,y)}{x,y}. \]
+\verb`\[\diff {f(x)}{x/k}, \quad \diff {f(x)}{(x/k)}.\]` $\Longrightarrow$
+\[ \diff {f(x)}{x/k}, \quad\diff {f(x)}{(x/k)}.\]
\end{centred}
-\noindent In the static case you \emph{can} follow the right parenthesis
-by a variable without generating an error.\emph{ }You can nest them,
-and you can include static parentheses within a dynamic pair; for
-example,
+To my eye, in this particular case, the parenthesized version seems
+necessary. The discussion applies equally to ordinary and partial
+derivatives. In thermodynamics and statistical mechanics one may want
+to differentiate in the reciprocal of the temperature, $1/\Theta$
+say:
\begin{centred}
-\noindent \verb`\[ \diffp[2(3+f(k))+1,1-3(f(k)-2)]{F(x,y)}{x,y} \]`
-$\Longrightarrow$ \[ \diffp[2(3+f(k))+1,1-3(f(k)-2)]{F(x,y)}{x,y}. \]
+\verb`\[ \diffp[2]q{\frac 1\Theta} \]` $\Longrightarrow$ \[ \diffp[2]q{\frac 1\Theta}.\]
\end{centred}
-\noindent However, the reverse is not possible: you can't have dynamic
-parentheses within a static pair.
-
-\paragraph*{Other refinements}
-
-Exponents and subscripts on a \emph{variable} are fine in an order
-specification, so long as the exponent or subscript consists of a
-\emph{single} token:
+\noindent As noted, when differentiating to first order, parenthesising
+is up to the user:
\begin{centred}
-\verb`\[ \diffp[m^2+2(k-1),m^2-(k+1)]F{x,y,z,w} \]` $\Longrightarrow$
-\[ \diffp[m^2+2(k-1),m^2-(k+1)]F{x,y,z,w}. \]
+\verb`\[ \diffp q{(\frac 1\Theta),V} \]` $\Longrightarrow$ \[ \diffp q{(\frac 1\Theta),V}. \]
\end{centred}
-\noindent Braced arguments containing \emph{multiple} tokens as exponents
-or subscripts to variables will generally not halt compilation but
-will usually give nonsensical results, as will \emph{signs} treated
-as superscripts or subscripts. Neither circumstance is checked for
-by \texttt{diffcoeff}.
-\paragraph*{Override}
+\chapter{Templates, defaults \& variants}
+
+\label{chap:Templates-defaults-variants} \verb`diffcoeff` is built
+on the facilities offered by the \verb`xtemplate` package (included
+in the \LaTeX 3 bundle {\ttfamily\verb`l3packages`}). The
+stuff of \verb`xtemplate` is \emph{templates}, their definition,
+their manipulation. For \verb`diffcoeff` a template is a list of
+parameter values determining how a derivative looks in the pdf. The
+parameters may be broad-brush settings like whether the derivative
+is built from \verb`\frac` or the slash \verb`/` or in compact form,
+or whether the operator symbol is \verb`d` or \verb`\partial` (or
+\verb`\nabla` or \verb`\delta` or \ldots ), or the parameters may
+be finer-grained, determining minutiae of spacing, easily missed at
+a casual glance but giving some cumulative overall effect.\emph{ }Access
+to the parameters is gained through the command \verb`\difdef`\footnote{In version 5; it has \emph{three} arguments and replaces the two-argument
+command \texttt{\textbackslash diffdef} in version 4 of \texttt{diffcoeff}.}, one argument of which is a \emph{key=value} list\emph{ }of parameter
+values. Each such list is given a name (the second argument of \verb`\difdef`)
+and is `turned into a derivative' by placing the name between dots
+as the first argument of the appropriate \verb`\difx`, \verb`\difxp`
+commands\footnote{And -- see Chapter~\ref{chap:Differentials-and-jacobians} -- of
+the differential and jacobian commands, \texttt{\textbackslash dl}
+and \texttt{\textbackslash jacob}.}. All this is discussed in §\ref{sec:Variant-forms} below.
+
+\section{Template structure}
+
+To write a derivative one doesn't want to have to type a long list
+of \emph{key=value} statements each time. The \emph{default} values
+given to keys is crucial. Only some of the defaults appropriate for,
+say, an upright fraction ordinary derivative are going to be relevant
+for a slash-fraction partial derivative let alone a compact form partial
+derivative. This suggests creating a primary template as a `super-repository'
+of default values and from this creating secondary or child templates
+in which (only) \emph{some }of the defaults are changed -- and, if
+necessary, creating from these child templates children of their own
+(grandchild templates) in which again some further defaults are adjusted.
+
+In \verb`diffcoeff`, the template that is the `primogenitor' of
+the lines of default inheritance is named \verb`DIF`. It is the repository
+of all possible keys used in all possible forms of derivative (at
+least in \verb`diffcoeff`!) and so has keys appropriate to upright-fraction,
+slash-fraction and compact forms of derivative; it has keys appropriate
+to multi-variable partial derivatives and single-variable ordinary
+derivatives, but it is not actually used to form derivatives. That
+is the role of its child templates \verb`DIFF`, \verb`DIFS` and
+\verb`DIFC` corresponding to derivatives of upright-fraction, slash-fraction
+and compact forms. These child templates inherit the defaults of \verb`DIF`
+save for some settings explicitly changed in the child template relevant
+to the specific forms of fraction specified by each.
+
+Apart from the operator symbol, most of the settings in the child
+templates \verb`DIFF`, \verb`DIFS` and \verb`DIFC` are also appropriate
+for partial derivatives. From a code design point of view, there is
+a certain neatness at not multiplying the number of templates in
+play, but actual use -- for instance, forming the `Rogues' gallery'
+of §\ref{sec:Rogues'-gallery} -- suggests the further step of creating
+additional templates specifically for \emph{partial} derivatives\emph{
+}in the three fraction forms. Apart from the operator symbol, the
+templates \verb`DIFFP`, \verb`DIFSP` and \verb`DIFCP` inherit nearly
+all the defaults of their parents \verb`DIFF`, \verb`DIFS` and \verb`DIFC`
+respectively.
+
+Again, actual use suggests two further templates, both direct children
+of \verb`DIF`, for the creation of jacobians, template \verb`DIFJ`,
+and differentials, template \verb`DIFL`, with default values appropriate
+to each. In all \verb`diffcoeff` uses nine templates, the arrows
+in Table~\ref{tab:DIF-defaults} indicating lines of inheritance
+of default values. Only the child and grandchild templates of \verb`DIF`
+are used for actual construction of derivatives (and jacobians and
+differentials). \verb`DIF` itself sits `above the fray'.
-There are limitations on what order specifications the \texttt{diffcoeff}
-package can `digest'; equally, it can digest a wide variety of such
-constructs, but it is \emph{not} a computer algebra system. In all
-those cases where it fails to calculate or present a correct total
-order, the order-override option is available. Yes, this is not as
-convenient as having the overall order calculated automatically but
-(let's remind ourselves) we are deep in overkill territory. Mixed
-partial derivatives are used far less often than the pure derivatives,
-and when they \emph{are} used it is nearly always to orders 1 or 2
-in the variables. Mixed partial derivatives to exotic orders of differentiation
-are rarely used, so that the limitations of the calculational algorithm
-are of little real moment -- and the override option is always available
-for such cases.
+\begin{table}
+\centering{}\caption{\protect\label{tab:Template-inheritance}Template inheritance}
+\begin{tabular}{ccccc}
+\multicolumn{5}{c}{\texttt{DIF}}\tabularnewline
+$\hphantom{\mathtt{DIF}}$ $\swarrow$ & $\,\,\,\sswarrow$ & $\downarrow$ & $\ssearrow\,\,\,$ & $\searrow$ $\hphantom{\mathtt{IFL}}$\tabularnewline
+\texttt{DIFC} & \texttt{DIFS} & \texttt{DIFF} & \texttt{DIFJ} & \texttt{DIFL}\tabularnewline
+$\downarrow$ & $\downarrow$ & $\downarrow$ & & \tabularnewline
+\texttt{DIFCP} & \texttt{DIFSP} & \texttt{DIFFP} & & \tabularnewline
+\end{tabular}
+\end{table}
-\subsection{Parentheses around multi-character variables}
-In thermodynamics and statistical mechanics one may want to differentiate
-in the reciprocal of the temperature, $1/T$ (or $1/\Theta$):
-\begin{centred}
-\verb`\[ \diffp[2]q{\frac 1\Theta} \]` $\Longrightarrow$ \[ \diffp[2]q{\frac 1\Theta}. \]
-\end{centred}
-\noindent In this case and for other \emph{higher order} derivatives
-of multi-character variables of differentiation, the parentheses are
-inserted automatically by \texttt{diffcoeff}. Precisely where parentheses
-should be placed is moot. The placement in this example is not strictly
-logical, although it feels intuitive, but the placement can be customised
-(§\ref{sec:Changing-defaults}).
+\section{Default values for template \texttt{DIF}}
-Parentheses are automatically inserted like this only for higher order
-derivatives. When the differentiation is to first order, parenthesising
-is up to the user:
-\begin{centred}
-\verb`\[ \diffp q{(\frac 1\Theta),V} \]` $\Longrightarrow$ \[ \diffp q{(\frac 1\Theta),V}. \]
-\end{centred}
+\label{sec:Default-values-DIF}Table~\ref{tab:DIF-defaults} lists
+the keys available for forming derivatives and the default values
+assigned in the `grandparent' template, the primogenitor, \verb`DIF`.
+Different forms of derivative demand different defaults for some keys.
+Where a key is relevant for more than one style of derivative the
+default value is chosen according to the following precedence scheme:
+\begin{enumerate}
+\item \emph{ordinary upright}-fraction derivatives in \emph{display}-style
+environments
+\item \emph{ordinary slash}-fraction derivatives in \emph{text}-style environments
+\item \emph{ordinary compact}-form derivatives in \emph{text}-style environments
+\end{enumerate}
+\noindent %
+\noindent\begin{minipage}[t]{1\columnwidth}%
+\begin{shaded}%
+\noindent Users of version 4 of \texttt{diffcoeff} will notice similarities
+with and differences from the earlier version. Some key names remain
+(\verb`op-symbol`), some names have changed (\verb`multi-term-sep`
+for \verb`denom-term-sep`), keys beginning with an asterisk, \verb`*`,
+lack a following hyphen (\verb`*derivand-sep` rather than \verb`*-derivand-sep`),
+some keys have vanished (the \verb`/` keys), and there are some new
+keys (\verb`lvwrap-Ldelim`, \verb`lvwrap-Rdelim`). The redesign
+of the user interface -- \verb`\difs`, \verb`\difsp` for the \verb`/`
+switch, the new compact form commands \verb`\difc`, \verb`\difcp`,
+and bringing the jacobian and differential within the \verb`DIF`
+template structure -- meant revisiting and rethinking the list of
+keys. In the end it seemed simpler (less confusing) to treat this
+as a completely new list rather than an amendment of the earlier one.\end{shaded}%
+\end{minipage}
+
+\medskip{}
+The first column in table~\ref{tab:DIF-defaults} lists key names,
+the second column default values, and the third column to which form
+or forms of derivative the key is \emph{relevant --} meaning that
+assigning a different value to the key can change the appearance of
+the corresponding derivative in some way. The identifiers have these
+meanings:
+\begin{description}
+\item [{f,~fp}] upright fraction ordinary derivative, partial derivative;
+\item [{s,~sp}] slash fraction ordinary derivative, partial derivative;
+\item [{c,~cp}] compact ordinary derivative, partial derivative;
+\item [{j}] jacobian;
+\item [{l}] differential.
+\end{description}
+In Table~\ref{tab:DIF-defaults} and following tables, all values
+specifying a space require the unit (\verb`mu`) to be included; a
+number alone does not suffice. (A `mu' is a `math unit', 1/18
+of a quad. A thin space \texttt{\textbackslash ,} is 3 mu.) `Elastic'
+spaces with stretch and shrink can be compacted, like \verb`3muplus1muminus2mu`
+for \verb`3 mu plus 1 mu minus 2 mu`.
+
+Available keys and their defaults are the following (if you are dissatisfied
+with some choices, they can be changed; see the discussion at §\ref{sec:ChangingDefaults}):
-\subsection{Jacobians}
-
-\texttt{diffcoeff} provides a command \texttt{\textbackslash jacob}
-for constructing Jacobians. For example
-\begin{centred}
-\verb`\[ \jacob{u,v,w}{x,y,z} \]` $\Longrightarrow$ \[ \jacob{u,v,w}{x,y,z}. \]
-\end{centred}
-The comma lists can contain any number of variables. \texttt{\textbackslash jacob}
-does \emph{not} check that the two arguments contain the same number
-of variables, so it is perfectly possible to form an object like \texttt{\textbackslash jacob\{u,v,w\}\{x,y\}}
-which as far as I know has no meaning.
-
-\section{Changing defaults; variant forms\protect\label{sec:Changing-defaults}}
-
-To write the range of different examples displayed in the Rogues'
-Gallery (§\ref{sec:Rogues'-gallery}) I have had to make extensive
-use of forms of derivative other than the default. \texttt{diffcoeff}
-is built on the facilities offered by the \texttt{xtemplate} package
-(included in the \LaTeX 3 bundle \texttt{l3packages)}. These facilities
-are harnessed by means of a command, \texttt{\textbackslash diffdef},
-and a further optional argument of the \texttt{\textbackslash diff}
-command.\texttt{ }
-
-\subsection{Default values: ordinary derivatives}
-
-Table~\ref{tab:Ordinary-derivatives} lists the keys available for
-forming derivatives and the default values\footnote{Note that a mu is a `math unit', 1/18 of a quad.}
-they have been assigned. These default values have been chosen to
-coincide with those relevant for \emph{ordinary} derivatives -- apart
-from the keys \texttt{denom-term-sep}, \texttt{/-denom-term-sep},
-\texttt{term-sep-adjust} and \texttt{/-term-sep-adjust} which are
-ignored for ordinary derivatives but apply to the case of mixed partial
-derivatives when there is more than one variable of differentiation.
-Keys with an opening slash, /, apply only to the slash form of the
-derivative; keys with an opening asterisk, {*}, apply only when the
-differentiand is appended.
-
-Note that these settings are, in general, font dependent. The values
-given are (in the author's opinion) appropriate for the default \LaTeX{}
-math fonts. There are also likely to be variations required for whether
-a derivative is used in a display-style or text-style or script-style
-expression. That matter is discussed below in §\ref{subsec:Text-and-script-style}.
-All values specifying a space require the unit (\texttt{mu}) to be
-given; a number alone does not suffice.
-\noindent \begin{center}
\begin{table}
-\centering{}\caption{{\small Defaults (ordinary derivatives})\protect\label{tab:Ordinary-derivatives}}
-\begin{tabular}{lr}
+\centering{}\caption{{\small\texttt{DIF}} {\small defaults}\protect\label{tab:DIF-defaults}}
+\begin{center}
+\begin{tabular}{lrl}
\toprule
-{\small key} & {\small default}\tabularnewline
-\midrule
-{\small op-symbol} & {\small\texttt{d}}\tabularnewline
-{\small op-symbol-alt} & {\small\texttt{op-symbol}}\tabularnewline
-{\small op-order-sep} & {\small\texttt{1 mu}}\tabularnewline
-{\small derivand-sep} & {\small\texttt{3 mu plus 1 mu minus 2 mu}}\tabularnewline
-{\small /-derivand-sep} & {\small\texttt{derivand-sep}}\tabularnewline
-{\small{*}-derivand-sep} & {\small\texttt{derivand-sep}}\tabularnewline
-{\small{*}/-derivand-sep} & {\small\texttt{/-derivand-sep}}\tabularnewline
-{\small denom-term-sep} & {\small\texttt{2 mu}}\tabularnewline
-{\small /-denom-term-sep} & {\small\texttt{1 mu}}\tabularnewline
-{\small term-sep-adjust} & {\small\texttt{-1 mu}}\tabularnewline
-{\small left-delim} & {\small\texttt{\textbackslash left .}}\tabularnewline
-{\small right-delim} & {\small\texttt{\textbackslash right |}}\tabularnewline
-{\small /-left-delim} & {\small\texttt{(}}\tabularnewline
-{\small /-right-delim} & {\small\texttt{)}}\tabularnewline
-{\small elbowroom} & {\small\texttt{0 mu}}\tabularnewline
-{\small /-elbowroom} & {\small\texttt{0 mu}}\tabularnewline
-{\small subscr-nudge} & {\small\texttt{0 mu}}\tabularnewline
-{\small /-subscr-nudge} & {\small\texttt{0 mu}}\tabularnewline
-{\small long-var-wrap} & {\small\texttt{d(v)}}\tabularnewline
-{\small{*}/-op-wrap} & {\small\texttt{true}}\tabularnewline
-{\small{*}-op-left} & {\small\texttt{false}}\tabularnewline
-{\small{*}-italic-nudge} & {\small\texttt{3 mu}}\tabularnewline
+{\small key} & {\small default} & {\small relevance}\tabularnewline
+\midrule
+{\small style} & {\small\texttt{frac}} & {\small f, fp, s, sp, c, cp, j}\tabularnewline
+slash-tok & {\small\texttt{/}} & {\small\phantom{{\small f, fp,}} s, sp, \phantom{{\small c, cp,}}
+j}\tabularnewline
+slash-sep & {\small\texttt{0 mu}} & {\small\phantom{{\small f, fp,}} s, sp, \phantom{{\small c, cp,}}
+j}\tabularnewline
+{\small derivand-sep} & {\small\texttt{3 mu plus 1 mu minus 2 mu}} & {\small f, fp, s, sp, c, cp}\tabularnewline
+{\small op-symbol} & {\small\texttt{\textbackslash mathrm\{d\}}} & {\small f, fp, s, sp, c, cp, j, l}\tabularnewline
+{\small op-symbol-alt} & {\small\texttt{op-symbol}} & {\small f, fp, s, sp, \phantom{{\small c, cp,}} j}\tabularnewline
+{\small op-order-nudge} & {\small\texttt{0 mu}} & {\small f, fp, s, sp, c, cp}\tabularnewline
+{\small var-sup-nudge} & {\small\texttt{1 mu}} & {\small f, fp, s, sp, \phantom{{\small c, cp,} j,} l}\tabularnewline
+{\small multi-term-sep} & {\small\texttt{2 mu plus 1 mu minus 1 mu}} & {\small f, fp, s, sp, c, cp, \phantom{j,} l}\tabularnewline
+{\small term-sep-adjust} & {\small\texttt{-1 mu}} & {\small f, fp, s, sp, c, cp, \phantom{j,} l}\tabularnewline
+{\small long-var-wrap} & {\small\texttt{d(v)}} & {\small f, fp, s, sp, \phantom{{\small c, cp,} j,} l}\tabularnewline
+{\small lvwrap-Ldelim} & {\small\texttt{\textbackslash mleft (}} & {\small f, fp, s, sp, \phantom{{\small c, cp,}} j, l}\tabularnewline
+{\small lvwrap-Rdelim} & {\small\texttt{\textbackslash mright )}} & {\small f, fp, s, sp, \phantom{{\small c, cp,}} j, l}\tabularnewline
+{\small lvwrap-sup-nudge} & {\small\texttt{-2 mu}} & {\small f, fp, s, sp, \phantom{{\small c, cp, j,}} l}\tabularnewline
+{\small outer-Ldelim} & {\small\texttt{\textbackslash left (}} & {\small f, fp, s, sp, c, cp, j, l}\tabularnewline
+{\small outer-Rdelim} & {\small\texttt{\textbackslash right )}} & {\small f, fp, s, sp, c, cp, j, l}\tabularnewline
+{\small elbowroom} & {\small\texttt{0 mu}} & {\small f, fp, s, sp, c, cp, j, l}\tabularnewline
+{\small sub-nudge} & {\small\texttt{-5 mu}} & {\small f, fp, s, sp, c, cp}\tabularnewline
+{\small op-sub-nudge} & {\small\texttt{0 mu}} & {\small\phantom{{\small f, fp, s, sp,}} c, cp}\tabularnewline
+{\small{*}derivand-sep} & {\small\texttt{derivand-sep}} & {\small f, fp, s, sp, c, cp}\tabularnewline
+{\small{*}op-set-left} & {\small\texttt{false}} & {\small f, fp, \phantom{{\small s, sp, c, cp,}} j}\tabularnewline
+{\small{*}italic-nudge} & {\small\texttt{0 mu}} & {\small f, fp, \phantom{{\small s, sp, c, cp,}} j}\tabularnewline
+{\small{*}inner-wrap} & {\small\texttt{false}} & {\small\phantom{{\small f, fp,}} s, sp}\tabularnewline
+{\small{*}inner-Ldelim} & {\small\texttt{(}} & {\small\phantom{{\small f, fp,}} s, sp}\tabularnewline
+{\small{*}inner-Rdelim} & {\small\texttt{)}} & {\small\phantom{{\small f, fp,}} s, sp}\tabularnewline
+{\small{*}outer-Ldelim} & {\small\texttt{\textbackslash big {[}}} & {\small\phantom{{\small f, fp,}} s, sp}\tabularnewline
+{\small{*}outer-Rdelim} & {\small\texttt{\textbackslash big {]}}} & {\small\phantom{{\small f, fp,}} s, sp}\tabularnewline
+{\small{*}sub-nudge} & {\small\texttt{0 mu}} & {\small\phantom{{\small f, fp,}} s, sp}\tabularnewline
\bottomrule
\end{tabular}
-\end{table}
\par\end{center}
+\end{table}
+
\begin{description}
-\item [{op-symbol}] the operator symbol; for ordinary derivatives, generally
-one of \texttt{d} or \texttt{\textbackslash mathrm\{d\}}, \texttt{D}
-or \texttt{\textbackslash mathrm\{D\}}, \texttt{\textbackslash delta}
-or \texttt{\textbackslash Delta}; for partial derivatives \texttt{\textbackslash partial};
-default = \texttt{d}
+\item [{style}] the fraction form of derivative;
+\begin{itemize}
+\item for upright-fraction derivatives, \verb`\diff`, \verb`\diffp`, a
+choice of \verb`frac`, \verb`tfrac` or \verb`dfrac`:
+\begin{itemize}
+\item \verb`frac` results in a fraction formed from \verb`\frac`, scalable
+\item \verb`tfrac` results in a fraction formed from \verb`\tfrac`, not
+scalable
+\item \verb`dfrac` results in a fraction formed from \verb`\dfrac`, not
+scalable
+\item default in templates \verb`DIFF`, \verb`DIFFP` = \verb`frac`
+\end{itemize}
+\item for slash-fraction derivatives,\verb`\difs`, \verb`\difsp`, a choice
+of \verb`/`, \verb`auto`, \verb`big`, \verb`Big`, \verb`bigg`
+or \verb`Bigg`
+\begin{itemize}
+\item \verb`/` forms the slash fraction with \verb`/`, not scalable
+\item \verb`auto` forms the slash fraction with \verb`\left. \middle/ \right.`,
+scalable
+\item \verb`big`, \verb`Big`, \verb`bigg` and \verb`Bigg` form the slash
+fraction with \verb`\big/`, \verb`\Big/`, \verb`\bigg/` and \verb`\Bigg/`
+respectively, not scalable
+\item default in templates \verb`DIFS`, \verb`DIFSP` = \verb`/`
+\end{itemize}
+\item for compact-form derivatives, \verb`\difc`, \verb`\difcp`, a choice
+of \texttt{\_} or \verb`dl`
+\begin{itemize}
+\item \_ forms derivatives of compact form like $\difc yx$, $\difcp[1,2]{z}{x,y}$
+\item \verb`dl` forms differentials like $\difc.dl.{}x$ and $\difcp.dl.[2]{}{x,y,z}$
+\item default in templates \verb`DIFC`, \verb`DIFCP` = \texttt{\_}
+\end{itemize}
+\item overall default in template \verb`DIF` = \verb`frac`
+\end{itemize}
+\item [{slash-tok}] token or tokens used for the slash fraction; (see §\ref{subsec:Other-notations}
+for a different assignment) default \verb`/`
+\item [{slash-sep}] space inserted on either side of the \textbf{slash-tok};
+ default \verb`0 mu`
+\item [{derivand-sep}] horizontal space added before the differentiand
+if the \verb`spaced` package option is set to \verb`1`, or before
+a multi-tokened differentiand if the \verb`spaced` package option
+is set to \verb`-1`; note that compact-form derivatives \emph{always
+}have this space inserted; default (appropriate for an upright-fraction
+derivative) = \verb`3mu plus 1mu minus 2mu`
+\item [{op-symbol}] the operator symbol; for ordinary derivatives generally
+one of \verb`d` or \verb`\mathrm{d}`, for partial derivatives \verb`\partial`;
+default = \verb`\mathrm{d}`
\item [{op-symbol-alt}] if different from \textbf{op-symbol} then used
-in the denominator while \textbf{op-symbol} is used in the numerator;
-e.g. for $\diff.nabla.{v^{i}}t$, \texttt{op-symbol = \textbackslash nabla}
-and \texttt{op-symbol-alt = d}; otherwise (and usually) defaults to
-\textbf{op-symbol}
-\item [{op-order-sep}] extra horizontal space added between the op-symbol
+in the denominator of a fraction-form derivative while \verb`op-symbol`
+is used in the numerator; e.g. for the acceleration $\diff.n.{v^{i}}t$,
+\verb`op-symbol = \nabla` and \verb`op-symbol-alt = d`; defaults
+to \textbf{op-symbol} default
+\item [{op-order-nudge}] extra horizontal space added between the op-symbol
and the superscripted order of differentiation in higher order derivatives;
-for the math-italic forms compare $d^{2}$ with $d^{\mkern1mu 2}$,
-$\partial^{2}$ with $\partial^{\mkern1mu 2}$ where the first symbol
-in each case has no extra space and the second has an extra 1 mu;
-default = \texttt{1 mu}
-\item [{derivand-sep}] horizontal space added before the differentiand
-(derivand) if the \verb`spaced` package option is used, or by the
-\verb`!` switch if it is not; the default has some stretch and shrink;
-default = \verb`3mu plus 1mu minus 2mu`
-\item [{/-derivand-sep}] for the slash form of derivative, horizontal space
-added before the differentiand (derivand) if the \verb`spaced` package
-option is used, or by the \verb`!` switch if it is not; default =
-\verb`derivand-sep`
-\item [{{*}-derivand-sep}] when the derivand is appended, horizontal space
-added before the differentiand (derivand) if the \verb`spaced` package
-option is used, or by the \verb`!` switch if it is not; default =
-\verb`derivand-sep`
-\item [{{*}/-derivand-sep}] for the slash form of derivative when the derivand
-is appended, horizontal space added before the differentiand (derivand)
-if the \verb`spaced` package option is used, or by the \verb`!`
-switch if it is not; default = \verb`/-derivand-sep`
-\item [{denom-term-sep}] (mixed partial derivatives only) horizontal spacing
-inserted between the differentials in the denominator of a mixed partial
-derivative to avoid a solid cluster like $\partial x\partial y\partial z$;
-with the default 2 mu this is $\dl.p.x\dl.p.2y\dl.p.2z$; default
-= \texttt{2 mu}
-\item [{/-denom-term-sep}] (mixed partial derivatives only) horizontal
-spacing inserted between the differentials in the denominator of a
-slash-form mixed partial derivative; because a slash-form derivative
-is already spread out horizontally, the default spacing is less than
-for the \texttt{\textbackslash frac} form derivative; default = \texttt{1
-mu}
-\item [{term-sep-adjust}] (mixed partial derivatives only) adjustment (i.e.
-reduction) to \textbf{denom-term-sep} or \textbf{/-denom-term-sep}
+for math-italic forms compare $d^{2}$ with $d^{\mkern1mu 2}$, $\partial^{2}$
+with $\partial^{\mkern1mu 2}$ where the first symbol in each case
+has no extra space and the second has an extra \verb`1 mu`; since
+\textbf{op-symbol }defaults to an upright `d', default = \verb`0 mu`
+\item [{var-sup-nudge}] extra horizontal space added between a variable
+in the denominator of a derivative and the superscripted order of
+differentiation in higher order derivatives (cf \textbf{op-order-nudge});
+default = \verb`1 mu`
+\item [{multi-term-sep}] horizontal spacing inserted between the differentials
+in, for example, the denominator of a mixed partial derivative to
+avoid a solid cluster like $\partial x\partial y\partial z$; with
+the default \verb`2 mu` this is spread a little, $\difcp.dl.{}{x,y,z}$;
+default = \verb`2 mu plus 1 mu minus 1 mu`
+\item [{term-sep-adjust}] adjustment (usually a reduction) to \textbf{multi-term-sep}
when differentiation in a variable occurs to an order other than 1;
-if, e.g., $\dl.p.x^{2}\dl.p.1y\dl.p.2z$ is the denominator of a mixed
+if, e.g., $\difcp.dl.[2]{}{x,y,z}$ is the denominator of a mixed
partial derivative in three variables, because of the superscript
the spacing between $\partial x^{2}$ and $\partial y$ is reduced
by\textbf{ term-sep-adjust} from the spacing between $\partial y$
-and $\partial z$; default = \texttt{-1 mu}
-\item [{left-delim}] the left member of a delimiter pair wrapping the derivative,
-the right member of which is subscripted to indicate a point of evaluation
-or variables held constant; default = \texttt{\textbackslash left
-.}
-\item [{right-delim}] the right member of a delimiter pair wrapping the
-derivative and subscripted to indicate a point of evaluation or variables
-held constant; default = \texttt{\textbackslash right |}
-\item [{/-left-delim}] for the slash form of derivative, the left member
-of a delimiter pair wrapping the derivative and subscripted to indicate
-a point of evaluation or variables held constant; default = \texttt{(}
-\item [{/-right-delim}] for the slash form of derivative, the right member
-of a delimiter pair wrapping the derivative, the right member of which
-is subscripted to indicate a point of evaluation or variables held
-constant; default = \texttt{)}
-\item [{elbowroom}] adjustment to the whitespace between the left and right
-delimiters and the enclosed derivative; negative values reduce the
-space; default = \texttt{0 mu}
-\item [{/-elbowroom}] adjustment to the whitespace between the left and
-right delimiters and the enclosed slash-form derivative; default =
-\texttt{0 mu}
-\item [{subscr-nudge}] horizontal adjustment of the subscript's placing
-relative to the \textbf{right-delim}iter, e.g., a negative value compensates
-for the curving inwards of a large right parenthesis; may be font
-dependent; default = \texttt{0 mu}
-\item [{/-subscr-nudge}] for the slash form of derivative, horizontal adjustment
-of the subscript's placing relative to the /-\textbf{right-delim}iter;
-may be font dependent; default = \texttt{0 mu}
+and $\partial z$; default = {\ttfamily\verb`-1 mu`}
\item [{long-var-wrap}] to avoid ambiguity in higher order derivatives
-it may be advisable to wrap multi-token variables of differentiation
-in parentheses; default = \texttt{d(v)}; the choices are
+it may aid clarity to wrap multi-token variables of differentiation
+in parentheses; the choices are
\begin{description}
-\item [{\texttt{dv}}] no wrapping, e.g. $dx_{i}^{2}$ or $d\frac{1}{\Theta}^{2}$,
-$\partial x_{i}^{2}$ or $\partial\frac{1}{\Theta}^{2}$,
-\item [{\texttt{d(v)}}] wrap the variable only, e.g. $d(x_{i})^{2}$ or
-$d(\frac{1}{\Theta})^{2}$, $\partial(x_{i})^{2}$ or $\partial(\frac{1}{\Theta})^{2}$
-\item [{\texttt{(dv)}}] wrap the op-symbol and variable, e.g. $(dx_{i})^{2}$
-or $(d\frac{1}{\Theta})^{2}$, $(\partial x_{i})^{2}$ or $(\partial\frac{1}{\Theta})^{2}$
+\item [{\texttt{dv\phantom{()}}}] no wrapping, e.g. $\mathrm{d}x_{i}^{2}$
+or $\partial\frac{1}{\Theta}^{2}$,
+\item [{\texttt{d(v)}}] wrap the variable only, e.g. $\mathrm{d}(x_{i})^{2}$
+or $\partial(\frac{1}{\Theta})^{2}$,
+\item [{\texttt{(dv)}}] wrap both op-symbol and variable, e.g. $(\mathrm{d}x_{i})^{2}$
+or $(\partial\frac{1}{\Theta})^{2}$;
+\item [{\texttt{\phantom{(dv)}}}] default = \verb`d(v)`
\end{description}
-\item [{{*}/-op-wrap}] a choice of \texttt{true} or \texttt{false} for
-slash forms of the derivative when the differentiand is appended,
-dictating whether the derivative is wrapped in parentheses, as here
-$\diffp*{F(x,y)}/x$, or not; default = \texttt{true}
-\item [{{*}-op-left}] a choice of \texttt{true} or \texttt{false} indicating
-whether the op-symbol is left-aligned or not when the differentiand
-is appended; generally it is centred; does not apply to slash forms
-of the derivative; default = \texttt{false}
-\item [{{*}-italic-nudge}] if \textbf{{*}-op-left} is \texttt{true}, makes
+\item [{lvwrap-Ldelim}] left delimiter when wrapping a long variable in
+a higher order derivative; also applies to the left delimiter used
+in a jacobian; default = \verb`\mleft (`
+\item [{lvwrap-Rdelim}] right delimiter when wrapping a long variable in
+a higher order derivative; also applies to the right delimiter used
+in a jacobian; default = \verb`\mright )`
+\item [{lvwrap-sup-nudge}] horizontal adjustment to the superscript position
+when a multi-token variable is wrapped in (e.g.) parentheses and its
+order of differentiation is not \verb`1`; default = \verb`-2 mu`
+\item [{outer-Ldelim}] the left member of a delimiter pair wrapping the
+derivative, the right member of which is subscripted to indicate a
+point of evaluation or variables held constant; ISO recommends parentheses
+for this purpose, hence default = {\ttfamily\verb`\left (`}
+\item [{outer-Rdelim}] the right member of a delimiter pair wrapping the
+derivative and subscripted to indicate a point of evaluation or variables
+held constant; ISO recommends parentheses for this purpose, hence
+default = {\ttfamily\verb`\right )`}
+\item [{elbowroom}] adjustment to the whitespace between \textbf{outer-Ldelim},
+\textbf{outer-Rdelim }and the enclosed derivative; negative values
+reduce the space; default = {\ttfamily\verb`0 mu`}
+\item [{sub-nudge}] horizontal adjustment of the subscript's placing relative
+to the \textbf{outer-Rdelim}iter for a point of evaluation or variable
+held constant; a negative value compensates for the curving inwards
+of a large right parenthesis; default = {\ttfamily\verb`-5 mu`}
+\item [{op-sub-nudge}] horizontal adjustment of the position of the subscript
+in derivatives of compact form relative to the operator; since \verb`\mathrm{d}`
+is the default operator, default = \verb`0 mu`
+\item [{{*}derivand-sep}] when the derivand is appended, horizontal space
+added before the differentiand (derivand) depending on the setting
+of the \verb`spaced` package option; default = \textbf{derivand-sep}
+default
+\item [{{*}op-set-left}] a choice of {\ttfamily\verb`true`}
+or {\ttfamily\verb`false`} indicating whether the op-symbol
+is left-aligned or not when the differentiand is appended; generally
+it is centred; applies only to upright-fraction forms of the derivative;
+default = {\ttfamily\verb`false`}
+\item [{{*}italic-nudge}] if \textbf{{*}op-set-left} is \verb`true`, makes
an italic adjustment in the numerator, so that the op-symbols in numerator
-and denominator align in the same slanting column; for an upright
-\texttt{d} this would be set to \texttt{0 mu}; default = \texttt{3
-mu}
+and denominator align in the same slanting column; for \verb`d` or
+\verb`\partial` an appropriate value might be \verb`3 mu`; because
+of the default \verb`\mathrm{d}`, default = \verb`0 mu`
+\item [{{*}inner-wrap}] when the differentiand is appended, a choice of
+\verb`true` or \verb`false` dictating whether the differential operator
+is wrapped in parentheses, as here $\difsp*{F(x,y)}x$, or not; for
+a slash-fraction derivative \verb`true` is an appropriate default,
+but the overall default, appropriate for an upright-fraction derivative,
+= \verb`false`
+\item [{{*}inner-Ldelim}] if \textbf{{*}inner-wrap} is \verb`true`, the\textbf{
+}left member of a delimiter pair around the differential operator;
+default = \verb`(`
+\item [{{*}inner-Rdelim}] if \textbf{{*}inner-wrap} is \verb`true`, the\textbf{
+}right member of a delimiter pair around the differential operator
+; default = \verb`)`
+\item [{{*}outer-Ldelim}] if \textbf{{*}inner-wrap} is \verb`true`, the
+left member of a delimiter pair around both the differential operator
+and appended differentiand, the right member of which may be subscripted
+to indicate a point of evaluation or variables held constant; to avoid
+too many parentheses, given the default values of {*}\textbf{inner-Ldelim},
+{*}\textbf{inner-Rdelim}, default = \verb`\bigl [`
+\item [{{*}outer-Rdelim}] if \textbf{{*}inner-wrap} is \verb`true`, the
+right member of a delimiter pair around the differential operator
+and appended differentiand; may be subscripted to indicate a point
+of evaluation or variables held constant; to avoid too many parentheses,
+given the default values of \textbf{{*}inner-Ldelim}, \textbf{{*}inner-Rdelim},
+default = \verb`\bigr ]`
+\item [{{*}sub-nudge}] if \textbf{{*}inner-wrap} is \verb`true`, horizontal
+adjustment of the subscript's placing relative to the \textbf{{*}outer-Rdelim}iter
+for a point of evaluation or variable held constant; a negative value
+compensates for the curving inwards of a large right parenthesis;
+since the default \textbf{{*}outer-Rdelim} is a square bracket,\textbf{
+}default = \verb`0 mu`
\end{description}
-\subsection{ISO defaults}
-
-\label{subsec:ISO-defaults}You may not like the default settings
-that come with \texttt{diffcoeff}. The package does not follow ISO
-80000-2 -- it does not use upright `d's nor does it wrap an ordinary
-differential coefficient in subscripted parentheses to indicate a
-point of evaluation. Both `defects' can be remedied by calling the
-package with the option \texttt{ISO}:\footnote{One can also use \texttt{ISO=true} to turn the option on and \texttt{ISO=false
-}to turn the option off. }
-\begin{lyxcode}
-\textbackslash usepackage{[}ISO{]}\{diffcoeff\}
-\end{lyxcode}
-\begin{wraptable}[10]{o}{0.4\columnwidth}%
-\centering{}\vspace{-4ex}
- \caption{{\small ISO default changes}\protect\label{tab:ISO-setting-changes}}
-\abovetopsep=.5ex %
-\begin{tabular}{lr}
-\toprule
-{\small key} & {\small default}\tabularnewline
-\midrule
-{\small op-symbol} & {\small\texttt{\textbackslash mathrm\{d\}}}\tabularnewline
-{\small op-order-sep} & {\small\texttt{0 mu}}\tabularnewline
-{\small left-delim} & {\small\texttt{\textbackslash left (}}\tabularnewline
-{\small right-delim} & {\small\texttt{\textbackslash right )}}\tabularnewline
-{\small subscr-nudge} & {\small\texttt{-6 mu}}\tabularnewline
-\bottomrule
-\end{tabular}\end{wraptable}%
-
-The uppercase is essential -- an option \texttt{iso} is not recognised.
-The \texttt{ISO} option results in changes to the default settings
-of Table~\ref{tab:Ordinary-derivatives} as listed in Table~\ref{tab:ISO-setting-changes}.
-Any settings not mentioned in Table~\ref{tab:ISO-setting-changes}
-retain the values presented in Table~\ref{tab:Ordinary-derivatives}.
-Note that the subscript nudge figure specified here is \emph{not}
-part of the standard, which makes no recommendation about the subscript's
-positioning. But: the \texttt{-6 mu} figure with a default or latin
-modern font gives a better representation of what is displayed in
-the standard than a zero figure.
-
-Because the `d' is upright with the \texttt{ISO} option, no extra
-space is required between the symbol and the superscript in a higher
-order derivative. Hence the zero value for the \texttt{op-order-sep}.
-ISO recommends subscripted parentheses to indicate a point of evaluation.
-Hence the other entries in the table. Because a large right parenthesis
-(penultimate setting) bends inwards, to the left, a negative value
-for the last entry ensures the subscript does not become detached
-from the derivative, looking lost in a sea of whitespace.
-
-Note that the \texttt{ISO} option will also produce upright `D's in
-derivatives formed from `D'; see §\ref{subsec:D-delta-Delta} below.
-
-\subsection{Partial derivatives}
-
-\begin{wraptable}{o}{0.4\columnwidth}%
-\centering{}\vspace{-4ex}
- \caption{{\small Default changes for partial derivatives}\protect\label{tab:Partial-deriv-defaults}}
-\abovetopsep=.5ex %
-\begin{tabular}{lr}
-\toprule
-{\small key} & {\small default}\tabularnewline
-\midrule
-{\small op-symbol } & {\small\texttt{\textbackslash partial}}\tabularnewline
-{\small left-delim} & {\small\texttt{\textbackslash left (}}\tabularnewline
-{\small right-delim} & {\small\texttt{\textbackslash right )}}\tabularnewline
-{\small subscr-nudge } & {\small\texttt{-6 mu}}\tabularnewline
-\bottomrule
-\end{tabular}\end{wraptable}%
-
-The default values given in Table~\ref{tab:Ordinary-derivatives},
-when they are relevant, apply to \emph{ordinary} derivatives. For
-partial derivatives, the defaults are those of Table~\ref{tab:Partial-deriv-defaults}.
-All other keys take the default values listed in Table~\ref{tab:Ordinary-derivatives}.
-The last three entries here are not an attempt at ISO compatibility
-but reflect the use of subscripted parentheses with partial derivatives
-to indicate variables held constant, for instance in the Maxwell relations
-of thermodynamics, one of which is
-\[
-\diffp SV[T]=\diffp PT[V].
-\]
-
-
-\subsection{Setting your own defaults: \texttt{\textbackslash diffdef\protect\label{subsec:diffdef}}}
-
-Versions 2 and later of the \texttt{diffcoeff} package provide a command,
-\texttt{\textbackslash diffdef}, that enables users to set their
-own defaults.\texttt{ }For example, if you wish to use upright `d's
-but not follow the ISO's use of subscripted parentheses to indicate
-a point of evaluation, enter in the preamble of your document the
-command
-\begin{lyxcode}
-\textbackslash diffdef~\{\}~~~~
-
-~~\{~~~~~~
-
-~~~~op-symbol~~~~=~\textbackslash mathrm\{d\},~~~~
+\subsection{Ordinary upright-fraction derivatives; template \texttt{DIFF}}
-~~~~op-order-sep~=~0~mu
+The defaults assigned in template \verb`DIF` are inherited by template
+\verb`DIFF` without change. Template \verb`DIFF` is therefore strictly
+unnecessary but, with templates \verb`DIFS` and \verb`DIFC` in mind,
+was created for the sake of a consistent naming scheme.
-~~\}
-\end{lyxcode}
-\noindent Since a list of settings, like this one, is a comma-\emph{separated}
-list, no comma is required for the last entry. That entry is a consequence
-of the first: upright symbols do not require any extra separation
-between the `d' and the superscript in a higher order derivative.
+The \verb`\diff` command uses the values in the \verb`DIFF` template
+to form an upright-fraction derivative. Only keys with an `f' in
+the third column of Table~\ref{tab:DIF-defaults} are used in this
+process. Keys without an `f' play no part in the process and their
+default values are ignored. See §\ref{subsec:DIFF-(upright-fraction-derivative)}
+for the complete list of \emph{relevant} \verb`DIFF` defaults.
-The other point to note is the empty pair of braces after the \texttt{\textbackslash diffdef}
-command. \emph{They matter}. Their emptiness is what determines that
-it is the \emph{default} values that are changed. If they contain
-some content, then that content provides a \emph{name} for the particular
-set of values in the following list. The \texttt{diffcoeff} package
-exploits this facility to cope with the wide variety of forms displayed
-in the Rogues' Gallery of §\ref{sec:Rogues'-gallery}.
-
-\subsubsection{Space before the differentiand}
+\begin{table}
+\caption{Defaults differing from the parent template}
-\label{subsec:A-final-flourish}\begin{wraptable}{o}{0.6\columnwidth}%
\begin{centering}
-\caption{Keys for spacing the derivand}
-\medskip{}
+\subfloat[\texttt{DIFS}\label{tab:DIFS-defaults}]{\centering{}%
\begin{tabular}{lr}
\toprule
{\small key} & {\small default}\tabularnewline
\midrule
-{\small derivand-sep} & {\small\texttt{3mu plus 1mu minus 2mu}}\tabularnewline
-{\small{*}-derivand-sep} & {\small\texttt{derivand-sep}}\tabularnewline
-{\small /-derivand-sep} & {\small\texttt{derivand-sep}}\tabularnewline
-{\small{*}/-derivand-sep} & {\small\texttt{ /-derivand-sep}}\tabularnewline
+{\small style} & {\small\texttt{/}}\tabularnewline
+{\small derivand-sep} & {\small\texttt{2muplus1muminus2mu}}\tabularnewline
+{\small outer-Ldelim} & {\small\texttt{(}}\tabularnewline
+{\small outer-Rdelim} & {\small\texttt{)}}\tabularnewline
+{\small sub-nudge} & {\small\texttt{0 mu}}\tabularnewline
+{\small{*}inner-wrap} & {\small\texttt{true}}\tabularnewline
\bottomrule
-\end{tabular}
+\end{tabular}}\hfil\subfloat[\texttt{DIFC}\label{tab:DIFC-defaults}]{\centering{}%
+\begin{tabular}{lr}
+\toprule
+{\small key} & {\small default}\tabularnewline
+\midrule
+{\small style} & {\small\texttt{\_}}\tabularnewline
+{\small derivand-sep} & {\small\texttt{1muplus1muminus1mu}}\tabularnewline
+{\small multi-term-sep} & {\small\texttt{1 mu}}\tabularnewline
+{\small term-sep-adjust} & {\small\texttt{0 mu}}\tabularnewline
+{\small outer-Ldelim} & {\small\texttt{\textbackslash bigl (}}\tabularnewline
+{\small outer-Rdelim} & {\small\texttt{\textbackslash bigr )}}\tabularnewline
+sub-nudge & {\small\texttt{-2 mu}}\tabularnewline
+\bottomrule
+\end{tabular}}
\par\end{centering}
-\end{wraptable}%
-The insertion of a small space before the differentiand is effected
-by the \verb`!` key inserted immediately before the differentiand
-argument in the \verb`\diff` command. You may wish to make the insertion
-of this space the \emph{default} behaviour. This is done by using
-the \verb`spaced` package option (which makes the \verb`!` switch
-now reverse this new default and put \emph{no} extra space before
-the derivand). The amount of space inserted is, by default, \verb`3mu plus 1mu minus 2mu`,
-meaning the space is generally $3$mu but can stretch to $4$mu or
-shrink to $1$mu as \TeX{} strives to fit content in a line or on the
-page.
-
-Perhaps this doesn't suit. You may want a fixed space here, with no
-stretch or shrink. The key to change is \verb`derivand-sep`. By default,
-this setting applies not only to the fraction form of derivative,
-but also to the slash form and to when the derivand is appended.
-
-If you feel a little less space should be used for slash derivatives,
-then the key to change is \verb`/-deriv-sep`. This changed value
-will also be used for an appended derivand in a slash derivative.
-
-Thus to meet both wishes you might put in the preamble of your document
-something like
-\begin{lyxcode}
-\textbackslash diffdef~\{\}~~~~
-
-~~\{~~~~~~
-
-~~~~derivand-sep~~~=~3~mu,~~~~
-
-~~~~/-derivand-sep~=~2~mu
-
-~~\}
-\end{lyxcode}
-This will insert a fixed space of $3$mu before the differentiand
-in both the numerator and when appended in the fraction form of derivative,
-and a fixed space of $2$mu in the slash form of derivative, both
-in the numerator and when appended.
-
-If you want a different spacing when the derivand is appended, the
-keys to change are \verb`*-derivand-sep` and \verb`*/-derivand-sep`.
-
-\paragraph{Selective spacing}
-
-I have treated the \verb`spaced` package option thus far as if it
-were an \verb`ON/OFF` switch and, indeed, the presence of the package
-option \verb`spaced` behaves as \verb`ON` and its absence as \verb`OFF`.
-Internally, however, \verb`spaced` is equivalent to \verb`spaced=1`
-and its absence to \verb`spaced=0`. Entering \verb`spaced=n` in
-the package option where \verb`n` is a positive integer is equivalent
-to entering \verb`spaced=1` (and hence to simply entering \verb`spaced`),
-but if \verb`n` is a negative integer, a new effect is produced.
-
-Entering \verb`spaced=-1` (or any negative integer) will insert a
-space (by default \verb`3mu plus 1mu minus 2mu`) before the differentiand
-provided the differentiand\emph{ is longer than a single token} but
-will insert no space before single-token differentiands. The switch
-\verb`!` reverses this behaviour.
-
-\subsection{Variant forms}
-
-For this package I needed to have a number of variant forms available
-to illustrate the wide variety of ways in which derivatives are displayed.
-The \texttt{\textbackslash diffdef} command in which the first argument
-is \emph{filled} provides one half of the means of doing this. I've
-given the single-letter name \texttt{p} to the following settings:
-\begin{lyxcode}
-\textbackslash diffdef~\{~p~\}
-
-~~\{
-
-~~~~op-symbol~~~~=~\textbackslash partial~,
-
-~~~~left-delim~~~=~\textbackslash left~(~~,
-
-~~~~right-delim~~=~\textbackslash right~)~,
-
-~~~~subscr-nudge~=~-6~mu
-
-~~\}
-\end{lyxcode}
-The second half of providing variant forms is to insert this name,
-\texttt{p}, between dots (periods, full stops) as the \emph{first}
-argument of the \texttt{\textbackslash diff} command. Thus, repeating
-an example at the end of §\ref{subsec:Partial-appending},
+\centering{}\subfloat[\texttt{DIFFP}\label{tab:DIFFP-defaults}]{\centering{}%
+\begin{tabular}{lr}
+\toprule
+{\small key} & {\small default}\tabularnewline
+\midrule
+{\small op-symbol} & {\small\texttt{\textbackslash partial}}\tabularnewline
+{\small op-order-nudge} & {\small\texttt{1 mu}}\tabularnewline
+{\small{*}italic-nudge} & {\small\texttt{3 mu}}\tabularnewline
+\bottomrule
+\end{tabular}}\hfil\subfloat[\texttt{DIFSP, DIFCP}\label{tab:DIFSP-DIFCP-defaults}]{\centering{}%
+\begin{tabular}{lr}
+\toprule
+{\small key} & {\small default}\tabularnewline
+\midrule
+{\small op-symbol} & {\small\texttt{\textbackslash partial}}\tabularnewline
+{\small op-order-nudge} & {\small\texttt{1 mu}}\tabularnewline
+\bottomrule
+\end{tabular}}
+\end{table}
+
+
+\subsection{Ordinary slash-fraction derivatives; template \texttt{DIFS}}
+
+When you use the command \verb`\difs` to form a slash-fraction derivative
+it is the keys in template \verb`DIF` with an `s' in the third
+column of Table~\ref{tab:DIF-defaults} which are used. Table~\ref{tab:DIFS-defaults}
+records those keys used for this purpose which are assigned default
+values \emph{different} from those in \verb`DIF`. See §\ref{subsec:DIFS-(slash-fraction-derivative)}
+for the complete list of \emph{relevant} \verb`DIFS` defaults.
+
+\subsection{Ordinary compact-form derivatives; template \texttt{DIFC}}
+
+When you use the command \verb`\difc` to form a compact derivative
+it is the keys in template \verb`DIF` with a `c' in the third column
+of Table~\ref{tab:DIF-defaults} which are used. Table~\ref{tab:DIFC-defaults}
+records those keys used for this purpose which are assigned default
+values \emph{different} from those in \verb`DIF`. See §\ref{subsec:DIFC-(compact-derivative)}
+for the complete list of \emph{relevant} \verb`DIFC` defaults.
+
+\subsection{Partial derivatives; templates \texttt{DIFFP}, \texttt{DIFSP}, \texttt{DIFCP}}
+
+The default values given in the tables so far apply to ordinary derivatives.
+For \emph{partial} derivatives, only a few defaults change. These
+are listed in Tables~\ref{tab:DIFFP-defaults}, \ref{tab:DIFSP-DIFCP-defaults}.
+All other keys take the default values of the respective parent templates,
+\verb`DIFF`, \verb`DIFS` and \verb`DIFC`.
+
+\section{Variant forms: the \texttt{\textbackslash difdef} command}
+
+\label{sec:Variant-forms}You may be dissatisfied with the scheme
+of default values listed in the preceding tables and wish to `Re-mould
+it nearer to the Heart's Desire'. How to do so is discussed in §\ref{sec:ChangingDefaults}
+below. In \emph{this} section it is assumed that the user is largely
+satisfied with the assigned defaults but has need to write an occasional
+derivative that deviates from the default form. For instance, to write
+the range of different examples displayed in the Rogues' Gallery (§\ref{sec:Rogues'-gallery})
+I had to make extensive use of such \emph{variant forms} of derivative.
+I needed forms that displayed different ways of indicating a point
+of evaluation, a form that showed a math-italic `d' rather than
+the default upright `d', forms that displayed different parenthesizing
+styles for higher-order derivatives with multi-token variable names,
+and so on.
+
+The process of defining and using such variants is a two-step process.
+The `using' part is easy: you simply put the name of the variant
+form between dots and append to the relevant \verb`\difx` or \verb`\difxp`
+command.
+
+The `defining' part makes use of a command \verb`\difdef`,
+\begin{verbatim}
+ \difdef{id-list}{variant-name}{key-value list}
+\end{verbatim}
+which has three \emph{mandatory} arguments:
+\begin{enumerate}
+\item \verb`id-list` A comma-list of identifiers, one or more of \verb`f`,
+\verb`s`, \verb`c`, \verb`fp`, \verb`sp`, \verb`cp`, \verb`j`,
+\verb`l` distinguishing the respective templates \verb`DIFF`, \verb`DIFS`,
+\verb`DIFC`, \verb`DIFFP`, \verb`DIFSP`, \verb`DIFCP`, \verb`DIFJ`
+and \verb`DIFL` (for the last two see Chapter~\ref{chap:Differentials-and-jacobians}).
+\item \verb`variant-name` A (preferably brief) name for the variant form;
+it may include characters other than letters, like numbers, punctuation
+marks (excluding full stops), mathematical symbols like \verb`+`
+and \verb`=`, but not control sequences or active characters, nor
+\verb`%` , \verb`#` or braces.
+\item \verb`key-value list` A \emph{key=value} list where the settings
+differ from the default settings for the relevant template or templates
+(as determined by the \verb`id-list`).
+\end{enumerate}
+In the preamble to the present document I have included the following
+definition:
+\begin{verbatim}
+ \difdef { f } { p }
+ {
+ op-symbol = \partial,
+ op-order-nudge = 1 mu
+ }
+\end{verbatim}
+This defines a variant, with name \verb`p`, of an ordinary upright-fraction
+derivative (the \verb`f` in the first argument) that displays as
+a partial derivative. To use the variant simply append the name, as
+a dot-delimited argument, to the \verb`\diff` command. For instance,
+repeating an earlier example from thermodynamics,
\begin{centred}
\verb`\[ \diff.p.*{\frac PT}U[V] = \diff.p.*{\frac 1T}V[U] \]` $\Longrightarrow$
-\[ \diff.p.*{\frac PT}U[V] = \diff.p.*{\frac 1T}V[U] \]
-\end{centred}
-\noindent The effect is exactly the same as previously, when the \texttt{\textbackslash diffp}
-command was used. Indeed, \texttt{diffcoeff} identifies \texttt{\textbackslash diffp}
-with \texttt{\textbackslash diff.p.}:
-\begin{lyxcode}
-\textbackslash NewDocumentCommand~\textbackslash diffp~\{~\}~\{~\textbackslash diff.p.~\}
-\end{lyxcode}
-Note that this identification of \texttt{\textbackslash diffp} with
-\texttt{\textbackslash diff.p.} means there is no equivalent dot-delimited
-argument available for \texttt{\textbackslash diffp}. The \emph{dot-delimited
-argument applies only to} \texttt{\textbackslash diff}.
-
-For example, to illustrate the upright-d form of derivative, without
-changing the default math-italic form (which I prefer), one might
-enter in the preamble
-\begin{lyxcode}
-\textbackslash diffdef~\{~up~\}~
-
-~~\{
-
-~~~~op-symbol~~~~=~\textbackslash mathrm\{d\},
-
-~~~~op-order-sep~=~0~mu
-
-~~\}
-\end{lyxcode}
-Apart from the \emph{key = value} settings, the critical feature here
-is the name, \texttt{up} (which is at your discretion and could equally
-be \texttt{upright} or \texttt{roman} or even \texttt{Fred} if you
-so fancied). This ensures that the changed settings apply only to
-this particular variant and do not `infect' the overall defaults.
-To use this variant, all that is needed is to add the name, between
-dots, to the \texttt{\textbackslash diff} command:
-\begin{centred}
-\verb`\[ \diff.up.yx \]` $\Longrightarrow$ \[ \diff.up.yx. \]
-\end{centred}
-\noindent Each variant derivative inherits all the default values
-that it does not explicitly countermand. Thus a point of evaluation
-is indicated by a vertical rule which is the \texttt{diffcoeff} default\footnote{\noindent But not the ISO recommendation.}:
-\begin{centred}
-\noindent \verb`\[ \diff.up.*{\frac{F(x)}{G(x)}}x[x=1] \]` $\Longrightarrow$
-\[ \diff.up.*{\frac{F(x)}{G(x)}}x[x=1] \]
-\end{centred}
-\noindent Dot-delimited arguments must always be the \emph{first}
-argument of the \texttt{\textbackslash diff} command, even preceding
-an asterisk (star) as in this example.
-
-As another example, suppose for the subscripted indication of variables
-held constant in a partial derivative that you want to see what things
-look like if the subscript is \emph{not }nudged in towards the right
-parenthesis. In that case define a variant form
-\begin{lyxcode}
-\textbackslash diffdef~\{~padrift~\}~\{~subscr-nudge~=~0~mu~\}
-\end{lyxcode}
-I have attached a name, \texttt{padrift},\texttt{ }to this setting,
-\begin{centred}
-\verb`\[ \diff.padrift.Fx[y] \]` $\Longrightarrow$ \[ \diff.padrift.Fx[y] \]
-\end{centred}
-\noindent since, to my eye, the subscript seems detached from the
-expression it qualifies -- is it perhaps a typo? -- and `adrift
-in a sea of whitespace'. This is to be compared with the default \verb`\[ \diffp Fx[y] \]`
-$\Longrightarrow$ \[ \diffp Fx[y] \]
-
-\noindent where the subscript is tucked in close to the right parenthesis
-and is clearly connected to it and the expression it delimits.
-
-Some might want to distinguish notationally a point of evaluation
-for a partial derivative from variables held constant, perhaps using
-a vertical rule for the former and (the default) parentheses for the
-latter. It would suffice then to add to the preamble
-\begin{lyxcode}
-\textbackslash diffdef~\{~pvrule~\}~\{~op-symbol~=~\textbackslash partial~\}~
-\end{lyxcode}
-(or some other name of your choosing). This gives
-\begin{centred}
-\verb`\[ \diff.pvrule.{F(x,y)}x[x=1] \]`$\Longrightarrow$ \[ \diff.pvrule.{F(x,y)}x[x=1] \]
-\end{centred}
-
-\subsubsection{Text-style and script-style derivatives\protect\label{subsec:Text-and-script-style}}
-
-As noted earlier, the \texttt{diffcoeff} package assumes that derivatives
-of fraction-like form will be used in display-style expressions and
-that the slash form will be used for inline use (text style). This
-is the usual practice. But if one does want to use the fraction form
-in an inline expression, say \texttt{\textbackslash diffp ST{[}V{]}}
-displaying as $\diffp ST[V]$, then some tweaking of settings is necessary:
-the subscript is obviously too close to the right parenthesis and,
-to my eye, there is too much `elbowroom' between the derivative and
-the enclosing parentheses. Hence define
+\[ \diff.p.*{\frac PT}U[V] = \diff.p.*{\frac 1T}V[U]\]
+\end{centred}
+\noindent The effect is exactly the same as previously and it would
+have been possible to define \verb`\diffp` as this variant by following
+the definition of the variant with the statement,
+\begin{verbatim}
+ \NewDocumentCommand \diffp { } { \diff.p. }
+\end{verbatim}
+\verb`diffcoeff` has not followed this path, instead choosing to
+put the status and configurability of partial derivatives on the same
+footing as ordinary derivatives.
\noindent %
\noindent\begin{minipage}[t]{1\columnwidth}%
-\begin{lyxcode}
-\textbackslash diffdef~\{~ptxt~\}~
-
-~~\{
-
-~~~~op-symbol~~~~~~=~\textbackslash partial,
-
-~~~~denom-term-sep~=~1~mu~~~~,
-
-~~~~left-delim~~~~~=~\textbackslash left~(~,
-
-~~~~right-delim~~~~=~\textbackslash right~),
+\begin{shaded}%
+The command \verb`\difdef` in version 5 of \verb`diffcoeff` takes
+\emph{three} mandatory arguments for defining variant forms of derivative.
+Do not confuse with the command \verb`\diffdef` of earlier versions
+of \verb`diffcoeff` which took \emph{two }mandatory arguments for
+this purpose. The third argument is required to identify which one
+or more of the fraction forms \verb`f`, \verb`s`, \verb`c`, \verb`fp`,
+\verb`sp`, \verb`cp` of the commands \verb`\difx`, \verb`\difxp`,
+the variant applies to. In earlier versions this was not necessary
+since there was only the one primary derivative command \verb`\diff`.\end{shaded}%
+\end{minipage}
-~~~~elbowroom~~~~~~=~-2~mu~~~,
+\medskip{}
-~~~~subscr-nudge~~~=~-3~mu~~~
+The present document comes with a number of variant definitions. These
+are divided into two groups. One, in the preamble, contains definitions,
+like the example just given, designed to illustrate various effects
+in this document -- as in the Rogues' Gallery. These preamble definitions
+are listed in §\ref{sec:Preamble-definitions}. The other, in the
+associated file \verb`diffcoeff5.def`, contains definitions that
+may be of more general usefulness; these are listed in §\ref{sec:The-file-diffcoeff5.def}.
+
+\subsection{The \texttt{.def} file}
+
+\label{subsec:The-.def-file}A \verb`.def` file (in \verb`diffcoeff`)
+is a text file containing a list of definitions of variant derivatives
+after the fashion of the example above. The reason for placing such
+variant definitions in a file is that they can be easily transferred
+from document to document by means of the \verb`def-file` package
+option. If the name of your \verb`.def` file is \verb`myfile`, then
+invoking \verb`diffcoeff` with the call
+\begin{verbatim}
+ \usepackage[def-file=myfile]{diffcoeff}
+\end{verbatim}
+makes the definitions in \verb`myfile.def` available to your current
+document -- provided \verb`diffcoeff` can find the file.
+
+The question is: where to put the \verb`.def` file? The directory
+of the current document is an obvious candidate and for the current
+document serves well, but it does mean copying the \verb`.def` file
+from directory to directory to work on \emph{different} documents.
+To make a definition file available for \emph{all} documents, place
+it in the \verb`texmf` tree, preferably not the one created by your
+\TeX{} distribution, but your own \emph{personal} \verb`texmf` tree.
+Provided your \TeX{} distribution knows about your personal \verb`texmf`
+tree and the files it contains, then a \verb`.def` file placed within
+it will be accessible to all documents.
+\noindent \begin{center}
+\noindent\begin{minipage}[t]{1\columnwidth}%
+\begin{shaded}%
+
+\subsubsection*{Personal \texttt{texmf} tree?}
+
+This is a directory created by you for `waifs and strays' of the \TeX{}
+system that are not included in standard distributions like MiK\TeX{}
+or \TeX Live. For instance, it is the place for personal packages
+designed for your own particular circumstances or preferences, and
+is structured like the standard \texttt{texmf} hierarchy but placed
+in another location so that there is no chance of its being overwritten
+when your \TeX{} distribution is updated. But that distribution needs
+to be alerted to the existence of your personal \texttt{texmf} tree
+and any new files added to it. For MiK\TeX , open the MiK\TeX{} console,
+click on \textsf{Settings} (in the column on the left) and then the
+\textsf{Directories} tab. Click the \textsf{+} button and navigate
+to your personal texmf tree to add it to the MiK\TeX{} search path,
+using the arrow keys to place it as high in the search path as possible.
+Having added it, you will then need to refresh the filename database
+by clicking on the \textsf{Tasks} menu and selecting the obvious entry.
+I am not familiar with \TeX Live but presume an analogous process
+will apply there.\end{shaded}%
+\end{minipage}
+\par\end{center}
-~~\}
-\end{lyxcode}
-%
+\begin{center}
+\medskip{}
+\noindent\begin{minipage}[t]{1\columnwidth}%
+\begin{shaded}%
+
+\subsubsection*{\texttt{diffcoeff.def}}
+
+In earlier versions of \verb`diffcoeff`, if there was no explicit
+\verb`def-file=<filename>` package option statement, then a file
+\verb`diffcoeff.def` was searched for and if found loaded. This is
+no longer the case. Version 5 of file of \verb`diffcoeff` searches
+for a \verb`.def` \emph{only if it is explicitly named} in a package
+option statement. (This decision was made at least in part to avoid
+conflict with a \verb`diffcoeff.def` file from an earlier version
+of \verb`diffcoeff` tucked away in some non-obvious place and producing
+obscure errors in the current version 5.) \end{shaded}%
\end{minipage}
+\par\end{center}
-We can now write, for the same example, \texttt{\textbackslash diff.ptxt.ST{[}V{]}}
-which displays as $\diff.ptxt.ST[V]$, where the subscript is better
-positioned and there is a better fit between parentheses and derivative.
+\subsubsection{Log file message}
+
+If the\verb`.def` file named in the package option statement cannot
+be located by \TeX , a message to that effect is sent to the terminal
+and log file, but \verb`diffcoeff` continues loading.
+
+\subsection{Examples of variants}
+
+The dot-delimited name argument must always be the \emph{first} argument
+of the \verb`\difx` or \verb`\difxp` command, even preceding an
+asterisk (star) signalling `append the differentiand'. Now for some
+examples.
+
+\paragraph{Acceleration}
+
+In tensor calculus acceleration is sometimes written $\difs.n.{v^{i}}t$,
+where different operator symbols occur in numerator and denominator.
+In the preamble to this document I have included the definition
+\begin{verbatim}
+ \difdef { f, s } { n }
+ {
+ op-symbol = \nabla,
+ op-symbol-alt = \mathrm{d}
+ }
+\end{verbatim}
+to give both upright- (the \verb`f`) and slash-fraction (the \verb`s`)
+forms of the acceleration. Appending tne dot-delimited name \verb`n`
+to \verb`\difs`, \verb`$ \difs.n.{v^i}t $` $\Longrightarrow$ $ \difs.n.{v^i}t $,
+and appending the dot-delimited name \verb`n` to \verb`\diff`,
+\begin{centred}
+\verb`\[ \diff.n.{v^i}t. \]` $\Longrightarrow$ \[ \diff.n.{v^i}t. \]
+\end{centred}
+
+\paragraph{Detached subscripts}
+
+To show the effect of the key \verb`sub-nudge`, the preamble contains
+the definition
+\begin{verbatim}
+ \difdef { fp } { wsp }
+ { sub-nudge = 0 mu }
+\end{verbatim}
+The name \verb`wsp` is a contraction of `whitespace'. The defintion
+applies only to an upright-fraction form of partial derivative (the
+\verb`fp` in the optional argument). By giving \verb`sub-nudge`
+a zero value in the \verb`wsp` variant, the subscript is cast adrift
+(perhaps to float away?) on a sea of whitespace. The default setting,
+\verb`sub-nudge=-5 mu`, maintains visual connection between subscript
+and right parenthesis:
+
+\verb`\[ \diffp.wsp.Fx[0],\quad \diffp Fx[0] \]` $\Longrightarrow$
+\[ \diffp.wsp.Fx[0],\quad \diffp Fx[0] \]
+
+\paragraph{Lagrange's equations}
+
+An earlier example used Lagrange's equations of motion, which showed
+a problem with the amount of whitespace introduced before a differentiand
+bounded by a \verb`\left`, \verb`\right` pair. The file \verb`diffcoeff5.def`
+contains the definition
+\begin{verbatim}
+ \difdef { f, fp } { *0 }
+ {
+ *derivand-sep = 0 mu ,
+ outer-Ldelim = \mleft ( ,
+ outer-Rdelim = \mright )
+ }
+\end{verbatim}
+The first thing to notice is that the name of the variant, \verb`*0`,
+is not formed from letters (there are other examples below). Now Lagrange's
+equations are rendered (just right to my eye!)
+\begin{centred}
+\verb`\[ \diffp L{q_{k}}-\diff.*0.**t{\diffp L{\dot{q}_{k}}[]}=0 \]`
+\[
+\diffp L{q_{k}}-\diff.*0.**t{\diffp L{\dot{q}_{k}}[]}=0.
+\]
+\end{centred}
-\subsubsection{Derivatives from D, \textbackslash delta, \textbackslash Delta\protect\label{subsec:D-delta-Delta}}
+\subsubsection{Editing variant forms}
+
+\noindent %
+\noindent\begin{minipage}[t]{1\columnwidth}%
+\begin{shaded}%
+
+\paragraph*{Bug in \texttt{xtemplate}}
+
+If you wish to successfully \emph{edit} a variant form that has (already)
+been defined -- by you or in \verb`diffcoeff` or in the \verb`.def`
+file\emph{ }-- then you will need a version of \verb`xtemplate`
+from 2022-12-17 or later. Earlier versions contained a bug that didn't
+otherwise affect the workings of \verb`diffcoeff` but did prevent
+changes being made to already defined variants.\end{shaded}%
+\end{minipage}\medskip{}
+
+You may wish to edit an already defined variant form -- perhaps to
+give a \emph{negative} value to \verb`*derivand-sep` in the last
+example. You don't need to repeat the full definition. It suffices
+to change the setting only of the relevant key or keys:
+\begin{verbatim}
+ \difdef { f, fp } { *0 }
+ { *derivand-sep = -3 mu }
+\end{verbatim}
+which gives for Lagrange's equations (too tight to my eye!)
+\[
+\difdef{f,fp}{*0}{*derivand-sep=-3mu}\diffp L{q_{k}}-\diff.*0.**t{\diffp L{\dot{q}_{k}}[]}=0.
+\]
-In addition to \texttt{\textbackslash diff.p.},\texttt{ diffcoeff}
-has three other \emph{built-in} variant forms that are commonly used:
-\texttt{\textbackslash diff.D.}, \texttt{\textbackslash diff.delta.},
-and \texttt{\textbackslash diff.Delta.}, corresponding to derivatives
-formed from $D$, $\delta$ and $\Delta$ respectively.
-In fluid dynamics the \emph{material }or \emph{substantive} derivative
-uses an uppercase $D$ in place of $d$. For example, the continuity
-equation is,
+\subsubsection{Parenthesizing multi-token variables}
+
+To illustrate the different modes of parenthesizing `long' variables
+in higher order derivatives, I have put these two definitions in \verb`diffcoeff5.def`:
+\begin{verbatim}
+ \difdef { f, fp } { (dv) }
+ { long-var-wrap = (dv) }
+
+ \difdef { f, fp }{ dv }
+ { long-var-wrap = dv }
+\end{verbatim}
+The three possibilities for wrapping multitoken variables can now
+be illustrated:
+\begin{verbatim}
+ \[ \diffp[2]f{x^{i}},\quad
+ \diffp.dv.[2]f{x^{i}},\quad
+ \diffp.(dv).[2]f{x^{i}} \]
+\end{verbatim}
+$\Longrightarrow$ \[ \diffp[2]f{x^i},\quad\diffp.dv.[2]f{x^i},\quad\diffp.(dv).[2]f{x^i} \]
+
+To my eye parenthesizing seems unnecessary in this case, but in the
+following desirable (as in the first, default, setting):
+\begin{verbatim}
+ \[ \diffp[2]F{1/T},\quad
+ \diffp.dv.[2]F{1/T},\quad
+ \diffp.(dv).[2]F{1/T} \]
+\end{verbatim}
+$\Longrightarrow$ \[ \diffp[2]F{1/T},\quad\diffp.dv.[2]F{1/T},\quad\diffp.(dv).[2]F{1/T} \]
+
+\subsubsection{Point of evaluation}
+
+\label{subsec:variantPoint-of-evaluation}Although ISO recommends
+subscripting parentheses to indicate a point of evaluation, some (like
+the author) prefer to subscript a vertical rule and save subscripted
+parentheses for the case of variables held constant in partial derivatives.
+The file \verb`diffcoeff5.def` contains the definition
+\begin{verbatim}
+ \difdef { f, fp, s, sp } { | }
+ {
+ outer-Ldelim = \left . ,
+ outer-Rdelim = \right |,
+ sub-nudge = 0 mu
+ }
+\end{verbatim}
+where the `pipe' character is used for the name of the variant.
+\begin{centred}
+\verb`\[ \diffp.|.{F(x,y)}x[x=1] \]` $\Longrightarrow$ \[ \diffp.|.{F(x,y)}x[x=1] \]
+\end{centred}
+For slash fractions, I think parentheses give a better result than
+a vertical rule:
+\begin{centred}
+\verb`$ \difs yx[0],\quad \difs.|.yx[0] $` $\Longrightarrow$ $\difs yx[0],\quad \difs.|.yx[0]$
+\end{centred}
+They tie the whole expression together. However, it is easy to create
+expressions that suffer from `parenthesis overload':
+\begin{centred}
+\verb`$ \difs{F(x)}{(2x)}[x=0],\quad\difs.|.{F(x)}{(2x)}[x=0] $`
+$\Longrightarrow$ $\difs{F(x)}{(2x)}[x=0],\quad\difs.|.{F(x)}{(2x)}[x=0]$
+\end{centred}
+The vertical rule is better in this case, but best of all in this
+case (to my eye) is the use of \emph{square} brackets. The file \verb`diffcoeff5.def`
+contains the definition
+\begin{verbatim}
+ \difdef { f, fp, s, sp } { ] }
+ {
+ outer-Ldelim = \left [ ,
+ outer-Rdelim = \right ],
+ elbowroom = 1 mu,
+ sub-nudge = 0 mu
+ }
+\end{verbatim}
+giving the result
+\begin{centred}
+\verb`$ \difs.].{F(x)}{(2x)}[x=0] $` $\Longrightarrow$ $ \difs.].{F(x)}{(2x)}[x=0] $,
+\end{centred}
+which both avoids `parenthesis overload' and is `tied together'
+by the square brackets (and at least gives a nod in the direction
+of the ISO standard).
+
+\subsubsection{Upright text-style derivatives}
+
+\verb`diffcoeff` assumes that derivatives of upright-fraction form
+will be used mainly in display-style expressions and that the slash
+form will be used mainly for inline use. But if one does want to use
+the fraction form in an inline expression, then \verb`$ \diffp ST $`
+displaying as $ \diffp ST $ is fine, but adding a trailing optional
+argument, \verb`$ \diffp ST[V] $`, to indicate (in the present example)
+a variable held constant is not: $\diffp ST[V]$. Clearly the subscript
+is too close to the right parenthesis and (to my eye) there is too
+much `elbowroom' between the derivative and the enclosing parentheses.
+Hence the file \verb`diffcoeff5.def` contains the following definition
+for text-style upright fraction derivatives:
+\begin{verbatim}
+ \difdef { f, fp } { t }
+ {
+ style = tfrac ,
+ derivand-sep = 1 mu plus 1 mu minus 1 mu,
+ multi-term-sep = 0 mu ,
+ term-sep-adjust = 0 mu ,
+ wrap-sup-nudge = 0 mu ,
+ outer-Ldelim = \bigl (,
+ outer-Rdelim = \bigr ),
+ elbowroom = -2 mu ,
+ sub-nudge = -3 mu
+ }
+\end{verbatim}
+With this definition, the variant form \verb`$ \diffp.t.ST[V] $`
+displays as $\diffp.t.ST[V]$. The subscript now is better positioned
+and there is a better fit between parentheses and derivative. Note
+that the \verb`style=tfrac` entry in the definition means \verb`\diffp.t.`
+will not scale in a display-style environment and may give a ridiculous
+result if used inappropriately:
+\begin{centred}
+\verb`\[ \frac AB\diffp.t.yx \]` $\Longrightarrow$ \[ \frac AB\diffp.t.yx \]
+\end{centred}
+For a non-scaling display-style derivative using \verb`\dfrac`, given
+the defaults in templates \verb`DIFF` and \verb`DIFFP`, the definition
+would be much simpler,
+\begin{verbatim}
+ \difdef { f, fp } { d } { style = dfrac }
+\end{verbatim}
+but there seems little point in so doing.
+
+\subsubsection{Slash-fraction styles}
+
+The default slash-fraction form \verb`$ \difs yx $` displaying as
+$ \difs yx $ does not scale. It is intended for inline use, but sometimes
+you may want a slash fraction of a different size -- perhaps a fraction
+is present in the differentiand or in the variable of differentiation.
+The file \verb`diffcoeff5.def` contains a definition of a scaling
+slash fraction (name \verb`0`) and a slightly larger-than-default
+slash fraction (name \verb`1`):
+\begin{verbatim}
+ \difdef { s, sp } { 0 }
+ {
+ style = auto ,
+ outer-Ldelim = \left [ ,
+ outer-Rdelim = \right ] ,
+ sub-nudge = 0 mu ,
+ *inner-Ldelim = \mleft ( ,
+ *inner-Rdelim = \mright ),
+ *outer-Ldelim = \left [ ,
+ *outer-Rdelim = \right ]
+ }
+ \difdef { s, sp } { 1 }
+ {
+ style = big ,
+ outer-Ldelim = \bigl (,
+ outer-Rdelim = \bigr ),
+ sub-nudge = -2.5 mu,
+ *inner-Ldelim = \bigl (,
+ *inner-Rdelim = \bigr ),
+ *outer-Ldelim = \bigl [,
+ *outer-Rdelim = \bigr ]
+ }
+\end{verbatim}
+The names arise from the sequence \verb`\big/`, \verb`\Big/`, \verb`\bigg/`,
+\verb`\Bigg/`, hence \verb`1`, \verb`2`, \verb`3`, \verb`4`,
+which leaves \verb`0` for the scaling form (which is built around
+\verb`\left.`, \verb`\middle/`, \verb`\right.`). \verb`diffcoeff5.def`
+does not contain definitions for the \verb`2`, \verb`3`, \verb`4`
+variants, only the two shown, because the larger sizes give ridiculous
+results. For the scaling variant, it is also easy to produce eyesores:
+\begin{centred}
+\verb`\[ \difsp.0.{\frac1Y}{\frac1X} \]` $\Longrightarrow$ \[ \difsp.0.{\frac1Y}{\frac1X} \]
+\end{centred}
+But for small size increases, the results can be pleasing. To the
+author's eye, both \verb`0` and \verb`1` variants give better results
+than the default:
+\begin{centred}
+\verb`$ \difsp.1.{F(x,y)}{\tfrac1x}[0] $` $\Longrightarrow$ $ \difsp.1.{F(x,y)}{\tfrac1x}[0] $
+
+\verb`$ \difsp.0.{F(x,y)}{\tfrac1x}[0] $` $\Longrightarrow$ $\difsp.0.{F(x,y)}{\tfrac1x}[0]\vphantom{\bigg|} $
+
+\verb`$ \difsp{F(x,y)}{\tfrac1x}[0] $` $\Longrightarrow$ $ \difsp{F(x,y)}{\tfrac1x}[0] $
+\end{centred}
+Subscripted \emph{square} brackets are chosen for the scaling variant
+so that the setting \verb`sub-nudge=0 mu` is appropriate at all scales.
+They provide good visual contrast with the parentheses of $F(x,y)$.
+
+\subsubsection{Compact--form derivatives}
+
+Two styles are available for compact-form derivatives, derivative
+style \verb`style=_`, and differential style \verb`style=dl`. The
+first is the default style; the orders of differentiation are applied
+to the operator symbol, in this example \verb`\partial`:
+\begin{centred}
+\verb`$ \difcp[3,2]{f}{x,y,z} $` $\Longrightarrow$ $ \difcp[3,2]{f}{x,y,z} $
+\end{centred}
+But suppose we define a variant form (as is done in \verb`diffcoeff5.def`):
+\begin{verbatim}
+ \difdef { cp } { dl } { style = dl }
+\end{verbatim}
+and use it to form a similar expression but without the differentiand,
+an empty argument in its place:
+\begin{centred}
+\verb`$ \difcp.dl.[3,2]{}{x,y,z} $` $\Longrightarrow$ $ \difcp.dl.[3,2]{}{x,y,z} $
+\end{centred}
+In this \verb`dl` style, the orders of differentiation are applied
+to the \emph{variables}. This allows discussion of, for example, the
+denominator of a mixed partial derivative -- perhaps a remark about
+minutiae of spacing.
+
+\subsubsection{D, \textbackslash delta, \textbackslash Delta derivatives}
+
+\label{subsec:D-delta-Delta}In introductory calculus texts a derivative-like
+symbol is created with the lowercase Greek delta, $\delta$ . An uppercase
+Greek delta, $\Delta$, is often used in a derivative-like symbol
+for an average. In fluid dynamics the \emph{material} (also \emph{substantive}
+or \emph{total}\,) derivative uses an uppercase $\mathrm{D}$ in
+place of $\mathrm{d}$. Texts on differential equations often use
+a $\mathrm{D}$ operator. The file \verb`diffcoeff5.def` contains
+the definitions
+\begin{verbatim}
+ \difdef { f, s } { gd }
+ { op-symbol = \delta }
+ \difdef { f, s } { gD }
+ { op-symbol = \Delta }
+ \difdef { f, s } { D }
+ { op-symbol = \mathrm{D} }
+ \difdef { c } { bD }
+ {
+ op-symbol = \mathbf{D},
+ op-sub-nudge = -2mu
+ }
+\end{verbatim}
+(where the `g' in the first two suggests `greek'), meaning one
+can write expressions like \verb`$ \difs.gd.yx $` $\Longrightarrow$
+$ \difs.gd.yx $, or \verb`$ \difs.gD.yx $` $\Longrightarrow$ $ \difs.gD.st$
+(for the average speed), or
\begin{centred}
\verb`\[ \diff.D.{\rho}t=\diffp\rho t + \mathbf{u\cdot}\nabla\rho \]`$\Longrightarrow$
\[ \diff.D.{\rho}t=\diffp\rho t + \mathbf{u\cdot}\nabla\rho \]
\end{centred}
-\noindent where \texttt{\textbackslash diff.D.} produces the D-derivative.
-If you want upright `D's, then the \texttt{ISO} package option will
-produce that effect. Alternatively,
-\begin{lyxcode}
-\textbackslash diffdef~\{~Up~\}~
-
-~~\{
-
-~~~~op-symbol~~~~=~\textbackslash mathrm\{D\},
-
-~~~~op-order-sep~=~0~mu
-
-~~\}
-\end{lyxcode}
-\noindent provides a variant with upright `D's.
-
-In introductory calculus texts the simple $\delta$-derivative is
-used. This is achieved with the \texttt{\textbackslash diff.delta.}
-command: \verb`\[ \diff.delta.yx \]` $\Longrightarrow$ \[ \diff.delta.yx. \]
-
-\noindent This form also features in analytical mechanics (in the
-Rogues' Gallery, the final example at (\ref{eq:eg6})).
-
-Similarly, \texttt{\textbackslash diff.Delta.} forms a derivative
-from $\Delta$:
-\begin{centred}
-\verb`$ \diff.Delta.y/x $` $\Longrightarrow$ $ \diff.Delta.y/x $
-\end{centred}
-\noindent where the slash form of the derivative is shown in this
-instance.
-
-Higher order forms of these derivatives, points of evaluation, appending
-the differentiand with a star argument, all follow exactly as for
-the `pure' \texttt{\textbackslash diff} command.
-
-\paragraph{The commands \textbackslash Diff, \textbackslash diffd, \textbackslash Diffd}
-
-For compatibility with version 1 of \texttt{diffcoeff}, the commands
-\texttt{\textbackslash Diff}, \texttt{\textbackslash diffd} and
-\texttt{\textbackslash Diffd} are available and also produce the
-$D$, $\delta$ and $\Delta$ derivatives. Just as \texttt{\textbackslash diffp}
-is identified with \texttt{\textbackslash diff.p.} for partial derivatives,
-these commands are identified with \texttt{\textbackslash diff.D.},
-\texttt{\textbackslash diff.delta.}, and \texttt{\textbackslash diff.Delta}
-through the commands
-\begin{lyxcode}
-\textbackslash NewDocumentCommand~\textbackslash Diff~\{\}~~\{\textbackslash diff.D.\}
-
-\textbackslash NewDocumentCommand~\textbackslash diffd~\{\}~\{\textbackslash diff.delta.\}
-
-\textbackslash NewDocumentCommand~\textbackslash Diffd~\{\}~\{\textbackslash diff.Delta.\}
-\end{lyxcode}
-Unless one is using such variant forms frequently, it seems simpler
-to remember that they are available as dot-delimited arguments to
-the \texttt{\textbackslash diff} command, using the obvious name
-in each case, rather than having to remember the precise camel-case
-form of name of the \texttt{\textbackslash Diff}, \texttt{\textbackslash diffd}
-and \texttt{\textbackslash Diffd} commands.
-
-\subsection{The \texttt{.def} file\protect\label{subsec:The-.def-file}}
-
-This mechanism of variant formation is how I have been able to illustrate
-in the Rogues' Gallery, §\ref{sec:Rogues'-gallery}, the wide variety
-of different usages culled from the literature. But the thought arises:
-if a variant is to be used only once or twice, isn't this a lot of
-bother? Why not just construct the variant derivative `by hand' out
-of \texttt{\textbackslash frac} and \texttt{\textbackslash mskip}
-for example? The reason for making such definitions is that they can
-be transferred from document to document. For instance, definitions
-placed in the preamble can be copied to the preamble of another document.
-
-But that is hardly optimal. Instead, \texttt{diffcoeff} allows such
-definitions to be placed in a text file with the the extension \texttt{.def}
-and a name of your choosing. For the present document the file is
-called \texttt{diffcoeff-doc.def} and has been placed in the same
-directory as \texttt{diffcoeff.tex}. To use these definitions, the
-\texttt{diffcoeff} package is called with the command
-\begin{lyxcode}
-\textbackslash usepackage{[}def-file=diffcoeff-doc{]}\{diffcoeff\}
-\end{lyxcode}
-But even this process still means copying a definition file from directory
-to directory as one works on different documents. The solution is
-to make a definition file available for \emph{all} documents and the
-way to do that is by placing it in the texmf tree, preferably not
-the one created by your \TeX{} distribution (perhaps MiKTeX or TexLive),
-but your own \emph{personal} texmf tree.
-
-\texttt{\vspace{2ex}
- }
-
-\noindent %
-\noindent\fbox{\begin{minipage}[t]{1\linewidth - 2\fboxsep - 2\fboxrule}%
-\textbf{Personal texmf tree? }
-
-This is a directory for `waifs and strays' of the \TeX{} system that
-are not included in standard distributions like MiK\TeX{} or \TeX Live.
-For instance, it is the place for personal packages designed for your
-own particular circumstances or preferences, and is structured like
-the standard MiK\TeX{} or \TeX Live hierarchy but placed in another
-location so that there is no chance of its being overwritten when
-MiK\TeX{} or \TeX Live are updated. However, those distributions need
-to be alerted to its existence. For MiK\TeX , open the MiK\TeX{} console,
-click on \textsf{Settings} and then the \textsf{Directories} tab.
-Click the \textsf{+} button and navigate to your personal texmf tree
-to add it to the MiK\TeX{} search path. Having added it, you will then
-need to refresh the filename database by clicking on the \textsf{Tasks}
-menu and selecting the obvious entry. I am not familiar with \TeX Live
-but presume an analogous process will apply there.%
-\end{minipage}}
-
-\medskip{}
-
-\noindent Provided your \LaTeX{} distribution knows about your personal
-texmf tree, then a \texttt{.def} file placed within it, will be accessible
-to all documents.
-
-\subsubsection{Structure of the \texttt{.def} file}
-
-The best way to see what a \texttt{.def} file looks like is to view
-\texttt{diffcoeff-doc.def }in a text editor.\footnote{This file should be in the same directory as \texttt{diffcoeff.pdf}
-and \texttt{diffcoeff.tex} in your \LaTeX{} distribution.}
-
-If you want your variant definitions to use defaults different from
-those supplied with the \texttt{diffcoeff} package, then the first
-definition in the \texttt{.def} file should be the one setting the
-new defaults, with an \emph{empty} first argument to the \texttt{\textbackslash diffdef}
-command:
-\begin{lyxcode}
-\textbackslash diffdef~\{\}~~~~
-
-~~\{~~~~~~
-
-~~~~key-1~=~value-1,~~~~
-
-~~~~key-2~=~value-2,
-
-~~~~...
-
-~~~~key-n~=~value-n
-
-~~\}
-\end{lyxcode}
-The key-value list is a comma-separated list; hence the last entry
-doesn't need to end with a comma. Nudge and separation values need
-to include the unit, \texttt{mu}; a numerical value alone will result
-in error.\texttt{ }Because a \texttt{.def} file\texttt{ }is a \LaTeX{}
-file, comments need to start with a \texttt{\%} character.
-
-\subsubsection{\texttt{diffcoeff.def}}
-
-Note that if the \texttt{diffcoeff} package is invoked without an
-explicit \texttt{def-file= <filename>} option statement, as here,
-\begin{lyxcode}
-\textbackslash usepackage\{diffcoeff\}
-\end{lyxcode}
-then it will search in the texmf tree (the \LaTeX{} distribution's
-and your personal one) and the document directory for a file \texttt{diffcoeff.def}
-and if found will load that. This file should contain definitions
-of those variants you are likely to use in multiple documents. In
-my personal texmf tree (which I've put at \texttt{E:\textbackslash texmf\textbackslash}
-on a Windows machine) the file \texttt{diffcoeff.def} is located in
-the directory \texttt{E:\textbackslash texmf\textbackslash tex\textbackslash latex\textbackslash diffcoeff\textbackslash}.
-(The backslashes are replaced by forward slashes on linux machines.)
-
-Variants likely to be of value only to a specific document should
-be added to the preamble of that document. Alternatively, they could
-be added to \texttt{diffcoeff.def} but that added-to file saved to
-the document directory under a \emph{different} name -- e.g. I've
-saved the variants required for the present document under the name
-\texttt{diffcoeff-doc.def}. Many of these variants were created solely
-to illustrate points in the present document and I have no intention
-of using them in my own work. Consequently my \texttt{diffcoeff.def}
-file is smaller, containing only a selection from \texttt{diffcoeff-doc.def}.
-
-\section{Differentials in integrals, etc.}
-
-Forms like $dx$ occur not only in derivatives but also in other contexts,\footnote{I thank \noun{Sergio Callegari} for drawing my attention to this rather
-obvious point, and its omission from previous versions of \texttt{diffcoeff}.} for example, the expression for a total differential like
+\noindent for the total derivative of $\rho$ (perhaps in fluid dynamics),
+or
+\begin{centred}
+\noindent \verb`$ \difc.bD.[2]y{x\,}+2\difc.bD.y{x\,}-4=0 $` $\Longrightarrow$
+$ \difc.bD.[2]y{x\,}+2\difc.bD.y{x\,}-4=0 $
+\end{centred}
+for an example in the study of differential equations.
+
+\subsection{Other notations}
+
+\label{subsec:Other-notations}\verb`diffcoeff` and this document
+are about defining \emph{derivatives} but it is worth pointing out
+that other notations can be built from the \verb`diffcoeff` constituents,
+in particular from the slash fraction forms. For example, some other
+token than \verb`/`, or indeed series of tokens, can be used to link
+numerator and denominator. It could be \verb`\vert` or \verb`\Vert`,
+displaying as $\vert$ and $\Vert$ respectively, or \verb`\otimes`
+(requiring for example \verb`\usepackage{stmaryrd}` in the preamble),
+displaying as $\otimes$, or the sequence of tokens \verb`\otimes\ldots\otimes`
+displaying as $\otimes\ldots\otimes$. The critical key is \verb`slash-tok`,
+with possible extra spacing on either side through the key \verb`slash-sep`.
+Or, one may want to void the \verb`op-symbol` key by giving it an
+empty value or do something like \verb`op-symbol=\mathbf`, or give
+\verb`outer-Ldelim`, \verb`outer-Rdelim` special values, e.g.,\verb`\langle`,
+\verb`\rvert`.
+
+In the preamble I have included the following definition, in order
+to mimic the \verb`\Braket` command of the \verb`braket` package,
+\begin{verbatim}
+ \difdef{ s }{ bk }
+ {
+ slash-tok = ,
+ op-symbol = ,
+ multi-term-sep = 3mu\middle|\mskip3mu ,
+ outer-Ldelim = \left\langle ,
+ outer-Rdelim = \right\rangle
+ }
+\end{verbatim}
+and supplemented it with the definition:
+\begin{verbatim}
+ \NewDocumentCommand \Braket { m }
+ {
+ \difoverride {\negmu}
+ \difs.bk.{}{#1}[]
+ }
+\end{verbatim}
+Testing the new command, \verb`\Braket`, gives this display:
+\begin{centred}
+\verb`\[ \Braket{\phi,\diffp[2]{}t,\psi} \]` $\Longrightarrow$ \[\Braket{\phi,\diffp[2]{}t,\psi} \]
+\end{centred}
+Comparison with the \verb`\Braket` command of the \verb`braket`
+package, which uses \verb`|` as the separator in the argument rather
+than commas, shows the displayed results to be the same (as far as
+I can judge).
+
+\section{Defaults: setting your own}
+
+\label{sec:ChangingDefaults}The use of variant forms of derivative
+assumes the user is reasonably satisfied with the default values of
+the various templates. The user may not be. You may want different
+defaults. That is again accomplished by means of the \verb`\difdef`
+command. The procedure is identical with that for defining a variant
+except that \emph{no} \verb`variant-name` is supplied; an empty argument
+is used instead.
+
+For example, suppose you wish to indicate a point of evaluation for
+ordinary upright-fraction derivatives by means of a subscripted vertical
+rule rather than parentheses. In §\ref{subsec:variantPoint-of-evaluation}
+we have seen how to create a variant form with this property but now
+we want to make it the default in the template \verb`DIFF`. That
+is easy -- simply omit any content from the second argument:
+\begin{verbatim}
+ \difdef { f } {}
+ {
+ outer-Ldelim = \left . ,
+ outer-Rdelim = \right |,
+ sub-nudge = 0 mu
+ }
+\end{verbatim}
+\noindent If this is placed in the preamble of your document or in
+your \verb`.def` file (see §\ref{subsec:The-.def-file}) then the
+command \verb`\diff yx[0]` will produce
+\[
+\diff.|.yx[0]
+\]
+by default. By leaving the second argument empty the \verb`\difdef`
+command has changed the default value of those templates indicated
+by the list of identifiers in the first argument -- in the present
+case only the template \verb`DIFF`. In particular, note that the
+new default is \emph{not} inherited by \verb`DIFFP`. Inheritance
+occurs \emph{only} at load time. How to change defaults that will
+be inherited is discussed below in §\ref{subsec:Changing-DIF-defaults}.
+
+If you wish to change other defaults of other templates follow the
+same procedure. In the first argument of the \verb`\difdef` command
+insert a comma-list of the derivative identifiers (\verb`f`, \verb`s`,
+\verb`c`, \verb`fp`, \verb`sp`, \verb`cp`, \verb`j` or \verb`l`)
+that you want the new defaults to apply to, \emph{leave the second
+argument empty}, and in the third argument provide the \emph{key=value}
+list of new defaults.
+
+For instance, you might prefer math-italic `d's rather than the
+upright ISO recommendation, and you want this to apply across \emph{all}
+ordinary-derivative templates. The most straightforward way of achieving
+that would be through the definition
+\begin{verbatim}
+ \difdef { f, s, c, l } {}
+ {
+ op-symbol = d ,
+ op-order-nudge = 1 mu
+ }
+\end{verbatim}
+which includes the list of identifiers \verb`f, s, c, l` in the first
+argument (the \verb`l` referring to the template \verb`DIFL` of
+the differential -- see §\ref{sec:Differentials}) and leaves the
+second argument empty. Thereafter, all ordinary derivatives will be
+graced with math-italic rather than upright `d's.
+
+\subsection{Changing defaults in \texttt{DIF}}
+
+\label{subsec:Changing-DIF-defaults}You might wonder if this last
+effect could not have been obtained more simply by changing the default
+in the `primogenitor' template \verb`DIF` -- perhaps leave both\emph{
+first }and second\emph{ }arguments empty in the \verb`\difdef` command.
+That, however, has no effect. The \verb`\difdef` command does nothing
+if the first argument is empty. Inheritance occurs only once, at time
+of birth -- \emph{load time} -- and not thereafter. If you want
+to make a change affecting a number of templates by changing a default
+in \verb`DIF`, then it has to be done at the time when \verb`diffcoeff`
+is loaded.
+
+There are two ways to do this. The first is to create a text file
+with the specific name \verb`diffcoeff.DIF` with the desired settings.
+For example, if we want math-italic `d's and a subscripted vertical
+rule for points of evaluation, then the file might look like
+\begin{verbatim}
+ op-symbol = d,
+ op-order-nudge = 1 mu,
+ outer-Ldelim = \left . ,
+ outer-Rdelim = \right |,
+ sub-nudge = 0 mu
+\end{verbatim}
+By locating the file in a place where your \TeX{} distribution can
+find it -- either in the directory of the current document or in
+your personal \verb`texmf` tree (see the earlier discussion at §\ref{subsec:The-.def-file},
+and in particular the need to alert your \TeX{} distro to the presence
+of the file) -- \verb`diffcoeff.DIF` will be read at load time and
+the new defaults not only incorporated into template \verb`DIF` but
+inherited by all child and grandchild templates unless explicitly
+countermanded (for example by \verb`op-symbol = \partial` and similar
+statements in the definitions of those templates).
+
+The second method is to use the package option \verb`DIF`. For instance
+loading \verb`diffcoeff` with the call
+\begin{verbatim}
+ \usepackage
+ [
+ DIF = { op-symbol = d,
+ op-order-nudge = 1 mu,
+ outer-Ldelim = \left . ,
+ outer-Rdelim = \right |,
+ sub-nudge = 0 mu }
+ ]{diffcoeff}
+\end{verbatim}
+will overwrite the built-in defaults with these new values, which
+will be inherited by child (and grandchild) templates unless explicitly
+countermanded. Notice that since \verb`DIF` is a comma list it requires
+braces around the list of \emph{key=value} statements\emph{.}
+
+If both methods of changing the template \verb`DIF` are employed,
+the order of use is, first, read and act on the file \verb`diffcoeff.DIF`,
+then read and act on the package option \verb`DIF`. (In other words,
+to avoid complicating the preamble, preferably use the file \verb`diffcoeff.DIF`;
+use the package option \verb`DIF` only for fine-tuning -- perhaps
+a setting specific to that particular document.)
+
+\chapter{Differentials and jacobians}
+
+\label{chap:Differentials-and-jacobians}In addition to the six derivative
+commands, \verb`\difx` and \verb`\difxp`, the \verb`diffcoeff`
+package has two further commands, \verb`\dl` and \verb`\jacob`,
+for writing differentials and jabobian determinants respectively.
+These commands use the settings of the templates \verb`DIFL` and
+\verb`DIFJ`, and both are correspondingly configurable by means of
+the \verb`\difdef` command.
+
+\section{Differentials}
+
+\label{sec:Differentials}Forms like $\dl x$ occur not only as components
+of derivatives but also in other contexts like the expression for
+a total differential,
\[
\dl P=\diffp Px\dl x+\diffp Py\dl y+\diffp Pz\dl z,
\]
-or an integral like $\int\sin x\dl2x$, or a multi-variable integral
+or in integrals, like $\int\sin x\dl x$, or multi-variable integrals
like
\[
-\iiintop_{-\infty}^{\infty}V(x,y,z)\dl3x\dl2y\dl2z.
+\iiintop_{-\infty}^{\infty}V(x,y,z)\dl{x,y,z}.
\]
-Surely we want the `d's in these expressions to correspond to their
-form (upright or math italic) in derivatives? If, for instance, the
-\texttt{ISO} package option has been set, one doesn't want to be writing
-\texttt{\textbackslash mathrm\{d\}} in every (or indeed any) integral.
-To this end, \texttt{diffcoeff} provides a command \texttt{\textbackslash dl}
-to write the `d' in a differential in a manner consistent with the
-default form used in derivatives. In the present document, the default
-form is math-italic and so
+They also occur in differential geometry and elsewhere in the form
+of line elements like
\begin{centred}
-\verb`$ \dl x $` $\Longrightarrow$ $ \dl x. $
+$\dl.+.{x,y,z}^2$ \quad{}and\quad{} $c^2\dl.-.{t,x,y,z}^2$.
\end{centred}
-\noindent It is also possible\footnote{\noindent From version 3.1 of \texttt{diffcoeff}; version 3.0 of the
-package produced a \LaTeX{} error.} to use the command before, for instance, \texttt{\textbackslash mathbf\{x\}}
-or \texttt{\textbackslash vec\{x\}}:
-\begin{centred}
-\verb`$ \dl \vec{x} $` $\Longrightarrow$ $ \dl \vec{x} $,~~~~\verb`$ \dl \mathbf{x} $`
-$\Longrightarrow$$ \dl \mathbf{x}. $
-\end{centred}
-
-\subsection{Options}
-
-There are two options available with the differential command.
-
-The first is the dotted name option discussed in §\ref{sec:Changing-defaults}.
-Thus, to illustrate a differential with an upright `d', write
+Surely we want the `d's in these expressions to correspond to their
+form (upright or math italic) in derivatives? To this end, \verb`diffcoeff`
+provides a command \verb`\dl` to write the `d' in a differential
+in a manner consistent with the default form used in derivatives.
+In the present document, the default form is upright and so
\begin{centred}
-\verb`$ \dl.up.x $` $\Longrightarrow$ $ \dl.up.x. $
+\verb`$ \dl x $` $\Longrightarrow$ $ \dl x. $
\end{centred}
-\noindent This presumes that a variant derivative with upright `d's
-has been defined and the definition is available, either in the preamble
-or in an accessible \texttt{.def} file, as discussed in the previous
-section. Alternatively, if you have defined your default derivative
-to use upright `d's (perhaps with the \texttt{ISO} option) then
-\texttt{\textbackslash dl} alone will suffice to produce an upright
-`d'.
-
-\subsubsection{Partial differential}
-
-\label{subsec:Partial-differential}Since the variant \texttt{\textbackslash diff.p.}
-is defined in \texttt{diffcoeff.sty} itself, \texttt{\textbackslash dl.p.}
-is always available and at 6 keystrokes offers a slightly shorter
-way of writing \texttt{\textbackslash partial} (8 keystrokes). However,
-there are sufficient contexts where expressions like \verb`\partial_x`
-are used, perhaps as a shortcut for a partial derivative, for it to
-be worthwhile to define an appropriate command for this variant. From
-version 4.0, \texttt{diffcoeff} therefore provides \verb`\dlp`, defined
-by
-\begin{lyxcode}
-\textbackslash NewDocumentCommand~\textbackslash dlp~\{\}~\{~\textbackslash dl.p.~\}
-\end{lyxcode}
-Thus, for instance, \verb`$ \dlp_x $` $\Longrightarrow$ $ \dlp_x $.
-
-\subsubsection{Spacing}
-
-This second option inserts spacing before the `d'. If \texttt{\textbackslash dl}
-is followed by a digit (0, 1, 2, ..., 9) it will insert a horizontal
-space of that number of mu before the `d'; (\texttt{\textbackslash dl0x}
-has the same effect as \texttt{\textbackslash dl x}.)\texttt{ }Thus,
-an alternative way of writing an example in Chapter~18 of \emph{The
-\TeX book} is
+\noindent To use the command before a multi-token variable of differentiation,
+put the variable in braces:
\begin{centred}
-\verb`$ \dl x\dl3y=r\dl3r\dl3\theta $` $\Longrightarrow$ $ \dl x\dl3y=r\dl3r\dl3\theta. $
+\verb`$ \dl{\vec{x}},\quad \dl{\mathbf{x}} $` $\Longrightarrow$
+$ \dl{\vec{x}},\quad \dl{\mathbf{x}} $.
\end{centred}
-\noindent To my eye this is too much space; I prefer
+For the triple integral above, writing the differentials required
+not three but just the \emph{one} command:
\begin{centred}
-\noindent \verb`$ \dl x\dl2y=r\dl2r\dl2\theta $` $\Longrightarrow$
-$ \dl x\dl2y=r\dl2r\dl2\theta. $
+\verb`$ \dl{x,y,z} $` $\Longrightarrow$ $ \dl{x,y,z} $.
\end{centred}
-\noindent I used \texttt{\textbackslash dl3x\textbackslash dl2y\textbackslash dl2z}
-when writing the triple integral above, \emph{no} extra spacing when
-writing the total differential expression, since the differentials
-are already distinct from the preceding fraction forms $\diff.ptxt.Px$
-etc., and \texttt{\textbackslash dl2x} when writing $\int\sin x\dl2x$.
-
-Note that only \emph{one} digit can be used. If two are used, as here,
-\verb`$ \dl20x $` $\Longrightarrow$ $ \dl20x $, the effect is unlikely
-to be what is wanted.
-
-From version 3.2 of \texttt{diffcoeff} it is possible to also add
-\emph{negative} space before the differential, which might be useful
-in special contexts, perhaps to construct a symbol:
+To write the line elements I made use of a dot-delimited argument
+producing a variant form of the differential (see below §\ref{subsec:Line-elements}):
\begin{centred}
-\verb`$ /\dl-9x $` $\Longrightarrow$ $ /\dl-9x. $
-\end{centred}
-\noindent For negative space before the differential, add a minus
-sign before the (single) digit.
+\verb`$ \dl.+.{x,y,z}^2 $` $\Longrightarrow$ $ \dl.+.{x,y,z}^2 $,
-The spacing digit option \emph{follows} the dot-delimited name option.
-For example, earlier, in the denominator of a mixed partial derivative,
-I have used what is effectively \texttt{\textbackslash dlp x\textbackslash dlp2y\textbackslash dlp2z},
-and the variation to that spacing when a higher-order differentiation
-occurs:
-\begin{centred}
-\verb`$ \dlp x^2\dlp1y\dlp2z $` $\Longrightarrow$ $ \dlp x^2\dlp1y\dlp2z. $
+\verb`$ c^2\dl.-.{t,x,y,z}^2 $` $\Longrightarrow$ $ c^2\dl.-.{t,x,y,z}^2 $.
\end{centred}
-\section{Rationale}
-
-Version 1 of the \texttt{diffcoeff} package arose from a need to simplify
-the parsing of differential coefficients for another program I was
-working on which was struggling to `read' all the possible permutations
-of \texttt{\textbackslash frac} or \texttt{\textbackslash tfrac}
-or \texttt{\textbackslash dfrac} or slash forms of the derivative,
-of \texttt{d} or \texttt{\textbackslash mathrm\{d\}} or \texttt{\textbackslash partial}
-or \texttt{D} or \texttt{\textbackslash mathrm\{D\}} or \texttt{\textbackslash nabla},\texttt{
-}and of points of evaluation delimited by vertical rules or parentheses.\texttt{ }Although
-regular expressions coped with most of these cases, it was \emph{messy}.
+\subsection{Template \texttt{DIFL}}
-There are other packages which have commands for the derivative (e.g.,
-\texttt{bropd}, \texttt{commath},\texttt{ esdiff}, \texttt{physymb})
-but none quite gave what I wanted -- although they probably cope
-with most users' needs. \texttt{esdiff} came closest to what I was
-seeking but failed when it came to combining algebraic and numeric
-orders of differentation in a mixed partial derivative (and made heavier
-use of braces than I liked in that case too).
-
-\subsection{\texttt{diffcoeff.sty}}
+\begin{wraptable}{o}{0.5\columnwidth}%
-I have tried to make using \texttt{diffcoeff} intuitive. Looking at
-the other packages mentioned, writing something like \texttt{\textbackslash diff{[}n{]}\{f\}\{x\}}
-(which can be trimmed to \texttt{\textbackslash diff{[}n{]}fx} for
-single-token arguments) seems `natural' -- only \texttt{physymb}
-deviates from the pattern.
-\begin{itemize}
-\item It seems consistent with this pattern to use a comma list for specifying
-the orders of differentiation of the variables in a higher order mixed
-partial derivative (and its suppression when all are of order 1)
-\item Having specified the orders, surely the program itself should calculate
-the overall order? \texttt{esdiff} does this for numerical orders;
-\texttt{diffcoeff} does this for both numeric and algebraic orders,
-\end{itemize}
-\begin{centred}
-\verb`\[ \diffp[m-(k+1),m+(k-1)]{F(x,y,z)}{x,y,z} \]`
-\end{centred}
-\begin{example}
-$\Longrightarrow$ \[ \diffp[m-(k+1),m+(k-1)]{F(x,y,z)}{x,y,z} \]
-\end{example}
+\begin{centering}
+\caption{\texttt{DIFL} defaults\protect\label{tab:DIFL-defaults}}
+\begin{center}
+\begin{tabular}{lrr}
+\toprule
+{\small key} & {\small default} & {\small comment}\tabularnewline
+\midrule
+{\small style} & {\small\texttt{dl}} & {\small locked}\tabularnewline
+{\small outer-Ldelim} & {\small\texttt{\textbackslash ,}} & \tabularnewline
+{\small outer-Rdelim} & & \tabularnewline
+\bottomrule
+\end{tabular}
+\par\end{center}
+\par\end{centering}
+\end{wraptable}%
+The differential command \verb`\dl` gives access to a template \verb`DIFL`
+which inherits the default values of the fundamental template \verb`DIF`
+with the (few) changes shown in Table~\ref{tab:DIFL-defaults}. Note
+that the \verb`style` key is fixed at the value \verb`dl`; it cannot
+be changed. The \verb`outer-Ldelim` key inserts a small space before
+the differential; the \verb`outer-Rdelim` key does nothing. For the
+differential, both \verb`outer-Ldelim` and \verb`outer-Rdelim` are
+\emph{always inserted}. This differs from the derivative for which
+\verb`outer-Ldelim` and \verb`outer-Rdelim` are inserted only if
+there is a trailing optional argument. It is as if the differential
+command \verb`\dl` had a built-in empty trailing optional argument.
+
+That so few of the \verb`DIF` defaults are changed in \verb`DIFL`
+indicates that much of the machinery of derivative formation is irrelevant
+for forming a differential. A list of \emph{relevant} keys for the
+creation of differentials -- those that have some effect on the appearance
+of the thing -- can be found at §\ref{subsec:DIFL-(differential)}.
+
+\subsection{Syntax and options}
+
+\label{subsec:DifferentialsSyntaxOptions}If all options are present
+the differential command has the syntax
+\begin{verbatim}
+ \dl.name.[order-spec]{variable(s)}^{exponent}
+\end{verbatim}
+where the arguments have the following significance:
+\begin{enumerate}
+\item \verb`name` (optional) A dot-delimited name to distinguish a variant
+form (non-default form) of differential; see §\ref{subsec:Variant-differentials}
+below.
+\item \verb`order-spec` (optional) The power or comma-list of powers to
+which the differential or differentials will be raised. If all powers
+are \verb`1` then no specification is needed; indeed, if fewer powers
+are specified than there are variables, all `missing' powers are
+assumed to be \verb`1`; see the discussion for mixed partial derivatives,
+§\ref{subsec:Mixed-partial-derivatives}.
+\item \verb`variable(s)` (mandatory) The variable or comma-list of variables
+the differential operator applies to. \verb`\dl x`, \verb`\dl{\vec{x}}`,
+\verb`\dl{x,y,z}` are all valid variable specifications, displaying
+as $\dl x$, $\dl{\vec{x}}$ and $\dl{x,y,z}$ respectively.
+\item \verb`exponent` (optional) An exponent to which all differentials
+will be raised; overrides the \verb`order-spec` ; see §\ref{subsec:Line-elements}
+for examples of use.
+\end{enumerate}
+Only the third argument is mandatory, although it may be empty.
+
+\subsection{Variant forms of differential}
+
+\label{subsec:Variant-differentials}The first argument of the differential
+command \verb`\dl` is the optional \verb`name` which is used --
+like the corresponding argument in the derivative commands -- to
+define \emph{variant forms}.
+
+To create such variant forms, the \verb`\defdif` command is again
+used, but with \verb`l` (lowercase \verb`L`) used as the identifier
+in the first argument. For example, you may want a `partial' differential,
+using \verb`\partial` in place of \verb`d`. It seems natural to
+give this the name \verb`p`:
+\begin{verbatim}
+ \difdef { l } { p }
+ { op-symbol = \partial }
+\end{verbatim}
+In fact just this definition can be found in the file \verb`diffcoeff5.def`,
+so that
+\begin{centred}
+\verb`$ \dl.p.x $` $\Longrightarrow$ $\dl.p.x$
+\end{centred}
+which is seven keystrokes in all versus ten (space included) for \verb`\partial x`.
+Defining \verb`\dlp` by writing
+\begin{centred}
+\verb`\NewDocumentCommand \dlp {} { \dl.p. }`.
+\end{centred}
+saves another keystroke. However, I doubt the few keystrokes saved
+justify the trouble of defining such a variant. The real reason one
+might do so is to ease the writing of expressions like $\dl.p.[3,2]{x,y,z}$
+-- perhaps in a document like the present one to discuss the minutiae
+of spacing in the denominators of mixed partial derivatives.
+\begin{centred}
+\verb`$\dl.p.[3,2]{x,y,z}$` $\Longrightarrow$ $\dl.p.[3,2]{x,y,z}$
+\end{centred}
+As you can see from the example, just as for mixed partial derivatives,
+if more than one variable is specified but the \verb`order-spec`
+contains fewer than that number of entries, \verb`diffcoeff` assumes
+the missing entries are \verb`1`.
+
+A second example of a variant form of differential is provided by
+the definition
+\begin{verbatim}
+ \difdef { l } { b }
+ { op-symbol = \mathrm{d}\mathbf }
+\end{verbatim}
+which can be found in the file \verb`diffcoeff5.def`. If you distinguish
+vectors, say, by boldface type, then you can avoid writing \verb`\mathbf`
+for differentials of vectors by using the variant form \verb`\dl.b.`:
+\begin{centred}
+\verb`$ \dl.b.x,\quad \dl.b.{x,y,z} $` $\Longrightarrow$ $ \dl.b.x ,\quad \dl.b.{x,y,z} $.
+\end{centred}
+
+\subsubsection{Line elements}
+
+\label{subsec:Line-elements}Variant forms can be used to write line
+elements of Pythagorean or Minkowskian form. The definition
+\begin{verbatim}
+ \difdef { l } { + }
+ {
+ multi-term-sep = 0 mu +,
+ term-sep-adjust = 0 mu ,
+ outer-Ldelim =
+ }
+\end{verbatim}
+which can be found in the file \verb`diffcoeff5.def`, inserts a \verb`+`
+sign between terms in the variable specification. Notice that the
+value assigned to the key \verb`multi-term-sep` begins with \verb`0 mu`.
+A dimension here \emph{initially} is essential. Also note that the
+thin space inserted by default before a differential by means of the
+\verb`outer-Ldelim` setting is now removed. But the intriguing feature
+of the definition is what follows the \verb`0 mu` in the \verb`multi-term-sep`
+value: a \verb`+` sign. Applying this variant to \verb`{x,y,z}`
+the result is $ \dl.+.{x,y,z} $, which may be mildly interesting
+but definitely becomes so when we add an exponent to the variable
+spec.:
+\begin{centred}
+\verb`$ \dl.+.{x,y,z}^2 $` $\Longrightarrow$ $ \dl.+.{x,y,z}^2 $.
+\end{centred}
+The exponent acts as if an order specification \verb`[2,2,2]` had
+been included. If an order specification \emph{is }included, whatever
+the values listed, the trailing exponent overrides it.
+
+Similarly, the file \verb`diffcoeff5.def` contains an identical definition
+save that the plus sign is replaced by a minus. This enables the writing
+of a Minkowski metric:
+\begin{centred}
+\verb`$ c^2\dl.-.{t,x,y,z}^2 $` $\Longrightarrow$ $ c^2\dl.-.{t,x,y,z}^2 $.
+\end{centred}
+
+\subsection{Changing defaults}
+
+To change the \emph{default} values of the \verb`DIFL` template use
+the \verb`\difdef` command but leave its second argument, the \verb`name`
+argument, empty. For instance if you want slightly less space by default
+before a differential than the thin space (\verb`\,` or \verb`3 mu`)
+specified in the \verb`DIFL` template -- say you want \verb`2 mu`
+-- then write
+\begin{verbatim}
+ \difdef { l } {} { outer-Ldelim = \twomu }
+\end{verbatim}
+and ensure that this is in your \verb`.def` file or in the preamble
+of your document. If you want a rubber length, say \verb`3 mu plus 1 mu minus 2 mu`
+(which can also be written more compactly as \verb`3muplus1muminus2mu`),
+then write (notice the \verb`\mskip`)
+\begin{verbatim}
+ \difdef { l } {}
+ { outer-Ldelim = \mskip 3muplus1muminus2mu }
+\end{verbatim}
+The crucial point is to leave the second argument of \verb`\difdef`,
+the \verb`variant name`, empty. That changes the \emph{default} values
+in \verb`DIFL` of the keys listed in the third argument of \verb`\difdef`.
+
+\subsection{Rationale}
+
+But why bother with the differential command at all? It only seems
+to complicate the simple typing of \verb`d` followed by \verb`x`.
+Admittely typing \verb`\dl x` requires fewer keystrokes than typing
+\verb`\mathrm{d}x` (or even \verb`\mathrm dx`), but there are other,
+more substantive, reasons why one might prefer an explicit command.
+\begin{enumerate}
+\item \emph{Consistency} with the derivative.
+\item \emph{Spacing} is inserted automatically before the differential,
+and between differentials in (e.g.) multiple integrals.
+\item \emph{Parsing integrals} for some other package or program is much
+easier to do when looking for a concluding differential command \verb`\dl`
+than when looking for \verb`d` or \verb`\mathrm{d}` or \verb`\mathnormal{d}`
+(or whatever) followed by an arbitrary variable name.
+\item \emph{Configurability}. There are values other than the defaults that
+can be given to keys to give novel effects for variant forms of differential
+-- see the examples \verb`\dl.b.`, \verb`\dl.+.` and \verb`\dl.-.`
+above.
+\end{enumerate}
-\begin{itemize}
-\item and where it fails either to calculate at all or to present the result
-in a preferred form, offers the order-override option:
-\end{itemize}
-\begin{centred}
-\verb`\[ \diffp[m+(k+1),m+(k-1)][2(m+k+1)]{F(x,y,z,w)}{x,y,z,w} \]`
-\end{centred}
-\begin{example}
-$\Longrightarrow$ \[ \diffp[m+(k+1),m+(k-1)][2(m+k+1)]{F(x,y,z,w)}{x,y,z,w} \]
-\end{example}
+\section{Jacobians}
-\begin{itemize}
-\item I wished to avoid the unnecessary writing of superscripts, subscripts
-and brace pairs. In the examples just given, no superscript tokens
-\texttt{\textasciicircum} are written by the user despite the higher-order
-differentiation in $x$ and $y$, and only the two inescapable brace
-pairs are required.
-\item The use of a comma list for the second mandatory argument in a partial
-derivative -- the list of variables -- makes differentiations in
-super- or subscripted symbols (as occurs prolifically in tensor calculus)
-easier to both write and read by avoiding unnecessary brace pairs.
-\end{itemize}
+\label{subsec:Jacobians}\verb`diffcoeff` provides a command {\ttfamily\verb`\jacob`}
+for writing jacobians -- not the determinant as such but the symbol
+conventionally used to denote the determinant. For example
\begin{centred}
-\verb`\[ \diffp{A_i}{ x^j,x^k } \]` $\Longrightarrow$ \[ \diffp{A_i}{ x^j,x^k } \]
+\verb`\[ \jacob{u,v,w}{x,y,z} \]` $\Longrightarrow$ \[ \jacob{u,v,w}{x,y,z} \]
\end{centred}
-\begin{itemize}
-\item Should a point of evaluation or variables held constant be considered
-part of the derivative? Thermodynamic usage was decisive here. The
-partial derivative alone is ambiguous -- the parentheses and subscript
-are essential to understand what is being stated:
+The comma lists can contain any number of variables, even one or none,
\[
-\diffp ST[V]
+\jacob uv,\quad\jacob{}{},
\]
-Hence provision for these extra elements was included in the derivative
-commands.
-\item Given the position of the subscripted symbol in the displayed derivative,
-it's positioning as the \emph{final} argument in the derivative command
-feels inevitable.
-\item Version 1 of \texttt{diffcoeff} used braces for this argument to avoid
-any possible confusion with a following mathematical expression. That
-use of braces is now deprecated in \texttt{xparse}, has been deprecated
-in \texttt{diffcoeff} since version 2, and is no longer compatible
-with version 4. Later versions of \texttt{diffcoeff} use square brackets,
-conforming with familiar \LaTeX{} practice. The only special remembering
-needed is avoidance of a space before the argument -- and if it does
-slip in, it won't cause a \LaTeX{} error. It will be treated as part
-of a following mathematical expression and displayed as such.
-\item The star option also prompted the question: is it needed? After all,
-one can always leave the first mandatory argument empty and append
-the differentiand `by hand'. But once the provision for points of
-evaluation or variables held constant was incorporated into the derivative
-commands, the star option became the simplest way of handling appended
-differentiands since the parentheses for a variable held constant
-must wrap around the differential operator \emph{and} differentiand.
-Once available, it provides a simple way of switching between (and
-comparing) the appearance of differentiand-in-the-numerator and differentiand-appended.
-\item The slash option was added to the derivative commands after seeing
-how widely such forms are used in texts at all levels. The placement
-of the slash, between the two mandatory arguments, seems more-or-less
-self-evident.
-\item A later option added to \texttt{\textbackslash diff} (and not present
-in version 1) was the dot-delimited name option. Once \texttt{xtemplate}
-was used as the basis of the package this seemed the most straightforward
-way of making available, ready to hand, the wealth of variants that
-\texttt{xtemplate} makes possible. (It's just a pity that the second
-dot is needed, and a single-dot naming scheme can't be used, but \texttt{xparse}
-forces my hand here.)
-\item Having added the dot-delimited name option, the use of a \texttt{def}
-file to store variants or preferred defaults is more-or-less forced,
-otherwise one is faced with making these definitions anew for each
-new document (or locating a previous document and copying from that
-to the new one).
-\item To handle possible differences between display-style and text-style
-(and script-style) derivatives (see §\ref{subsec:Text-and-script-style})
-I considered using \TeX 's \texttt{\textbackslash mathchoice} command.
-This command takes four arguments, corresponding to display-, text-,
-script- and scriptscript-styles and would require forming four derivatives
-each time a derivative is used, `just in case'. In fact fraction-form
-derivatives are used overwhelmingly in display-style expressions,
-the slash form being used for inline use. Given the ease of defining
-a fraction-form variant for text-style use, and the rareness of such
-use, employing variants seemed the way to go. It is the one adopted
-and avoids the computational burden associated with the use of \texttt{\textbackslash mathchoice}.
-\item After version 2 of the package appeared on CTAN, it was pointed out
-to me that there was an issue of consistency between the form of `d'
-used in a derivative (upright or math-italic) and the form used in
-an integral. I had overlooked this matter completely and in version
-3 of the package remedied the omission with the differential command
-\texttt{\textbackslash dl}. A spacing option for \texttt{\textbackslash dl}
-was almost inevitable. From version 4 the partial analogue \texttt{\textbackslash dlp}
-has been added.
-\item Space before the differentiand was requested by a user. Once considered
-it became clear that there are (at least) two ways of thinking of
-a derivative: as $\diff y/x$, a ratio of differentials where $\dl y$
-is a unit and it makes no sense to insert space between the `d'
-and the `y', and as
-\[
-\diff!{F(x)}x
-\]
-where the function $F(x)$ is being operated on by $\diff{}/x$ and
-it is natural to insert space between the `d' and the `F'. With
-that realisation came the need for a simple switch-like package option
-(\verb`spaced`) to turn spacing on or off, and a switch-like argument
-(\verb`!`) to countermand the package option in exceptional cases
-(version 4).
-\end{itemize}
+nor need the numbers in numerator and denominator be equal. \verb`\jacob`
+does \emph{not} check such things. It is perfectly possible to form
+unbalanced objects like
+\begin{centred}
+\verb`\[ \jacob{u,v,w}{x,y},\quad\jacob{u,v}{x,y,z}. \]` $\Longrightarrow$
+\[ \jacob{u,v,w}{x,y},\quad\jacob{u,v}{x,y,z}. \]
+\end{centred}
+Perhaps there are contexts where these are meaningful?
-\section{Version comparison}
+\subsection{Template \texttt{DIFJ}}
-\label{sec:Version-comparison}Unlike version 1, version 2 and later
-are built on the the \texttt{xtemplate} package which makes certain
-facilities available which it would be silly not to exploit. Hence
-the coding in the later versions is completely different and there
-are consequences.
-\begin{enumerate}
-\item From version 2.0
-\begin{enumerate}
-\item The \texttt{\textbackslash diffset} command, formerly used to tweak
-the display of derivatives, has been superseded by the \texttt{\textbackslash diffdef}
-command. \texttt{\textbackslash diffset} now sends a message warning
-of its obsolescence to the terminal and \LaTeX{} log but is otherwise
-functionless. It should not interfere with the compilation of a document
-but any intended fine-tuning of the display by means of the \texttt{\textbackslash diffset}
-command\texttt{ }will not eventuate. The warning message is: \texttt{Obsolete
-command: \textbackslash diffset has been superseded by the \textbackslash diffdef
-command.} \texttt{See the diffcoeff} \texttt{doc\-umentation for
-further information.} The \texttt{\textbackslash diffdef} command
-is discussed in §\ref{subsec:diffdef};
-\item The optional trailing argument used to indicate a point of evaluation
-or variables held constant is now delimited by square brackets, \texttt{{[}}
-and \texttt{{]}}, as other optional arguments are. For compatibility
-with version 1, versions 2 and 3 still accepted braces to delimit
-this argument but from version 4 of \texttt{diffcoeff} only the square-bracket
-delimited argument is accepted. (The use of braces around \emph{optional}
-arguments while once accepted is now deprecated in \texttt{xparse}
-on which \texttt{diffcoeff} depends);
-\item The commands \texttt{\textbackslash Diff}, \texttt{\textbackslash diffd}
-and \texttt{\textbackslash Diffd} used to construct derivatives from
-$D$, $\delta$ and $\Delta$ in version 1, are still available but
-deprecated. A new optional argument in the \texttt{\textbackslash diff}
-command offers these and a host of other possibilities and is now
-the preferred method of forming such variants; see §\ref{subsec:D-delta-Delta}.
-\end{enumerate}
-\item Version 3.0
-\begin{enumerate}
-\item adds a command, \texttt{\textbackslash dl} (from \emph{d}ifferentia\emph{l})
-to write differentials like $dx$ that occur in integrals and in other
-contexts in a manner consistent with the form used in derivatives.
-After all, if one is using upright `d's in derivatives, similarly
-upright `d's should occur in these other contexts;\footnote{This rather obvious lack in version 2 was pointed out to me by Sergio
-Callegari.}
-\item provides some simple spacing commands that can be useful for tweaking
-standard spacing.
-\end{enumerate}
-\item Version 3.1 enables the differential command to be used before forms
-like \texttt{\textbackslash vec\{x\}} (an overlooked possibility
-causing an error in earlier versions).
-\item Version 3.2
+\begin{wraptable}{o}{0.45\columnwidth}%
+\centering{}\caption{\texttt{DIFJ} defaults\protect\label{tab:DIFJ-defaults}}
+\begin{center}
+\begin{tabular}{lr}
+\toprule
+{\small key} & {\small default}\tabularnewline
+\midrule
+{\small op-symbol} & {\small\texttt{\textbackslash partial}}\tabularnewline
+{\small outer-Ldelim} & \tabularnewline
+{\small outer-Rdelim} & \tabularnewline
+\bottomrule
+\end{tabular}
+\par\end{center}\end{wraptable}%
+Jacobians are configurable. Like other commands of \verb`diffcoeff`,
+\verb`\jacob` gives access to a template, in this case \verb`DIFJ`,
+which is a child of the fundamental template \verb`DIF` and inherits
+most of its default values with only a few changes as shown in Table~\ref{tab:DIFJ-defaults}.
+Note that the keys \verb`outer-Ldelim` and \verb`outer-Rdelim` are
+both empty and, as with the differential, are \emph{always inserted}
+-- which is why they are empty by default.
+
+The lack of entries in Table~\ref{tab:DIFJ-defaults} is because
+many keys are irrelevant for forming jacobians -- it doesn't matter
+what their default values are. For a list of \emph{relevant} keys
+-- ones that have some effect on the appearance of a jacobian --
+see §\ref{subsec:DIFJ-(jacobian)}.
+
+\subsection{Syntax and variant forms}
+
+The \verb`\jacob` command has only three arguments. The syntax is
+simple:
+\begin{verbatim}
+ \jacob.name. {numer} {denom}
+\end{verbatim}
+The arguments have the following significance:
\begin{enumerate}
-\item allows negative spacing before the differential command \texttt{\textbackslash dl};
-\item fixes a bug in which an ordinary derivative as the differentiand of
-a partial derivative displayed as a partial derivative. It now displays,
-as it should, as an ordinary derivative.
+\item \verb`name` (optional) The dot-delimited name of a variant form of
+jacobian.
+\item \verb`numer` (mandatory) A comma list of variables forming the numerator
+of the jacobian.
+\item \verb`denom` (mandatory) A comma list of variables forming the denominator
+of the jacobian.
\end{enumerate}
-\item Version 4.0
+The default form of jacobian is an upright fraction with \verb`\partial`
+operators and parentheses around the variable lists in both numerator
+and denominator.
+
+If you want a jacobian in, say, slash-fraction form then once again
+the \verb`\difdef` command is used. The file \verb`diffcoeff5.def`
+contains the definition
+\begin{verbatim}
+ \difdef { j } { s } { style = / }
+\end{verbatim}
+To access this style, use the name -- which is at your discretion
+but here I have chosen \verb`s` (\verb`/` also suggests itself)
+-- between dots after the \verb`\jacob` command:
+\begin{centred}
+\verb`$ \jacob.s.{u,v,w}{x,y,z} $` $\Longrightarrow$ $ \jacob.s.{u,v,w}{x,y,z}. $
+\end{centred}
+If you want to change the operator symbol from \verb`\partial` to
+\verb`D`, as I have seen used, then the definition is:
+\begin{verbatim}
+ \difdef { j } { D } { op-symbol = D }
+\end{verbatim}
+(Again the name is at your discretion but \verb`D` seems obvious.)
+I have added this to the preamble of the present document, so that
+\begin{centred}
+\verb`\[ \jacob.D.{u,v,w}{x,y,z} \]` $\Longrightarrow$ \[ \jacob.D.{u,v,w}{x,y,z}.\]
+\end{centred}
+If you want square brackets rather than parentheses around the variable
+lists, then \verb`lvwrap-Ldelim` and \verb`lvwrap-Rdelim` (perhaps
+not intuitively) are the keys to change:
+\begin{verbatim}
+ \difdef { j } { [ }
+ {
+ lvwrap-Ldelim = \onemu\mleft [,
+ lvwrap-Rdelim = \mright ]
+ }
+\end{verbatim}
+the \verb`\onemu` giving, to my eye, better spacing between the \verb`\partial`
+symbols and the left brackets. This definition, too, has been added
+to the preamble so that
+\begin{centred}
+\verb`\[ \jacob.[.{u,v,w}{x,y,z} \]` $\Longrightarrow$ \[ \jacob.[.{u,v,w}{x,y,z}. \]
+\end{centred}
+
+\subsection{Changing defaults}
+
+To change the \emph{default} values of the \verb`DIFJ` template leave
+the second argument of the \verb`\difdef` command -- the \verb`variant-name`
+-- empty. For instance, if you want square brackets to be your default
+setting, the \verb`\difdef` command would be
+\begin{verbatim}
+ \difdef { j } {}
+ {
+ lvwrap-Ldelim = \onemu\mleft [,
+ lvwrap-Rdelim = \mright ]
+ }
+\end{verbatim}
+The only difference from the previous definition is the absence of
+the name from the second argument, which is now empty. If this definition
+were added to the preamble or to the \verb`.def` file of your current
+document then writing \verb`\jacob{u,v,w}{x,y,z}` would give the
+same result as obtained above with the variant \verb`\jacob.[.{u,v,w}{x,y,z}`.
+
+\chapter{Reference}
+
+\label{chap:Reference}For convenience I list here the commands of
+\verb`diffcoeff`, the template defaults, and the files and preamble
+definitions associated with this document.
+
+\section{Commands}
+
+\verb`\diff`, \verb`\diffp`, \verb`\difs`, \verb`\difsp`, \verb`\difc`,
+\verb`\difcp` (sometimes summarised as \verb`\difx` and \verb`\difxp`),
+ordinary and partial derivatives of upright-fraction, slash-fraction
+and compact forms respectively, with arguments (all optional unless
+otherwise indicated) and their delimiters:
\begin{enumerate}
-\item enables the insertion of a small space before the differentiand, either
-as the default behaviour (package option \verb`spaced`) or at explicit
-request (argument \verb`!` of the \verb`\diff` command); see §\ref{subsec:Spacing-before-derivand}.
-\item prevents the ligature $df$ that marred previous versions; this is
-now rendered $\dl f$.
-\item offers the document command \verb`\dlp` for the \emph{partial} differential;
-see §\ref{subsec:Partial-differential};
-\item no longer accepts \emph{the braced form} of the\emph{ }trailing optional
-argument specifying a point of evaluation or (for partial derivatives)
-variables held constant. This was a relic from version 1 of \texttt{diffcoeff},
-and has been deprecated since version 2.
+\item \verb`.name.` name of variant form of derivative;
+\item \verb`*` append-differentiand switch;
+\item \verb`*` reverse order of mandatory arguments 6 and 7 when differentiand
+is appended, available only if first star is also present;
+\item \verb`[order(s)]` order of differentiation, or comma list of orders
+of differentiation (for mixed partial derivatives);
+\item \verb`{differentiand}` (mandatory) function being differentiated;
+\item \verb`{variable(s)}` (mandatory) differentiation variable or, for
+mixed partial derivatives, comma list of differentiation variables;
+\item \verb`[pt of eval/const vars]` point of evaluation or, for partial
+derivatives, variables held constant.
\end{enumerate}
-\item Version 4.1
+\begin{description}
+\item [{\texttt{\textbackslash difoverride}}] order-override command with
+one mandatory argument:
+\end{description}
\begin{enumerate}
-\item changes the code for the \verb`long-var-wrap` setting to avoid a
-problem arising from a change in \verb`xtemplate`;
-\item improves spacing between operator and variable in \emph{denominators}
-of differential coefficients (e.g. prevents ligatures).
-\end{enumerate}
+\item \verb`{total order}` total order of differentiation; may be (and
+generally is) empty.\newpage{}
\end{enumerate}
-
-\section{Commands}
\begin{description}
-\item [{\texttt{\textbackslash diff}}] arguments (all optional unless
-otherwise indicated):
+\item [{\texttt{\textbackslash jacob}}] jacobian with arguments and delimiters:
+\end{description}
\begin{enumerate}
-\item .\emph{name}. for the given settings
-\item {*} append-differentiand switch
-\item {[}\emph{order}{]} or {[}\emph{comma-list of orders}{]} of differentiation
-\item {[}\emph{order-override}{]}
-\item ! countermand before-differentiand spacing of the \verb`spaced` package
-option
-\item \{\emph{differentiand}\} (mandatory)
-\item / slash-form switch
-\item \{\emph{comma list of differentiation variables}\} (mandatory)
-\item {[}\emph{point of evaluation/variables held constant}{]}
+\item \verb`.name.` (optional) name of variant form of jacobian;
+\item \verb`{numer}` (mandatory) comma list of variables forming the numerator;
+\item \verb`{denom}` (mandatory) comma list of variables forming the denominator.
\end{enumerate}
-\item [{\texttt{\textbackslash diffdef}}] arguments (all mandatory):
+\begin{description}
+\item [{\texttt{\textbackslash dl}}] differential with arguments and delimiters:
\begin{enumerate}
-\item \{\emph{name}\}
-\item \{\emph{key=value comma list}\}
+\item \verb`.name.` (optional) name of variant form of differential;
+\item \verb`[order(s)]` (optional) order of differential or comma list
+of orders of differentials;
+\item \verb`{variable(s)}` (mandatory) variable or comma list of variables;
+\item \verb`^{exponent}` (optional) exponent that overrides the \verb`order(s)`
+specification, raising each differential to this power.
\end{enumerate}
-\item [{\texttt{\textbackslash diffp}}] \texttt{= \textbackslash diff.p.}
-\item [{\texttt{\textbackslash dl}}] arguments (all optional):
+\item [{\texttt{\textbackslash difdef}}] with arguments (all mandatory)
+and delimiters:
\begin{enumerate}
-\item .\emph{name}. (as for \texttt{\textbackslash diff})
-\item \emph{minus sign} (optional, use only if negative spacing before the
-`d' is wanted)
-\item \emph{digit} (insert spacing of this number of mu before the `d')
+\item \verb`{id(s)}` comma list of one, some or all of the identifiers
+\verb`f`, \verb`s`, \verb`c`, \verb`fp`, \verb`sp`, \verb`cp`,
+\verb`j`, \verb`l` identifying upright fraction, slash fraction
+and compact ordinary derivatives; upright fraction, slash fraction
+and compact partial derivatives, and jacobians and differentials;
+\item \verb`{name}` name for a variant form of derivative; as well as letters
+may include numbers and other keyboard characters, but not braces,
+\verb`%` or \verb`#`;
+\item \verb`{settings}` comma list of changed \emph{key=value} settings.
\end{enumerate}
-\item [{\texttt{\textbackslash dpl}}] \texttt{= \textbackslash dl.p.}
\item [{\texttt{\textbackslash negmu}}] insert a $-1$ mu space
\item [{\texttt{\textbackslash nilmu}}] insert a $0$ mu space
\item [{\texttt{\textbackslash onemu}}] insert a $1$ mu space
\item [{\texttt{\textbackslash twomu}}] insert a $2$ mu space
\end{description}
-Deprecated (why try remembering the special names when the forms on
-the right are self-explanatory):
-\begin{description}
-\item [{\texttt{\textbackslash Diff}}] preferred form: \texttt{\textbackslash diff.D.}
-\item [{\texttt{\textbackslash diffd}}] preferred form \texttt{\textbackslash diff.delta.}
-\item [{\texttt{\textbackslash Diffd}}] preferred form\texttt{ \textbackslash diff.Delta.}
-\end{description}
+\section{Templates}
+
+The following lists record the default values of the templates used
+by \verb`diffcoeff`. A marginal \verb`>` indicates where a setting
+differs from that in \verb`DIF`, \verb`>>` where a setting differs
+from that in \verb`DIFF`, \verb`DIFS` or \verb`DIFC` as the case
+may be. For the latter templates, only \emph{relevant }keys have been
+listed -- those which affect the appearance of the derivative (or
+jacobian or differential).
+
+\subsection{\texttt{DIF} (primogenitor)}
+\begin{verbatim}
+ style = frac,
+ slash-tok = /,
+ slash-sep = 0 mu,
+ derivand-sep = 3 mu plus 1 mu minus 2 mu,
+ op-symbol = \mathrm{d},
+ op-symbol-alt = \KeyValue{ op-symbol },
+ op-order-nudge = 0 mu,
+ var-sup-nudge = 1 mu,
+ multi-term-sep = 2 mu plus 1 mu minus 1 mu,
+ term-sep-adjust = -1 mu,
+ long-var-wrap = d(v),
+ lvwrap-Ldelim = \mleft (,
+ lvwrap-Rdelim = \mright ),
+ lvwrap-sup-nudge = -2 mu,
+ outer-Ldelim = \left (,
+ outer-Rdelim = \right ),
+ elbowroom = 0 mu,
+ sub-nudge = -5 mu,
+ op-sub-nudge = 0 mu,
+ *derivand-sep = \KeyValue{ derivand-sep },
+ *op-set-left = false,
+ *italic-nudge = 0 mu,
+ *inner-wrap = false,
+ *inner-Ldelim = (,
+ *inner-Rdelim = ),
+ *outer-Ldelim = \big [,
+ *outer-Rdelim = \big ],
+ *sub-nudge = 0 mu
+\end{verbatim}
+
+\subsection{\texttt{DIFF} (upright-fraction derivative)}
+
+\label{subsec:DIFF-(upright-fraction-derivative)}Relevant keys and
+default values for template \verb`DIFF`.
+\begin{verbatim}
+ style = frac,
+ derivand-sep = 3 mu plus 1 mu minus 2 mu,
+ op-symbol = \mathrm{d},
+ op-symbol-alt = \KeyValue { op-symbol },
+ op-order-nudge = 0 mu,
+ var-sup-nudge = 1 mu,
+ multi-term-sep = 2 mu plus 1 mu minus 1 mu,
+ term-sep-adjust = -1 mu,
+ long-var-wrap = d(v),
+ lvwrap-Ldelim = \mleft (,
+ lvwrap-Rdelim = \mright ),
+ lvwrap-sup-nudge = -2 mu,
+ outer-Ldelim = \left (,
+ outer-Rdelim = \right ),
+ elbowroom = 0 mu,
+ sub-nudge = -5 mu,
+ *derivand-sep = \KeyValue { derivand-sep },
+ *op-set-left = false,
+ *italic-nudge = 0 mu
+\end{verbatim}
+
+\subsubsection{\texttt{DIFFP}}
+
+\verb`DIFF` defaults as above with these changes:
+\begin{verbatim}
+>> op-symbol = \partial,
+>> op-order-nudge = 1 mu,
+>> *italic-nudge = 3 mu
+\end{verbatim}
+
+\subsection{\texttt{DIFS} (slash-fraction derivative)}
+
+\label{subsec:DIFS-(slash-fraction-derivative)}Relevant keys and
+default values for template \verb`DIFS`.
+\begin{verbatim}
+> style = /,
+ slash-tok = /,
+ slash-sep = 0 mu,
+> derivand-sep = 2 mu plus 1 mu minus 2 mu,
+ op-symbol = \mathrm{d},
+ op-symbol-alt = \KeyValue { op-symbol },
+ op-order-nudge = 0 mu,
+ var-sup-nudge = 1 mu,
+ multi-term-sep = 2 mu plus 1 mu minus 1 mu,
+ term-sep-adjust = -1 mu,
+ long-var-wrap = d(v),
+ lvwrap-Ldelim = \mleft (,
+ lvwrap-Rdelim = \mright ),
+ lvwrap-sup-nudge = -2 mu,
+> outer-Ldelim = (,
+> outer-Rdelim = ),
+ elbowroom = 0 mu,
+> sub-nudge = 0 mu,
+ *derivand-sep = \KeyValue { derivand-sep },
+> *inner-wrap = true,
+ *inner-Ldelim = (,
+ *inner-Rdelim = ),
+ *outer-Ldelim = \big [,
+ *outer-Rdelim = \big ],
+ *sub-nudge = 0 mu
+\end{verbatim}
+
+\subsubsection{\texttt{DIFSP}}
+
+\verb`DIFS` defaults as above with these changes:
+\begin{verbatim}
+>> op-symbol = \partial,
+>> op-order-nudge = 1 mu
+\end{verbatim}
+
+\subsection{\texttt{DIFC} (compact derivative)}
+
+\label{subsec:DIFC-(compact-derivative)}Relevant keys and default
+values for template \verb`DIFC`.
+\begin{verbatim}
+> style = _ ,
+> derivand-sep = 1 mu plus 1 mu minus 2 mu,
+ op-symbol = \mathrm{d},
+ op-order-nudge = 0 mu,
+> multi-term-sep = 1 mu,
+> term-sep-adjust = 0 mu,
+> outer-Ldelim = \bigl (,
+> outer-Rdelim = \bigr ),
+ elbowroom = 0 mu,
+> sub-nudge = -2 mu,
+ op-sub-nudge = 0 mu,
+ *derivand-sep = \KeyValue { derivand-sep }
+\end{verbatim}
+
+\subsubsection{\texttt{DIFCP}}
+
+\verb`DIFC` defaults as above with these changes:
+\begin{verbatim}
+>> op-symbol = \partial,
+>> op-order-nudge = 1 mu
+\end{verbatim}
+
+\subsection{\texttt{DIFJ} (jacobian)}
+
+\label{subsec:DIFJ-(jacobian)}Relevant keys and default values for
+template \verb`DIFJ`.
+\begin{verbatim}
+ style = frac,
+ slash-tok = /,
+ slash-sep = 0 mu,
+> op-symbol = \partial,
+ op-symbol-alt = \KeyValue{ op-symbol },
+ lvwrap-Ldelim = \mleft (,
+ lvwrap-Rdelim = \mright ),
+> outer-Ldelim = ,
+> outer-Rdelim = ,
+ elbowroom = 0 mu ,
+ *op-set-left = false,
+ *italic-nudge = 0 mu
+\end{verbatim}
+
+\subsection{\texttt{DIFL} (differential)}
+
+\label{subsec:DIFL-(differential)}Relevant keys and default values
+for template \verb`DIFL`.
+\begin{verbatim}
+ op-symbol = \mathrm{d},
+ var-sup-nudge = 1 mu,
+ multi-term-sep = 2 mu plus 1 mu minus 1 mu,
+ term-sep-adjust = -1 mu,
+> long-var-wrap = dv,
+ lvwrap-Ldelim = \mleft (,
+ lvwrap-Rdelim = \mright ),
+ lvwrap-sup-nudge = -2 mu,
+> outer-Ldelim = \, ,
+> outer-Rdelim = ,
+ elbowroom = 0 mu
+\end{verbatim}
+
+\section{The file \texttt{diffcoeff5.def}}
+
+\label{sec:The-file-diffcoeff5.def}
+\begin{verbatim}
+% file `diffcoeff5.def'
+% definitions for variant forms
+% 2023/01/03
+% Andrew Parsloe ajparsloe@gmail.com
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% material derivative
+\difdef { f, s } { D }
+ { op-symbol = \mathrm{D} }
+% math italic
+\difdef { f, s, c } { d' }
+ {
+ op-symbol = d,
+ op-order-nudge = 1 mu
+ }
+\difdef { f, s, c } { D' }
+ {
+ op-symbol = D,
+ op-order-nudge = 1 mu
+ }
+% Greek
+\difdef { f, s } { gd }
+ { op-symbol = \delta }
+\difdef { f, s } { gD }
+ { op-symbol = \Delta }
+% spaceless appending
+\difdef { f, fp } { *0 }
+ {
+ *derivand-sep = 0 mu ,
+ outer-Ldelim = \mleft ( ,
+ outer-Rdelim = \mright )
+ }
+% tfrac, nonscalable
+\difdef { f, fp } { t }
+ {
+ style = tfrac ,
+ derivand-sep = 1 mu plus 1 mu minus 1 mu,
+ multi-term-sep = 0 mu ,
+ term-sep-adjust = 0 mu ,
+ lvwrap-sup-nudge = 0 mu ,
+ outer-Ldelim = \bigl (,
+ outer-Rdelim = \bigr ),
+ elbowroom = -2 mu ,
+ sub-nudge = -3 mu
+ }
+% slash fractions: 0=scalable,
+% 1=big, 2=Big, 3=bigg, 4=Bigg
+% but > 1 gives eyesores
+\difdef { s, sp } { 0 }
+ {
+ style = auto ,
+ outer-Ldelim = \left [ ,
+ outer-Rdelim = \right ] ,
+ sub-nudge = 0 mu ,
+ *inner-Ldelim = \mleft ( ,
+ *inner-Rdelim = \mright ),
+ *outer-Ldelim = \left [ ,
+ *outer-Rdelim = \right ]
+ }
+\difdef { s, sp } { 1 }
+ {
+ style = big ,
+ outer-Ldelim = \bigl (,
+ outer-Rdelim = \bigr ),
+ sub-nudge = -2.5 mu,
+ *inner-Ldelim = \bigl (,
+ *inner-Rdelim = \bigr ),
+ *outer-Ldelim = \bigl [,
+ *outer-Rdelim = \bigr ]
+ }
+% vrule point of evaluation
+\difdef { f, fp, s, sp } { | }
+ {
+ outer-Ldelim = \left . ,
+ outer-Rdelim = \right |,
+ sub-nudge = 0 mu
+ }
+% sq. bracket pt of eval.
+\difdef { f, fp, s, sp } { ] }
+ {
+ outer-Ldelim = \left [ ,
+ outer-Rdelim = \right ],
+ elbowroom = 1 mu,
+ sub-nudge = 0 mu
+ }
+% long var wrap
+\difdef { f, fp } { (dv) }
+ { long-var-wrap = (dv) }
+\difdef { f, fp } { dv }
+ { long-var-wrap = dv }
+% compact, D operator
+\difdef { c } { D }
+ {
+ op-symbol = \mathrm{D},
+ op-sub-nudge = -2mu
+ }
+\difdef { c } { D' }
+ {
+ op-symbol = D,
+ op-sub-nudge = -2mu
+ }
+% bold
+\difdef { c } { bD }
+ {
+ op-symbol = \mathbf{D},
+ op-sub-nudge = -2mu
+ }
+% differential style
+\difdef { c, cp } { dl }
+ { style = dl }
+%%%%%%%%%%% differential %%%%%%%%%%
+% partial
+\difdef { l } { p }
+ { op-symbol = \partial }
+% bold
+\difdef { l } { b }
+ { op-symbol = \mathrm{d}\mathbf }
+
+% line elements: Pythagoras (+)
+\difdef { l } { + }
+ {
+ multi-term-sep = 0 mu +,
+ term-sep-adjust = 0 mu ,
+ outer-Ldelim =
+ }
+% Minkowski (-)
+\difdef { l } { - }
+ {
+ multi-term-sep = 0 mu -,
+ term-sep-adjust = 0 mu ,
+ outer-Ldelim =
+ }
+%%%%%%%%%% jacobian %%%%%%%%%%
+% slash fraction
+\difdef { j } { s }
+ { style = / }
+\end{verbatim}
+
+\section{Preamble definitions}
+
+\label{sec:Preamble-definitions}The preamble to the present document
+contains the command
+\begin{verbatim}
+\usepackage[def-file=diffcoeff5,spaced=-1]{diffcoeff}
+\end{verbatim}
+and definitions:
+\begin{verbatim}
+% nabla in numer, d in denom
+\difdef { f, s } { n }
+ {
+ op-symbol = \nabla,
+ op-symbol-alt = \mathrm{d}
+ }
+% no sub nudge (a sea of white space)
+\difdef { fp } { wsp }
+ { sub-nudge = 0 mu }
+% align op left; no italic nudge
+\difdef { f } { left0 }
+ {
+ *op-set-left = true,
+ *italic-nudge = 0 mu
+ }
+% align op left; italic nudge
+\difdef { fp } { left }
+ {
+ op-symbol = \partial,
+ op-order-nudge = 1 mu,
+ *op-set-left = true,
+ *italic-nudge = 3 mu
+ }
+% partial variant of \diff
+\difdef { f } { p }
+ {
+ op-symbol = \partial,
+ op-order-nudge = 1 mu
+ }
+% partial, 3mu sep of terms
+\difdef { fp, sp } { 3mu }
+ { multi-term-sep = 3 mu }
+% D jacobian
+\difdef { j } { D }
+ { op-symbol = D }
+% square bracket jabobian
+\difdef { j } { [ }
+ {
+ lvwrap-Ldelim = \onemu\mleft [,
+ lvwrap-Rdelim = \mright ]
+ }
+% mimicking the \Braket command
+% of the braket package
+\difdef{ s }{ bk }
+ {
+ slash-tok = ,
+ op-symbol = ,
+ multi-term-sep = 3mu\middle|\mskip3mu ,
+ outer-Ldelim=\left\langle ,
+ outer-Rdelim=\right\rangle
+ }
+\NewDocumentCommand \Braket { m }
+ {
+ \difoverride {\negmu}
+ \difs.bk.{}{#1}[]
+ }
+\end{verbatim}
+
+\section{\texttt{\textbackslash DeclareChildTemplate}}
+
+\verb`xtemplate` provides only a single function, \verb`\DeclareRestrictedTemplate`,
+for creating a child template from a parent. \emph{All} the keys of
+the child template are present in the parent. The child inherits not
+only the keys of the parent but the default settings of those keys.
+Some of those settings are `marked' so that they cannot be changed
+by any \emph{instance} of the child (the \emph{restricted} keys) .
+
+Unfortunately there is no similar function available in \verb`xtemplate`
+at present by which one can create a child with \emph{new} as well
+as restricted default values. I found I could achieve this functionality
+with the following code cobbled together from publicly declared functions
+in \verb`xtemplate`.
+\begin{verbatim}
+% Child template with both new and restricted defaults
+% #1 object; #2 parent template; #3 child template;
+% #4 restricted, #5 new defaults (both key=value)
+\NewDocumentCommand \DeclareChildTemplate { m m m m m }
+ {
+ \DeclareRestrictedTemplate {#1} {#2} {#3} {}
+ \EditTemplateDefaults {#1} {#3} {#5}
+ \DeclareRestrictedTemplate {#1} {#3} {#3} {#4}
+ }
+\end{verbatim}
+The first \verb`\DeclareRestrictedTemplate` call creates the child
+template \verb`#3` from the parent template \verb`#2`, inheriting
+all its keys and default values. \emph{No} restrictions are imposed
+at this stage because the following \verb`\EditTemplateDefaults`
+would immediately cancel them. That statement specifies the \emph{new}
+defaults \verb`#5` of the child -- those that differ from the parent.
+The default settings \verb`#4` of the parent that are restricted
+to particular values in the child are imposed by the second \verb`\DeclareRestrictedTemplate`
+call through the aritifice of treating the child template \verb`#3`
+as a child of itself. In that way its new defaults are not lost.
\end{document}
diff --git a/macros/latex/contrib/diffcoeff/diffcoeff4.pdf b/macros/latex/contrib/diffcoeff/diffcoeff4.pdf
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+/Root 769 0 R
+/Info 770 0 R
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+749908
+%%EOF
diff --git a/macros/latex/contrib/diffcoeff/diffcoeff4.sty b/macros/latex/contrib/diffcoeff/diffcoeff4.sty
new file mode 100644
index 0000000000..3125ae5902
--- /dev/null
+++ b/macros/latex/contrib/diffcoeff/diffcoeff4.sty
@@ -0,0 +1,744 @@
+% This is file `diffcoeff4.sty'.
+%
+% This work may be distributed and/or modified under the conditions
+% of the LaTeX Project Public License, either version 1.3c
+% (2008-05-04) of this license or any later version; see
+% http://www.latex-project.org/lppl.txt
+%
+% Andrew Parsloe ajparsloe@gmail.com
+%
+\RequirePackage{expl3}
+\RequirePackage{xparse,l3keys2e,xtemplate}
+\ProvidesExplPackage {diffcoeff4} {2022/07/30} {4.2}
+ {Write differential coefficients easily and consistently.}
+%
+\keys_define:nn { diffcoeff4 }
+ {
+ ISO .bool_set:N = \l__diffcoeff_ISO_bool,
+ spaced .int_set:N = \l__diffcoeff_spaced_int,
+ spaced .default:n = 1,
+ spaced .initial:n = 0,
+ def-file .tl_gset:N = \g__diffcoeff_def_tl,
+ def-file .initial:n = diffcoeff,
+ def-file .default:n = diffcoeff
+ }
+\ProcessKeysPackageOptions { diffcoeff4 }
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\cs_generate_variant:Nn \tl_if_eq:nnTF { nV }
+
+\tl_new:N \l__diffcoeff_oporder_tl
+\tl_new:N \l__diffcoeff_derivand_tl
+\tl_new:N \l__diffcoeff_type_tl
+\tl_new:N \l__diffcoeff_tot_order_tl
+\tl_new:N \l__diffcoeff_curr_num_tl
+\tl_new:N \l__diffcoeff_curr_var_tl
+\tl_new:N \l__diffcoeff_paren_tl
+
+\tl_const:Nn \c__diffcoeff_digits_tl { 1234567890 }
+
+\seq_new:N \l__diffcoeff_orders_seq
+\seq_new:N \l__diffcoeff_vars_seq
+\seq_new:N \l__diffcoeff_denom_seq
+\seq_new:N \l__diffcoeff_paren_seq
+
+\prop_new:N \l__diffcoeff_vars_prop
+
+\bool_new:N \l__diffcoeff_op_left_bool
+\bool_new:N \l__diffcoeff_single_var_bool
+\bool_new:N \l__diffcoeff_opwrap_bool
+\bool_new:N \l__diffcoeff_integ_bool
+\bool_new:N \l__diffcoeff_spaced_bool
+\bool_new:N \l__diffcoeff_altsep_bool
+
+\int_new:N \l__diffcoeff_vars_int
+\int_new:N \l__diffcoeff_format_int
+\int_new:N \l__diffcoeff_curr_tok_int
+\int_new:N \l__diffcoeff_curr_state_int
+\int_new:N \l__diffcoeff_nos_int
+\int_new:N \l__diffcoeff_parenvar_int
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\DeclareObjectType { derivative } { 3 }
+
+% defaults: ordinary deriv. values
+\DeclareTemplateInterface { derivative } { DERIV } { 3 }
+ {
+ op-symbol : tokenlist = d ,
+ op-symbol-alt : tokenlist = \KeyValue { op-symbol },
+ op-order-sep : muskip = 1 mu ,
+ derivand-sep : muskip = 3 mu plus 1 mu minus 2 mu,
+ long-var-wrap : choice { dv, d(v), (dv) }
+ = d(v) ,
+ denom-term-sep : muskip = 2 mu ,
+ term-sep-adjust : muskip = -1 mu ,
+ left-delim : tokenlist = \left . ,
+ right-delim : tokenlist = \right |,
+ elbowroom : muskip = 0 mu ,
+ subscr-nudge : muskip = 0 mu ,
+ *-derivand-sep : muskip = \KeyValue { derivand-sep },
+ *-op-left : boolean = false ,
+ *-italic-nudge : muskip = 3 mu ,
+ /-derivand-sep : muskip = \KeyValue { derivand-sep },
+ /-denom-term-sep : muskip = 1 mu ,
+ /-left-delim : tokenlist = ( ,
+ /-right-delim : tokenlist = ) ,
+ /-elbowroom : muskip = 0 mu ,
+ /-subscr-nudge : muskip = 0 mu ,
+ */-derivand-sep : muskip = \KeyValue { /-derivand-sep },
+ */-op-wrap : boolean = true
+ }
+% #1 order spec(seqvar); #2 order override(tlvar)
+% #3 derivand(tlvar); #4 denominator(seqvar)
+% #5 subscript(tlvar)
+\DeclareTemplateCode { derivative } { DERIV } { 3 }
+ {
+ op-symbol = \l__diffcoeff_op_tl,
+ op-symbol-alt = \l__diffcoeff_op_alt_tl,
+ op-order-sep = \l__diffcoeff_oporder_muskip,
+ derivand-sep = \l__diffcoeff_derivsep_muskip,
+ long-var-wrap = {
+ dv = \cs_set_eq:NN \__diffcoeff_wrap_longvars:nn
+ \__diffcoeff_wrap_longvars_dv:nn,
+ d(v) = \cs_set_eq:NN \__diffcoeff_wrap_longvars:nn
+ \__diffcoeff_wrap_longvars_dvi:nn,
+ (dv) = \cs_set_eq:NN \__diffcoeff_wrap_longvars:nn
+ \__diffcoeff_wrap_longvars_dvii:nn,
+ unknown = \cs_set_eq:NN \__diffcoeff_wrap_longvars:nn
+ \__diffcoeff_wrap_longvars_dvi:nn
+ },
+ denom-term-sep = \l__diffcoeff_varsep_muskip,
+ term-sep-adjust = \l__diffcoeff_sep_adj_muskip,
+ left-delim = \l__diffcoeff_ldelim_tl,
+ right-delim = \l__diffcoeff_rdelim_tl,
+ elbowroom = \l__diffcoeff_elbowrm_muskip ,
+ subscr-nudge = \l__diffcoeff_subnudge_muskip,
+ *-derivand-sep = \l__diffcoeff_derivsepi_muskip,
+ *-op-left = \l__diffcoeff_op_left_bool,
+ *-italic-nudge = \l__diffcoeff_opnudge_muskip,
+ /-derivand-sep = \l__diffcoeff_derivsepii_muskip,
+ /-denom-term-sep = \l_tmpb_muskip,
+ /-left-delim = \l__diffcoeff_ldelimi_tl,
+ /-right-delim = \l__diffcoeff_rdelimi_tl,
+ /-elbowroom = \l_tmpc_muskip,
+ /-subscr-nudge = \l_tmpd_muskip,
+ */-derivand-sep = \l__diffcoeff_derivsepiii_muskip,
+ */-op-wrap = \l__diffcoeff_opwrap_bool
+ }
+ {
+ \AssignTemplateKeys
+
+ \bool_if:NF\l__diffcoeff_integ_bool
+ {
+ \int_compare:nNnT { \l__diffcoeff_format_int } > { 1 }
+ { \__diffcoeff_slash_vals: }
+ \__diffcoeff_build:nnn { #1 } { #2 } { #3 }
+ }
+ }
+%%%%%%%%%%
+\cs_new:Npn \__diffcoeff_slash_vals:
+ {
+ \muskip_set:Nn \l__diffcoeff_varsep_muskip \l_tmpb_muskip
+ \muskip_set:Nn \l__diffcoeff_elbowrm_muskip \l_tmpc_muskip
+ \muskip_set:Nn \l__diffcoeff_subnudge_muskip \l_tmpd_muskip
+ \tl_set:NV \l__diffcoeff_ldelim_tl \l__diffcoeff_ldelimi_tl
+ \tl_set:NV \l__diffcoeff_rdelim_tl \l__diffcoeff_rdelimi_tl
+ }
+% #1 diff'and; #2 vars clist; #3 trailing arg
+\cs_new:Npn \__diffcoeff_build:nnn #1#2#3
+ {
+ \tl_set:Nn \l__diffcoeff_derivand_tl { #1 }
+ \seq_set_from_clist:Nn \l__diffcoeff_vars_seq { #2 }
+ \bool_if:nT
+ {
+ !\l__diffcoeff_opwrap_bool &&
+ \int_compare_p:nNn { \l__diffcoeff_format_int } > { 1 }
+ }
+ { \int_set:Nn \l__diffcoeff_format_int { 4 } }
+ \__diffcoeff_spaced:n { \l__diffcoeff_spaced_int }
+ \bool_if:nTF
+ {
+ ( \l__diffcoeff_altsep_bool && !\l__diffcoeff_spaced_bool )
+ || ( !\l__diffcoeff_altsep_bool && \l__diffcoeff_spaced_bool )
+ }
+ { \__diffcoeff_derivsep: }
+ { \tl_put_left:Nn \l__diffcoeff_derivand_tl { \mskip 0 mu } }
+ \tl_if_novalue:nF { #3 }
+ { \l__diffcoeff_ldelim_tl \mskip \l__diffcoeff_elbowrm_muskip }
+ \bool_if:NTF \l__diffcoeff_single_var_bool
+ {
+ \tl_set:Nx \l_tmpa_tl { \seq_use:Nn \l__diffcoeff_vars_seq { , } }
+ \__diffcoeff_single:NNN \l__diffcoeff_tot_order_tl \l__diffcoeff_derivand_tl \l_tmpa_tl
+ }
+ {
+ \int_zero:N \l_tmpa_int
+ \seq_mapthread_function:NNN \l__diffcoeff_orders_seq
+ \l__diffcoeff_vars_seq \__diffcoeff_map_orders:nn
+ \__diffcoeff_mixed:NNN \l__diffcoeff_tot_order_tl
+ \l__diffcoeff_derivand_tl \l__diffcoeff_denom_seq
+ }
+ \tl_if_novalue:nF { #3 }
+ {
+ \mskip \l__diffcoeff_elbowrm_muskip \l__diffcoeff_rdelim_tl
+ \tl_if_empty:nF { #3 }
+ {
+ \c_math_subscript_token
+ { \mskip \l__diffcoeff_subnudge_muskip { #3 } }
+ }
+ }
+ }
+%%%%%%%%%%%%%%%%%%%%
+\cs_new_protected:Npn \__diffcoeff_spaced:n #1
+ {
+ \int_case:nn { \int_sign:n { #1 } }
+ {
+ { 1 } { \bool_set_true:N \l__diffcoeff_spaced_bool }
+ { 0 } { \bool_set_false:N \l__diffcoeff_spaced_bool }
+ { -1 }
+ {
+ \int_compare:nNnTF { 1 } <
+ { \tl_count:N \l__diffcoeff_derivand_tl }
+ { \bool_set_true:N \l__diffcoeff_spaced_bool }
+ { \bool_set_false:N \l__diffcoeff_spaced_bool }
+ }
+ }
+ }
+\cs_new_protected:Npn \__diffcoeff_derivsep:
+ {
+ \tl_put_left:Nx \l__diffcoeff_derivand_tl
+ {
+ \int_case:nn { \l__diffcoeff_format_int }
+ {
+ { 0 } { \mskip \l__diffcoeff_derivsep_muskip }
+ { 1 } { \mskip \l__diffcoeff_derivsepi_muskip }
+ { 2 } { \mskip \l__diffcoeff_derivsepii_muskip }
+ { 3 } { \mskip \l__diffcoeff_derivsepiii_muskip }
+ { 4 } { \mskip \l__diffcoeff_derivsepiii_muskip }
+ }
+ }
+ }
+\cs_new:Npn \__diffcoeff_wrap_longvars_dv:nn #1#2
+ { \l__diffcoeff_op_alt_tl { {}#2 }^{ #1 } }
+\cs_new:Npn \__diffcoeff_wrap_longvars_dvi:nn #1#2
+ { \l__diffcoeff_op_alt_tl { {}(#2) }^{ #1 } }
+\cs_new:Npn \__diffcoeff_wrap_longvars_dvii:nn #1#2
+ { (\l__diffcoeff_op_alt_tl { {}#2) }^{ #1 } }
+% (ptl) form denom #1 from orders seq & #2 from vars seq
+\cs_new_protected:Npn \__diffcoeff_map_orders:nn #1#2
+ {
+ \tl_if_eq:nnTF { #1 } { 1 }
+ { \seq_put_right:Nn \l__diffcoeff_denom_seq { \l__diffcoeff_op_alt_tl { #2 } } }
+ {
+ \int_compare:nNnTF { \tl_count:n { #2 } } = { 1 }
+ {
+ \seq_put_right:Nn \l__diffcoeff_denom_seq
+ { \l__diffcoeff_op_alt_tl { #2 }^{ #1 } }
+ }
+ {
+ \seq_put_right:Nn \l__diffcoeff_denom_seq
+ { \__diffcoeff_wrap_longvars:nn { #1\vphantom{)} } { #2 } }
+ }
+ }
+ }
+% #1 order(tlvar) ; #2 diff'iand(tlvar); #3 denom(tlvar)
+\cs_new:Npn \__diffcoeff_single:NNN #1#2#3
+ {
+ \__diffcoeff_numer:N { #1 }
+ \__diffcoeff_form_deriv:NNn
+ \l__diffcoeff_oporder_tl
+ \l__diffcoeff_derivand_tl
+ { \__diffcoeff_denom_single:NN #1 #3 }
+ }
+% #1 total order; #2 derivand; #3 denom seq
+\cs_new_protected:Npn \__diffcoeff_mixed:NNN #1#2#3
+ {
+ \__diffcoeff_numer:N #1
+ \__diffcoeff_form_deriv:NNn
+ \l__diffcoeff_oporder_tl
+ \l__diffcoeff_derivand_tl
+ { \__diffcoeff_denom_sep:N #3 }
+ }
+\cs_new:Npn \__diffcoeff_denom_sep:N #1
+ {
+ \int_zero:N \l_tmpa_int
+ \seq_map_inline:Nn #1
+ {
+ \int_incr:N \l_tmpa_int ##1
+ \int_compare:nNnT { \l_tmpa_int } < { \l__diffcoeff_vars_int }
+ {
+ \seq_pop:NN \l__diffcoeff_orders_seq \l_tmpa_tl
+ \str_if_eq:VnTF \l_tmpa_tl { 1 }
+ { \mskip \l__diffcoeff_varsep_muskip }
+ {
+ \mskip \muskip_eval:n { \l__diffcoeff_varsep_muskip +
+ \l__diffcoeff_sep_adj_muskip }
+ }
+ }
+ }
+ }
+% #1(tl) total order
+\cs_new_protected:Npn \__diffcoeff_numer:N #1
+ {
+ \bool_if:NTF \l__diffcoeff_op_left_bool
+ {
+ \tl_set:Nn \l__diffcoeff_oporder_tl
+ { \mskip \l__diffcoeff_opnudge_muskip }
+ }
+ { \tl_clear:N \l__diffcoeff_oporder_tl }
+ \tl_put_right:No \l__diffcoeff_oporder_tl \l__diffcoeff_op_tl
+ \exp_args:NnV \tl_if_eq:nnF { 1 } #1
+ {
+ \tl_put_right:Nn \l__diffcoeff_oporder_tl
+ { \mskip \l__diffcoeff_oporder_muskip ^ { #1 } }
+ }
+ \bool_if:NT \l__diffcoeff_op_left_bool
+ { \tl_put_right:Nn \l__diffcoeff_oporder_tl { \hfill } }
+ }
+% #1 order; #2 var
+\cs_new_protected:Npn \__diffcoeff_denom_single:NN #1#2
+ {
+ \tl_if_eq:nVTF { 1 } #1
+ { \l__diffcoeff_op_alt_tl {}#2 }
+ {
+ \int_compare:nNnTF { \tl_count:N #2 } = { 1 }
+ { \l__diffcoeff_op_alt_tl {}#2^{ #1 } }
+ { \__diffcoeff_wrap_longvars:nn { #1\vphantom) } { #2 } }
+ }
+ }
+% #1 op+order; #2 diff'iand; #3 denom
+% 0 frac; 1 frac append; 2 slash ; 3 ( slash ) append; 4 slash append
+\cs_new:Npn \__diffcoeff_form_deriv:NNn #1#2#3
+ {
+ \int_case:nn { \l__diffcoeff_format_int }
+ {
+ { 0 } { \frac { #1 #2 } { #3 } }
+ { 1 } { \frac { #1 } { #3 } #2 }
+ { 2 } { #1 #2 / #3 }
+ { 3 } { ( #1 / #3 ) #2 }
+ { 4 } { #1 / #3 #2 }
+ }
+ }
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% differential
+% #1 variant; #2 = space in mu before d (0--9)
+% note \group_end placement for \vec{x} etc
+\NewDocumentCommand \dl { d.. t- m }
+ {
+ \group_begin:
+ \bool_set_true:N \l__diffcoeff_integ_bool
+ \bool_set_true:N \l__diffcoeff_single_var_bool
+ \seq_set_from_clist:Nn \l__diffcoeff_orders_seq { 1 }
+ \tl_set:Nn \l__diffcoeff_tot_order_tl { 1 }
+ \IfValueTF { #1 }
+ { \tl_set:Nn \l__diffcoeff_type_tl { .#1 } }
+ { \tl_set:Nn \l__diffcoeff_type_tl { } }
+ \UseInstance { derivative } { ord\l__diffcoeff_type_tl }
+ \c_empty_tl \c_empty_seq \c_empty_tl
+ \tl_if_in:NnTF \c__diffcoeff_digits_tl { #3 }
+ { \mskip \IfBooleanT #2 { - }#3 mu \l__diffcoeff_op_tl \group_end: }
+ { \l__diffcoeff_op_tl \group_end: {} #3 }
+ }
+\NewDocumentCommand \negmu {} { \mskip -1 mu }
+\NewDocumentCommand \nilmu {} { \mskip 0 mu }
+\NewDocumentCommand \onemu {} { \mskip 1 mu }
+\NewDocumentCommand \twomu {} { \mskip 2 mu }
+% derivative
+% #1(tl) = name of variant; #2(*)= append diff'iand boolean
+% #3(clist) = orders of diff. in each var.; #4(tl) = order override
+% #5(bool) spacing switch; #6(tl) = diff'iand; #7( / ) = slash boolean
+% #8(clist) = vars of diff.; #9(tl) = pt of eval./vars held const
+\NewDocumentCommand \diff { d.. s O{1} o t! >{\TrimSpaces} m t/ m !o }
+ {
+ \group_begin:
+ \IfBooleanTF #5
+ { \bool_set_true:N \l__diffcoeff_altsep_bool }
+ { \bool_set_false:N \l__diffcoeff_altsep_bool }
+ \seq_set_from_clist:Nn \l__diffcoeff_orders_seq { #3 }
+ \int_set:Nn \l_tmpb_int { \seq_count:N \l__diffcoeff_orders_seq }
+ \int_set:Nn \l__diffcoeff_vars_int { \clist_count:n { #8 } }
+ \int_compare:nNnTF { \l__diffcoeff_vars_int } = { 1 }
+ { \bool_set_true:N \l__diffcoeff_single_var_bool }
+ {
+ \int_compare:nNnTF { \l__diffcoeff_vars_int } < { \l_tmpb_int }
+ {
+ \msg_error:nnxxxx { diffcoeff } { numbers-conflict }
+ { \int_use:N \l__diffcoeff_vars_int } { \int_use:N \l_tmpb_int }
+ { \seq_use:Nn \l__diffcoeff_orders_seq { , } }
+ { \clist_use:nn { #8 } { , } }
+ }
+ { % pad orders seq if nec.
+ \int_step_inline:nnnn
+ { 1 + \l_tmpb_int } { 1 } { \l__diffcoeff_vars_int }
+ { \seq_put_right:Nn \l__diffcoeff_orders_seq { 1 } }
+ }
+ }
+ % override/calc total order
+ \IfValueTF { #4 }
+ { \tl_set:Nn \l__diffcoeff_tot_order_tl { #4 } }
+ {
+ \bool_if:NTF \l__diffcoeff_single_var_bool
+ { \tl_set:Nn \l__diffcoeff_tot_order_tl { #3 } }
+ {
+ \__diffcoeff_calc_tot_order:NN \l__diffcoeff_orders_seq
+ \l__diffcoeff_tot_order_tl
+ }
+ }
+ \IfValueTF { #1 }
+ { \tl_set:Nn \l__diffcoeff_type_tl { .#1 } }
+ { \tl_set:Nn \l__diffcoeff_type_tl { } }
+ % append? slash?
+ \int_zero:N \l__diffcoeff_format_int
+ \IfBooleanT #2 { \int_incr:N \l__diffcoeff_format_int }
+ \IfBooleanT #7 { \int_add:Nn \l__diffcoeff_format_int { 2 } }
+ \UseInstance { derivative } { ord\l__diffcoeff_type_tl } {#6}{#8}{#9}
+ \group_end:
+ } % end of \diff
+%%%%%%%%%%%%%%%%%%%
+% #2(seq) expr in; #1(tlv) expr out
+\cs_new:Npn \__diffcoeff_calc_tot_order:NN #1 #2
+ {
+ \tl_clear:N \l__diffcoeff_nos_tl
+ \exp_args:Nx\__diffcoeff_digest_expr:n { \seq_use:Nn #1 { + } }
+ \prop_if_empty:NTF \l__diffcoeff_vars_prop
+ { \tl_set:NV #2 \l__diffcoeff_nos_tl }
+ { \__diffcoeff_evaluate:NN \l__diffcoeff_vars_prop #2 }
+ }
+\cs_new:Npn \__diffcoeff_digest_expr:n #1
+ {
+ \tl_set:Nn \l__diffcoeff_curr_num_tl { + }
+ \tl_set:Nn \l__diffcoeff_paren_tl { +1 }
+ \tl_set:Nn \l__diffcoeff_nos_tl { 0 }
+ \int_zero:N \l__diffcoeff_curr_state_int
+ \int_zero:N \l__diffcoeff_curr_tok_int
+ \tl_map_inline:nn { #1+ }
+ {
+ \__diffcoeff_get_curr_ndx:nN { ##1 } \l__diffcoeff_curr_tok_int
+ \__diffcoeff_transitions:nNN { ##1 }
+ \l__diffcoeff_curr_state_int \l__diffcoeff_curr_tok_int
+ }
+ \int_set:Nn \l__diffcoeff_nos_int { \l__diffcoeff_nos_tl }
+ \tl_set:Nx \l__diffcoeff_nos_tl { \int_use:N \l__diffcoeff_nos_int }
+ \int_compare:nNnT { \l__diffcoeff_nos_int } = { 0 }
+ { \tl_clear:N \l__diffcoeff_nos_tl }
+ }
+% #1 curr tok (tl); #2 <== curr tok ndx (int)
+\cs_new_protected:Npn \__diffcoeff_get_curr_ndx:nN #1#2
+ {
+ \tl_if_in:NnTF \c__diffcoeff_digits_tl { #1 }
+ { \int_set:Nn #2 { 1 } } % digit
+ {
+ \str_case:nnF { #1 }
+ {
+ { + } { \int_set:Nn #2 { 0 } }
+ { - } { \int_set:Nn #2 { 0 } }
+ { ( } { \int_set:Nn #2 { 3 } }
+ { ) } { \int_set:Nn #2 { 4 } }
+ }
+ { \int_set:Nn #2 { 2 } } % var
+ }
+ }
+% #1(tl) curr tok; #2(int) curr state; #3(int) curr tok ndx
+\cs_new:Npn \__diffcoeff_transitions:nNN #1#2#3
+ {
+ \int_case:nn { #2 }
+ {
+ { 0 } % sgn + -
+ { \__diffcoeff_sgn_transitions:nNN { #1 }#2#3 }
+ { 1 } % num
+ { \__diffcoeff_num_transitions:nNN { #1 }#2#3 }
+ { 2 } % alg
+ { \__diffcoeff_alg_transitions:nNN { #1 }#2#3 }
+ { 4 } % )
+ { \__diffcoeff_rpar_transitions:nNN { #1 }#2#3 }
+ }
+ }
+% transitions from the signed state
+% #1(tl) curr tok; #2(int) 0, curr state; #3 curr tok ndx
+\cs_new_protected:Npn \__diffcoeff_sgn_transitions:nNN #1#2#3
+ {
+ \int_case:nnT { #3 }
+ {
+ { 0 } % tok = s
+ {
+ \tl_if_eq:nVTF { #1 } \l__diffcoeff_curr_num_tl
+ { \tl_set:Nn \l__diffcoeff_curr_num_tl { + } }
+ { \tl_set:Nn \l__diffcoeff_curr_num_tl { - } }
+ }
+ { 1 } % tok = d
+ { \tl_put_right:Nn \l__diffcoeff_curr_num_tl { #1 } }
+ { 2 } % tok = v
+ {
+ \tl_put_right:Nn \l__diffcoeff_curr_num_tl { 1 }
+ \tl_set:Nn \l__diffcoeff_curr_var_tl { #1 }
+ }
+ { 3 } % tok = (
+ {
+ \seq_push:NV \l__diffcoeff_paren_seq \l__diffcoeff_paren_tl
+ \tl_put_left:NV \l__diffcoeff_paren_tl \l__diffcoeff_curr_num_tl
+ \tl_set:Nn \l__diffcoeff_curr_num_tl { + }
+ \int_set:Nn #3 { 0 }
+ }
+ }
+ { \int_set_eq:NN #2 #3 }
+ }
+% transitions from the numeric state
+% #1 = curr. tok.; #2 = 0, curr. state; #3 curr. tok. index
+\cs_new_protected:Npn \__diffcoeff_num_transitions:nNN #1#2#3
+ {
+ \int_case:nnT { #3 }
+ {
+ { 0 } % tok = s
+ {
+ \tl_put_right:NV\l__diffcoeff_nos_tl
+ { \l__diffcoeff_paren_tl * \l__diffcoeff_curr_num_tl }
+ \tl_set:Nn \l__diffcoeff_curr_num_tl { #1 }
+ }
+ { 1 } % tok = d
+ { \tl_put_right:Nn \l__diffcoeff_curr_num_tl { #1 } }
+ { 2 } % tok = v
+ {
+ \tl_if_in:nnTF { ^ \times * / \div } { #1 }
+ {
+ \msg_error:nnxxx { diffcoeff } { order-specification }
+ { \seq_use:Nn \l__diffcoeff_orders_seq { , } }
+ { #1 } { number }
+ }
+ { \tl_set:Nn \l__diffcoeff_curr_var_tl { #1 } }
+ }
+ { 3 } % tok = (
+ {
+ \seq_push:NV \l__diffcoeff_paren_seq \l__diffcoeff_paren_tl
+ \tl_put_left:Nn \l__diffcoeff_paren_tl { * }
+ \tl_put_left:NV \l__diffcoeff_paren_tl \l__diffcoeff_curr_num_tl
+ \tl_set:Nn \l__diffcoeff_curr_num_tl { + }
+ \int_set:Nn #3 { 0 }
+ }
+ { 4 } % tok = )
+ {
+ \tl_put_right:NV \l__diffcoeff_nos_tl
+ { \l__diffcoeff_paren_tl * \l__diffcoeff_curr_num_tl }
+ }
+ }
+ {
+ \int_set_eq:NN #2 #3 }
+ }
+% transitions from the algebraic state
+% #1 = curr. tok.; #2 = 2, curr. state; #3 curr. tok. index
+\cs_new:Npn \__diffcoeff_alg_transitions:nNN #1#2#3
+ {
+ \int_case:nnT { #3 }
+ {
+ { 0 } % tok = s
+ {
+ \int_compare:nNnTF { \l__diffcoeff_parenvar_int } = { 0 }
+ {
+ \__diffcoeff_store_var:NNN \l__diffcoeff_curr_var_tl
+ \l__diffcoeff_paren_tl \l__diffcoeff_curr_num_tl
+ \tl_clear:N \l__diffcoeff_curr_var_tl
+ \tl_set:Nn \l__diffcoeff_curr_num_tl { #1 }
+ }
+ {
+ \tl_put_right:Nn \l__diffcoeff_curr_var_tl { #1 }
+ \int_set:Nn #3 { 2 }
+ }
+ }
+ { 1 } % tok = d
+ {
+ \tl_put_right:Nn \l__diffcoeff_curr_var_tl { #1 }
+ \int_set:Nn #3 { 2 }
+ }
+ { 2 } % tok = v
+ { \tl_put_right:Nn \l__diffcoeff_curr_var_tl { #1 } }
+ { 3 } % tok = (
+ {
+ \tl_put_right:Nn \l__diffcoeff_curr_var_tl { #1 }
+ \int_set:Nn #3 { 2 }
+ \int_incr:N \l__diffcoeff_parenvar_int
+ }
+ { 4 } % tok = )
+ {
+ \int_compare:nNnTF { \l__diffcoeff_parenvar_int } = { 0 }
+ {
+ \__diffcoeff_store_var:NNN \l__diffcoeff_curr_var_tl
+ \l__diffcoeff_paren_tl \l__diffcoeff_curr_num_tl
+ \tl_clear:N \l__diffcoeff_curr_var_tl
+ }
+ {
+ \tl_put_right:Nn \l__diffcoeff_curr_var_tl { #1 }
+ \int_set:Nn #3 { 2 }
+ \int_decr:N \l__diffcoeff_parenvar_int
+ }
+ }
+ }
+ { \int_set_eq:NN #2 #3 }
+ }
+% transitions from the ) state
+% #1 = curr. tok.; #2 = 4, curr. state; #3 curr. tok. index
+\cs_new:Npn \__diffcoeff_rpar_transitions:nNN #1#2#3
+ {
+ \int_compare:nNnTF { \int_mod:nn { #3 } { 4} } = { 0 }
+ {
+ \tl_set:Nn \l__diffcoeff_curr_num_tl { #1 }
+ \seq_pop:NN \l__diffcoeff_paren_seq \l__diffcoeff_paren_tl
+ \int_set_eq:NN #2 #3
+ }
+ {
+ \msg_error:nnxxx { diffcoeff } { order-specification }
+ { \seq_use:Nn \l__diffcoeff_orders_seq { , } } { #1 } { ) }
+ }
+ }
+% #1 is var. (tlvar); #2 is num. (tlvar); #3 num. coeff. (tlvar)
+\cs_new:Npn \__diffcoeff_store_var:NNN #1#2#3
+ {
+ \prop_get:NVNF \l__diffcoeff_vars_prop #1 \l_tmpa_tl
+ { \tl_clear:N \l_tmpa_tl }
+ \tl_put_right:NV \l_tmpa_tl { #2 * #3 }
+ \prop_put:NVV \l__diffcoeff_vars_prop #1 \l_tmpa_tl
+ }
+% #1 (propv) key=var, val=coeff; #2 <= total order
+\cs_new_protected:Npn \__diffcoeff_evaluate:NN #1#2
+ {
+ \prop_map_inline:Nn #1 { \seq_put_left:Nn \l_tmpa_seq { ##1 } }
+ \seq_sort:Nn \l_tmpa_seq
+ {
+ \int_compare:nNnTF { \tl_count:n { ##1 } } < { \tl_count:n { ##2 } }
+ { \sort_return_same: } { \sort_return_swapped: }
+ }
+ \seq_map_inline:Nn \l_tmpa_seq
+ {
+ \prop_pop:NnN #1 { ##1 } \l_tmpb_tl
+ \seq_put_right:Nx \l_tmpb_seq { \int_eval:n \l_tmpb_tl }
+ }
+ \tl_clear:N \l_tmpa_tl
+ \seq_mapthread_function:NNN \l_tmpa_seq \l_tmpb_seq
+ \__diffcoeff_tot_order:nn
+ \exp_args:NV \tl_if_head_eq_charcode:nNTF \l_tmpa_tl +
+ {
+ \tl_set:Nx \l_tmpb_tl { \tl_tail:N \l_tmpa_tl }
+ \int_compare:nNnT { \l__diffcoeff_nos_int } > { 0 }
+ { \tl_put_left:Nn \l__diffcoeff_nos_tl { + } }
+ \tl_concat:NNN #2 \l_tmpb_tl \l__diffcoeff_nos_tl
+ }
+ {
+ \int_compare:nNnTF { \l__diffcoeff_nos_int } > { 0 }
+ { \tl_concat:NNN #2 \l__diffcoeff_nos_tl \l_tmpa_tl }
+ { \tl_concat:NNN #2 \l_tmpa_tl \l__diffcoeff_nos_tl }
+ }
+ \tl_set_rescan:Nno #2 { } #2
+ }
+\cs_new:Npn \__diffcoeff_tot_order:nn #1#2
+ {
+ \int_compare:nNnTF { #2 } > { 0 }
+ {
+ \int_compare:nNnTF { #2 } = { 1 }
+ { \tl_put_left:Nn \l_tmpa_tl { +#1 } }
+ { \tl_put_left:Nn \l_tmpa_tl { +#2#1 } }
+ }
+ {
+ \int_compare:nNnT { #2 } < { 0 }
+ {
+ \int_compare:nNnTF { #2 } = { -1 }
+ { \tl_put_right:Nn \l_tmpa_tl { -#1 } }
+ { \tl_put_right:Nn \l_tmpa_tl { #2#1 } }
+ }
+ }
+ }
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% create new instances or edit existing ones
+% #1 = name; #2 = key-value list
+\NewDocumentCommand \diffdef { > { \TrimSpaces } m m }
+ {
+ \tl_if_empty:nTF { #1 }
+ {
+ \EditTemplateDefaults { derivative }
+ { DERIV } { #2 }
+ \EditInstance { derivative } { ord } { #2 }
+ }
+ {
+ \IfInstanceExistTF { derivative } { ord.#1 }
+ { \EditInstance { derivative } { ord.#1 } { #2 } }
+ {
+ \DeclareInstance { derivative } { ord.#1 }
+ { DERIV } { #2 }
+ }
+ }
+ }
+% relic from version 1
+\NewDocumentCommand \diffset { o }
+ { \msg_warning:nn { diffcoeff } { obsolete } }
+
+% ordinary & D
+\DeclareInstance { derivative } { ord } { DERIV } { }
+\bool_if:NTF \l__diffcoeff_ISO_bool
+ {
+ \diffdef { }
+ {
+ op-symbol = \mathrm{d},
+ op-order-sep = 0 mu ,
+ left-delim = \left ( ,
+ right-delim = \right ) ,
+ subscr-nudge = -6 mu
+ }
+ \diffdef { D } { op-symbol = \mathrm{D} }
+ }
+ { \diffdef { D } { op-symbol = D } }
+
+% partial
+\diffdef { p }
+ {
+ op-symbol = \partial ,
+ left-delim = \left ( ,
+ right-delim = \right ) ,
+ subscr-nudge = -6 mu
+ }
+\NewDocumentCommand \diffp {} { \diff.p. }
+\NewDocumentCommand \dlp {} { \dl.p. }
+
+% delta
+\diffdef { delta }
+ {
+ op-symbol = \delta ,
+ op-order-sep = 0 mu
+ }
+\diffdef { Delta }
+ {
+ op-symbol = \Delta ,
+ op-order-sep = 0 mu
+ }
+% for compatibility with version 1
+\NewDocumentCommand \Diff { } { \diff.D. }
+\NewDocumentCommand \diffd { } { \diff.delta. }
+\NewDocumentCommand \Diffd { } { \diff.Delta. }
+
+% user-defined
+\file_if_exist:nT { \g__diffcoeff_def_tl.def }
+ { \file_input:n { \g__diffcoeff_def_tl.def } }
+%%%%%%%%%%%%%%%%%%%%
+% Jacobian
+\NewDocumentCommand \jacob { m t/ m }
+ {
+ \group_begin:
+ \IfBooleanTF #2
+ { \partial(#1) / \partial(#3) }
+ { \frac{ \partial(#1) } { \partial(#3) } }
+ \group_end:
+ }
+%%%%%%%%%%%%%%%%%%%%
+% messages
+\msg_new:nnn { diffcoeff } { order-specification }
+ {
+ #3~followed~by~#2~in~the~order~specification~[#1]~\msg_line_context:.~
+ Diffcoeff~cannot~calculate~the~overall~order~of~differentiation~in~
+ this~case.~Use~the~order-override~option~to~enter~the~overall~order.
+ }
+\msg_new:nnn { diffcoeff } { obsolete }
+ {
+ Obsolete~command:~\diffset is~superseded~by~the~\diffdef\
+ command.~\msg_see_documentation_text:n { diffcoeff }
+ }
+\msg_new:nnn { diffcoeff } { numbers-conflict }
+ {
+ #2~orders~of~differentiation~specified~for~#1~variables;~
+ orders~[#3]\ (\msg_line_context:)~for~variables~#4.
+ }
+% end of file diffcoeff4.sty \ No newline at end of file
diff --git a/macros/latex/contrib/diffcoeff/diffcoeff4.tex b/macros/latex/contrib/diffcoeff/diffcoeff4.tex
new file mode 100644
index 0000000000..fa8a06be0d
--- /dev/null
+++ b/macros/latex/contrib/diffcoeff/diffcoeff4.tex
@@ -0,0 +1,2272 @@
+%% LyX 2.4.0-alpha3 created this file. For more info, see https://www.lyx.org/.
+%% Do not edit unless you really know what you are doing.
+\documentclass[english]{article}
+\usepackage{lmodern}
+\renewcommand{\sfdefault}{lmss}
+\renewcommand{\ttdefault}{lmtt}
+\usepackage[T1]{fontenc}
+\usepackage{textcomp}
+\usepackage[latin9]{inputenc}
+\synctex=-1
+\usepackage{color}
+\definecolor{shadecolor}{rgb}{1, 0.667969, 0.5}
+\usepackage{babel}
+\usepackage{cprotect}
+\usepackage{wrapfig}
+\usepackage{booktabs}
+\usepackage{calc}
+\usepackage{framed}
+\usepackage{url}
+\usepackage{amsmath}
+\usepackage{amssymb}
+\usepackage{esint}
+\usepackage[unicode=true,pdfusetitle,
+ bookmarks=true,bookmarksnumbered=true,bookmarksopen=true,bookmarksopenlevel=2,
+ breaklinks=true,pdfborder={0 0 1},backref=section,colorlinks=true,pdfpagemode=FullScreen]
+ {hyperref}
+\hypersetup{
+ pdfborderstyle=}
+
+\makeatletter
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% LyX specific LaTeX commands.
+\newcommand{\noun}[1]{\textsc{#1}}
+%% Because html converters don't know tabularnewline
+\providecommand{\tabularnewline}{\\}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Textclass specific LaTeX commands.
+\newenvironment{centred}%
+ {\begin{center}\baselineskip=13pt\parskip=1pt }{\end{center}}
+\newenvironment{example}%
+{\begin{center}\ttfamily}{\end{center}}
+\newenvironment{lyxcode}
+ {\par\begin{list}{}{
+ \setlength{\rightmargin}{\leftmargin}
+ \setlength{\listparindent}{0pt}% needed for AMS classes
+ \raggedright
+ \setlength{\itemsep}{0pt}
+ \setlength{\parsep}{0pt}
+ \normalfont\ttfamily}%
+ \item[]}
+ {\end{list}}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% User specified LaTeX commands.
+\usepackage[def-file=diffcoeff-doc]{diffcoeff}[=v4]
+
+\makeatother
+
+\begin{document}
+\title{\texttt{diffcoeff}~\\
+ a \LaTeX{} package to ease\texttt{ }the~\\
+ writing of differential coefficients \\
+ Version 4.2}
+\author{Andrew Parsloe\\
+{\small (ajparsloe@gmail.com)}}
+\maketitle
+\begin{abstract}
+\noindent This package eases the consistent writing of ordinary, partial
+and other derivatives of arbitrary (algebraic or numeric) order. For
+mixed partial derivatives, the total order of differentiation is calculated
+by the package. Optional arguments allow for points of evaluation
+(ordinary derivatives), or variables held constant (partial derivatives),
+and the placement of the differentiand in numerator or appended. The
+package uses \texttt{xtemplate}, allowing systematic fine-tuning of
+the display and generation and use of variant forms, including derivatives
+built from $D$, $\Delta$ or $\delta$. A command for differentials
+ensures the $\dl x$ (or $\dl.up.x$) used in integrals is consistent
+with the form used in derivatives.
+\end{abstract}
+\noindent %
+\noindent\begin{minipage}[t]{1\columnwidth}%
+\begin{shaded}%
+
+\subsubsection*{Version 4.2/version 5.0 incompatibility}
+
+Version 4.2 of \verb`diffcoeff` is issued at the same time as version
+5.0. The latter is a complete rewrite of the package with many changes
+to the user interface, arising above all from separating the fraction
+types into separate commands (\verb`\diff`, \verb`\diffp` for upright
+fractions; \verb`\difs`, \verb`\difsp` for slash fractions; and
+\verb`\difc`, \verb`\difcp` for a new, compact style of derivative).
+Although some elements of the earlier version are carried over, most
+documents that use version 4 will fail to compile properly with version
+5. To enable older documents to continue to compile, the \verb`\usepackage`
+statement in the preamble needs a trailing optional argument added
+to it:
+\begin{verbatim}
+ \usepackage[<options>]{diffcoeff}[=v4]
+\end{verbatim}
+The trailing argument \verb`[=v4]` (no spaces!) ensures \verb`diffcoeff4.sty`
+rather than \verb`diffcoeff.sty` is used to compile the document.
+Otherwise, version 4.2 makes no visible change to \verb`diffcoeff`
+version 4.1 other than to documentation. (It also tidies a line of
+code for the differential command \verb`\dl`.)\end{shaded}%
+\end{minipage}
+
+\tableofcontents{}
+
+\section{Introduction}
+
+The \LaTeX{} package \texttt{diffcoeff} is written in the expl3 language
+of \LaTeX 3\texttt{ }and requires the bundles \texttt{l3kernel} which
+is now part of standard \LaTeX{} (since early 2020) and \texttt{l3packages}
+(the latter for the \texttt{xparse}, \texttt{l3keys2e} and especially
+\texttt{xtemplate} packages\texttt{)}. The package is loaded by entering
+\begin{lyxcode}
+\textbackslash usepackage{[}<options>{]}\{diffcoeff\}{[}=v4{]}
+\end{lyxcode}
+in the preamble of your document, where \verb`<options>` are package
+options input by the user; see below. The trailing optional argument,
+\verb`[=v4]`, is necessary to ensure your document compiles with
+version 4 of \verb`diffcoeff` rather than the new version 5 in which
+there are many changes to the user interface.
+
+\subsubsection*{Note on terminology}
+
+I refer throughout to the quantity or function being differentiated
+as the \emph{differentiand} or \emph{derivand }(in line with \emph{integrand},
+\emph{operand}, etc.).
+
+\subsubsection*{New in version 4.0}
+
+(See §\ref{sec:Version-comparison} for a comparison of versions.)
+Version 4.0
+\begin{enumerate}
+\item enables the insertion of a small space before the differentiand, either
+as the default behaviour (package option \verb`spaced`) or at explicit
+request (argument \verb`!` of the \verb`\diff` command); see §\ref{subsec:Spacing-before-derivand};
+\item prevents the ligature $df$ that marred previous versions; this is
+now rendered $\dl f$;
+\item offers the document command \verb`\dlp` for the \emph{partial} differential;
+see §\ref{subsec:Partial-differential};
+\item no longer accepts \emph{the braced form} of the\emph{ }trailing optional
+argument specifying a point of evaluation or (for partial derivatives)
+variables held constant. This was a relic from version 1 of \texttt{diffcoeff},
+and has been deprecated since version 2.
+\end{enumerate}
+
+\subsubsection*{New in version 4.1}
+\begin{enumerate}
+\item changes the code handling the \verb`long-var-wrap` setting to avoid
+a problem with a change in \verb`xtemplate` (see \url{https://tex.stackexchange.com/questions/646976/error-with-package-diffcoeff})\footnote{Based on a suggestion from \noun{Joseph Wright}.};
+\item prevents (hitherto overlooked) ligatures in the \emph{denominators}
+of differential coefficients.
+\end{enumerate}
+
+\subsubsection*{New in version 4.2}
+\begin{enumerate}
+\item tidies a line of code in the definition of the differential (has no
+visible effect);
+\item amends documentation in light of the issue of version 5 and the resulting
+interface changes.
+\end{enumerate}
+
+\subsection{Package options}
+
+\label{subsec:Package-options}There are three package options, which
+are entered in a comma-separated list in the optional argument of
+the \texttt{\textbackslash usepackage} command.
+\begin{enumerate}
+\item The first is a switch, \texttt{ISO}, which turns on formatting conforming
+to ISO recommendations, principally upright `d's:
+\begin{lyxcode}
+\textbackslash usepackage{[}ISO{]}\{diffcoeff\}{[}=v4{]}
+\end{lyxcode}
+The full effect of this option is disscussed in §\ref{sec:Changing-defaults}.
+\item The second is another switch, \texttt{spaced}, and \emph{is new with
+version 4 }of \texttt{diffcoeff}. This switch ensures a small space
+is inserted before the differentiand:
+\begin{lyxcode}
+\textbackslash usepackage{[}spaced{]}\{diffcoeff\}{[}=v4{]}
+\end{lyxcode}
+This is discussed in §\ref{subsec:Spacing-before-derivand}.
+\item The third requires a filename \texttt{<filename>} for a file \texttt{<filename>.def}
+containing definitions of variant forms of derivative:
+\begin{lyxcode}
+\textbackslash usepackage{[}def-file=<filename>{]}\{diffcoeff\}{[}=v4{]}
+\end{lyxcode}
+This is discussed in §\ref{subsec:The-.def-file}. For the present
+document, the call is
+\begin{lyxcode}
+\textbackslash usepackage{[}def-file=diffcoeff-doc{]}\{diffcoeff\}{[}=v4{]}
+\end{lyxcode}
+\end{enumerate}
+
+\section{A Rogues' Gallery of derivatives}
+
+\label{sec:Rogues'-gallery}Browsing through texts on statistical
+mechanics, relativity and classical mechanics I find the following
+choice examples of derivatives `disporting every which way'.
+
+Multi-character variables of differentiation un-parenthesized:
+
+\begin{equation}
+\diffp{\frac{\psi}{\Theta}}{\frac{1}{\Theta}},\quad\diffp{E/T}{1/T},\quad\diffp{\ln f}{\ln x_{0}},\quad\diffp\psi{a_{i},\frac{1}{\Theta}},\quad\diffp{\mathcal{L}}{\eta_{,i}^{(r)}}.\label{eq:eg1}
+\end{equation}
+Multi-character variables of differentiation parenthesized:
+\begin{equation}
+\diffp H{\displaystyle \diffp S{q_{k}}[]},\quad\diffp\varepsilon{(1/\Theta)}.\label{eq:eg2}
+\end{equation}
+Higher-order derivatives where the parentheses do not or sometimes
+do include the operator:
+\begin{equation}
+\diffp[2]q{\frac{1}{\Theta}},\quad\diffp[2]q{1/\Theta},\quad\diffp[2]\varepsilon{a_{i}},\quad\diff.wrapall.[2]{\phi^{i}(x^{i})}{x^{i}}.\label{eq:eg3}
+\end{equation}
+Should the $d$ or $\partial$ be included within the parentheses,
+as in the last of (\ref{eq:eg3}), or not, as in the others? Logic
+says `yes'; practice suggests (generally) `no'.
+
+Indicating a point of evaluation is similarly varied:
+\begin{equation}
+\diff.pvrule.\phi\varepsilon[\varepsilon=\varepsilon_{0}],\quad\diff.pvrule.[2]\phi\varepsilon[\varepsilon=\varepsilon_{0}],\quad\diff.psqbra.{b^{\beta}}{a^{\alpha}}[b=0],\quad\diff.paren.uv[v=0].\label{eq:eg4}
+\end{equation}
+ISO 80000-2 (item 2.11.13) favours the last of these -- parentheses
+-- for ordinary derivatives. Presumably, partial derivatives should
+follow suit, although parentheses are also used to indicate variables
+held constant:
+\begin{equation}
+\diffp*{\frac{P}{T}}U[V],\quad\diffp S{N_{2}}[U,V,N_{1}],\quad\diffp S/T[V].\label{eq:eg5}
+\end{equation}
+
+Other symbols besides $d$ and $\partial$ are used to denote derivative-like
+quantities. From introductory calculus and from classical mechanics
+and thermodynamics come $\delta$ and $\Delta$, from fluid mechanics
+comes $D$:
+\begin{equation}
+\diff.delta.yx,\quad\diff.D.\rho t,\quad\diff.pDelta.UT[V],\quad\diff.Delta.U/T,\quad\diff.delta.{\mathcal{L}}{\eta^{(r)}}.\label{eq:eg6}
+\end{equation}
+
+There are those, like the International Organization for Standardization
+(ISO), who stipulate (or prefer) an upright `d' for their derivatives:
+\begin{equation}
+\diff.up.yx.\label{eq:eg11}
+\end{equation}
+When the differentiand is too big or awkward to sit in the numerator
+and is appended to the operator, the $d$ or $\partial$ in the numerator
+is generally centred -- but not always. In texts prior to the age
+of computerised typesetting one will sometimes find the symbol pushed
+to the \emph{left}:
+\begin{equation}
+\diff.pleft.*{\diffp{x^{i^{*}}}{x^{k^{*}}}{}}{x^{l^{*}}},\quad\diff.left.*{\left(\frac{m\mathbf{q}_{x}}{\sqrt{1-q^{2}}}\right)}{t}.\label{eq:eg12}
+\end{equation}
+The observant will note an italic adjustment with the first expression,
+so that the $\partial$ in the numerator and the $\partial$ in the
+denominator line up in a slanting column, but no such adjustment for
+the $d$-s in the second derivative.
+
+Then there is the case when the operator in the numerator differs
+from that in the denominator. For instance, in tensor calculus acceleration
+is sometimes written
+\[
+\diff.nabla.{v^{i}}t=\diff{v^{i}}t+\Gamma_{k\hphantom{i}h}^{\hphantom{k}i}v^{h}\diff{y^{k}}t
+\]
+where $\nabla v^{i}$ is the `absolute differential' of the velocity
+$v^{i}$.
+
+Version 2 or later of the \texttt{diffcoeff} package has the generative
+power to cope with all these variations -- see §\ref{sec:Changing-defaults}
+-- although it is unlikely an author should need to call on this
+capacity to anything like the extent required for this Rogues' Gallery.
+
+Finally and new with version 4 of \texttt{diffcoeff}, is the ability
+to insert space before the differentiand, something that had to be
+done explicitly by the user before. One way of thinking of a derivative
+is as an operator $\diff{}x$ applied to a function $F(x)$ producing
+another function $F'(x)$, a \emph{derived }function, the derivative.
+Although the original function is included in the numerator of the
+differential coefficient, a small space between the $d$ and $F$
+feels natural to separate the thing operated on from the thing operating:
+\[
+F'(x)=\diff!{F(x)}x.
+\]
+\texttt{diffcoeff} can now produce such spaced derivatives, either
+as the default behaviour or at explicit request; see §\ref{subsec:Spacing-before-derivand}.
+
+\section{Ordinary derivatives }
+
+\label{sec:Ordinary-derivatives}Writing\textbf{ }\texttt{\textbackslash diff\{y\}\{x\}}
+will produce $\diff{y}{x}$ in text style (i.e., placed between \texttt{\textbackslash (
+\textbackslash )} or \texttt{\$ \$}) or
+\[
+\diff{y}{x}
+\]
+in display style (i.e., placed between \texttt{\textbackslash{[}
+\textbackslash{]}} ). In fact \texttt{\textbackslash diff yx} (omitting
+the braces) will produce these results, with a saving on keystrokes.
+The braces are needed only when an argument -- the differentiand
+or the variable of differentiation -- is multi-token.
+\begin{itemize}
+\item If you want upright `$\mathrm{d}$'s as default, as ISO 80000-2 recommends,
+rather than the math-italic `$d$'s used here, this can easily be
+done with the package option \texttt{ISO}; see §\ref{sec:Changing-defaults}
+on changing default settings.
+\end{itemize}
+For inclusion in a line of text you might prefer to use a slash-fraction
+form of derivative. That is achieved by inserting a slash, `/', between
+numerator and denominator arguments: \texttt{\textbackslash diff\{\textbackslash ln
+x\}/x} produces $\diff{\ln x}/x$. Braces are required for the numerator
+in this case since it contains more than one token.
+
+\subsection{Spacing before the differentiand}
+
+\label{subsec:Spacing-before-derivand}There are (at least) two different
+ways in which we think of derivatives.\footnote{I thank \noun{Hans Schülein} for first raising this issue with me
+and for subsequent thoughtful comments. } We are all familiar with the argument presented in elementary calculus
+books where a curve is shown, and a point on the curve through which
+a chord has been drawn. The chord is a side -- the hypotenuse --
+of a small right-angled triangle, the other sides having lengths $\delta x$
+and $\delta y$ and being parallel to the coordinate axes. The slope
+of the chord is $\diffd yx$. By drawing smaller and smaller chords
+through the point, the ratio $\diffd yx$ approaches the slope of
+the tangent to the curve at the point. We write
+\[
+\diff yx
+\]
+for the limit of $\diffd yx$. It is natural to think of $\dl y$
+and $\dl x$ as tiny lengths, like $\delta y$ and $\delta x$, in
+which case it would be quite wrong to insert space between the $d$
+and the $y$ (let alone the $d$ and the $x$). $dy$ is a single
+object, called a differential, and we write expressions like
+\begin{centred}
+\verb`\[ dy=\diff yx dx \]` $\Longrightarrow$
+\[
+\dl y=\diff yx\dl x
+\]
+\end{centred}
+and justly call the `fraction' in this expression a differential
+coefficient.
+
+But there is another way of viewing differentiation: as a process
+producing (or \emph{deriving}) one function, $f'(x)$, from another,
+$f(x)$. Here the sense is of applying $\diff{}x$ to $f(x)$. Although
+we include $f(x)$ in the numerator it is not attached to the $d$
+and should be separated from it by a small space:
+\begin{centred}
+\verb`\[ f'(x)=\diff!{f(x)}x \]` $\Longrightarrow$
+\[
+f'(x)=\diff!{f(x)}x.
+\]
+\end{centred}
+Here the fraction on the right is another name for the derived function
+$f'$ and is justly called the derivative of $f$. As you can see
+a small space has been inserted between the $d$ and the $f$ in the
+numerator. By default the space is \texttt{3 mu} but with the ability
+to stretch by \texttt{1 mu} or shrink by\texttt{ 2 mu}{\ttfamily\footnote{In \TeX -speak, \texttt{3mu plus 1mu minus 2mu}. }}
+as \TeX{} adjusts lines to fit on the page. (A `mu' is a `math unit'
+and is one eighteenth of a quad.) To achieve this result I have inserted
+an exclamation mark \verb`!` before the braces delimiting the differentiand.
+\begin{itemize}
+\item You may want all or most of your derivatives to have this space and
+therefore will not want to be inserting exclamation marks in every
+\texttt{\textbackslash diff} command. The \texttt{spaced} package
+option switches the default behaviour to spaced derivatives (in which
+case the \texttt{!} switch now creates an \emph{un-spaced} derivative).
+The size of the space inserted by default can be easily changed; see
+§\ref{sec:Changing-defaults}.
+\end{itemize}
+The present document uses the un-spaced default. For backwards compatibility
+(and perhaps because the author has done this for the last 60 years),
+this is the \textquoteleft out-of-the-box\textquoteright{} default
+that \texttt{diffcoeff} uses. Authors should make a habit of using
+one form predominantly. (There is also the possibility which I haven't
+emphasized of spacing multi-token differentiands and leaving single-token
+differentiands unspaced; see §\ref{subsec:A-final-flourish}.)
+
+Slash-form derivatives also allow space before the differentiand.
+By default this has the same value as applied to the fraction form
+of derivative (but can be changed; see §\ref{sec:Changing-defaults}):
+\begin{centred}
+\verb`$ \diff!{\ln\sin x}/x $` $\Longrightarrow$ $ \diff!{\ln\sin x}/x$.
+\end{centred}
+The \verb`\diff` command has other optional arguments (e.g. to specify
+the order of differentiation) but always the exclamation mark, if
+used, immediately precedes the differentiand. It is the positioning
+of the differentiand that it affects after all and its placement immediately
+before that argument seems natural.
+
+\subsubsection{Ligatures: }
+
+Prior to v.4 of \texttt{diffcoeff}, \texttt{\textbackslash diff fx}
+produced the tight pairing evident in
+\[
+\frac{df}{dx}.
+\]
+This was a bug. From version 4.0 of \texttt{diffcoeff}, such ligatures
+are prevented: \verb`\[ \diff fx \]` $\Longrightarrow$ \[ \diff fx.\]
+
+\subsubsection{Spacing commands}
+
+\label{subsec:Spacing-commands}The \texttt{diffcoeff} package also
+offers four simple spacing commands to fine-tune the display of derivatives
+and of other quantities. These are
+\begin{description}
+\item [{\texttt{\textbackslash negmu}}] insert spacing of $-1$ mu
+\item [{\texttt{\textbackslash nilmu}}] insert spacing of $0$ mu (cf.
+use of an empty brace pair \texttt{\textbf{\{\}}} )
+\item [{\texttt{\textbackslash onemu}}] insert spacing of $1$ mu
+\item [{\texttt{\textbackslash twomu}}] insert spacing of $2$ mu
+\end{description}
+
+\subsection{Appending the differentiand: \texttt{\textbackslash diff{*}}}
+
+Some differentiands are too big or awkward to be placed neatly in
+the numerator of a derivative and it is natural to append them to
+a preceding differential operator. One way to do this is to leave
+the numerator argument empty in the \texttt{\textbackslash diff}
+command and follow the command with the differentiand. A better way
+is to star the \texttt{\textbackslash diff} command. This tells \texttt{diffcoeff}
+to append the differentiand. Thus suppose the differentiand is a polynomial,
+say $ax^{2}+bx+c$. Add a star (an asterisk) to the \texttt{\textbackslash diff}
+command:
+\begin{centred}
+\verb`\[ \diff*{(ax^2+bx+c)}x \]` $\Longrightarrow$ \[\diff*{(ax^{2}+bx+c)}x\]
+\end{centred}
+With the \texttt{!} switch or \texttt{spaced} package option, additional
+space (by default \texttt{3mu plus 1mu minus 2mu}) is inserted between
+the operator and the differentiand:
+\begin{centred}
+\verb`\[ \diff*!{(ax^2+bx+c)}x \]` $\Longrightarrow$ \[\diff*!{(ax^{2}+bx+c)}x.\]
+\end{centred}
+A virtue of using an asterisk to append the differentiand is that
+if one isn't sure whether a differentiand should be appended or not,
+it is an easy matter to simply insert or delete the asterisk to compare
+the results. For example, a second derivative is an iterated derivative
+-- one in which a derivative forms the differentiand of another derivative:
+\begin{centred}
+\verb`\[ \diff[2]yx = \diff*{\diff yx}x \]` $\Longrightarrow$ \[ \diff[2]yx=\diff*{\diff yx}x \]
+\end{centred}
+\noindent which is more elegant to my eye than
+\begin{centred}
+\noindent \verb`\[ \diff[2]yx = \diff!{\diff yx}x \]` $\Longrightarrow$
+\[ \diff[2]yx=\diff!{\diff yx}x \]
+\end{centred}
+\noindent although whether the \emph{meaning} is clearer is moot.\emph{
+}It is easy to switch between the two forms on the right, simply by
+inserting or removing the asterisk.
+
+In slash style with the star option, the polynomial example becomes
+\begin{centred}
+\verb`\[ \diff*{(ax^2+bx+c)}/x \]` $\Longrightarrow$ \[ \diff*{(ax^2+bx+c)}/x \]
+\end{centred}
+\noindent where the parentheses around the differential operator are
+automatically inserted by \texttt{diffcoeff}. Like other elements
+of automatic formatting, this is user-adjustable; see §\ref{sec:Changing-defaults}.
+
+With the \texttt{!} switch or \texttt{spaced} package option, this
+becomes
+\begin{centred}
+\verb`\[ \diff*!{(ax^2+bx+c)}/x \]` $\Longrightarrow$ \[ \diff*!{(ax^2+bx+c)}/x \]
+\end{centred}
+
+\subsection{Point of evaluation}
+
+\label{subsec:Point-of-evaluation}If you want to specify a point
+at which the derivative is evaluated, append a final optional argument.
+Note that there \emph{must be no space} before the left square bracket
+of the argument:\footnote{In v.1 of \texttt{diffcoeff}, this was brace-delimited. From v.2,
+square-brackets have been used and braces deprecated. From v.4, braces
+are no longer accepted.}
+\begin{centred}
+\verb`\[ \diff[2]yx[0] \]` $\Longrightarrow\quad{\displaystyle \diff[2]yx[0]}$
+\end{centred}
+\noindent If a space does slip in before the final optional argument,
+it will not cause a \LaTeX{} error. Instead, the argument will be treated
+as a square-bracketed mathematical expression following the derivative,
+and typeset as such.
+\begin{itemize}
+\item If you prefer to use subscripted \emph{parentheses} around the derivative
+to indicate a point of evaluation -- as ISO 80000-2 recommends --
+then this can easily be done; see §\ref{sec:Changing-defaults} on
+changing default settings. Or, more simply, use the \texttt{ISO} package
+option.
+\end{itemize}
+Because the slash form spreads the derivative out horizontally, parentheses
+are preferred here to indicate a point of evaluation:
+\begin{centred}
+\verb`$ \diff{\ln sin x}/{sin x}[x=\pi/6] $` $\Longrightarrow$ $ \diff{\ln\sin x}/{\sin x}[x=\pi/6] $.
+\end{centred}
+\noindent A vertical rule (or `pipe') can easily become too remote
+from the opening $d$ of the differential coefficient: $\diff.svrule.{\ln\sin x}/{\sin x}[x=\pi/6]$;
+parentheses tie the whole cluster of symbols together.
+
+\subsubsection{Superscripts}
+
+It is easy to add a superscript to a derivative to indicate evaluation
+at two points and the difference between the values:
+\begin{centred}
+\verb`\[ \diff {\sin x}x[0]^{\pi/2} \]` ${\displaystyle \Longrightarrow}$
+\[ \diff{\sin x}x[0]^{\pi/2} \]
+\end{centred}
+\noindent If you want only the superscript, no subscript, include
+the final optional argument but leave it empty. Thus, for a particle
+of mass $m$ moving along a line, distance $x$ at time $t$, the
+kinetic energy is:
+\begin{centred}
+\noindent \verb`$ \tfrac 12 m \diff x/t[]^2 $` $\Longrightarrow$
+$\tfrac{1}{2}m\diff x/t[]^{2}$.
+\end{centred}
+
+\subsection{Order of differentiation}
+
+An optional first argument allows the order of differentiation to
+be specified. The order need not be a number; an algebraic order of
+differentiation is perfectly acceptable as is a mix of the two:
+\begin{centred}
+\verb`\[ \diff[2]yx \]` $\Longrightarrow$ \[ \diff[2]yx,\]\verb`\[ \diff[n+1]yx \]`
+$\Longrightarrow$ \[ \diff[n+1]yx.\]
+\end{centred}
+As mentioned, the braces can be and have been omitted around the $x$
+and $y$; the square brackets around the optional argument, the order
+of differentiation, are essential. For a first-order derivative, no
+optional argument is needed and entering \texttt{1} as the optional
+argument has no effect:
+\begin{centred}
+\verb`$ \diff[1]yx $` $\Longrightarrow$$\diff[1]yx$.
+\end{centred}
+In slash style, \texttt{\$\textbackslash diff{[}2{]}y/x\$} produces
+$\diff[2]y/x$, and \texttt{\$\textbackslash diff{[}n+1{]}y/x\$}
+produces $\diff[n+1]y/x$.
+
+\subsection{Multi-character variables of differentiation}
+
+Differentiating a function of a function may involve a multi-character
+differentiation variable. For instance, to differentiate $\ln\sin x$
+in $x$ means forming the product
+\begin{centred}
+\verb`\[ \diff!{\ln\sin x}{\sin x}\diff{\sin x}x \]` $\Longrightarrow$
+\[\diff!{\ln\sin x}{\sin x}\diff{\sin x}x.\]
+\end{centred}
+\noindent (Although I am mainly using un-spaced differentiands in
+this document, a space before the differentiand in the first of these
+derivatives -- the \verb`!` switch -- improves the appearance of
+the expression to my eye.)
+
+Forming the \emph{second} derivative of $\ln\sin x$ will now involve
+forming (among other quantities)
+\begin{centred}
+\noindent \verb`\[\diff[2]{\ln\sin x}{\sin x}\]` $\Longrightarrow$
+\[\diff[2]{\ln\sin x}{\sin x}\]
+\end{centred}
+\noindent Parentheses have been inserted automatically by \texttt{diffcoeff}
+around $\sin x$ in the denominator to avoid any visual hint that
+we are differentiating in the sine of $x^{2}$.
+
+The question is: are the parentheses in the right place? Logically,
+no. They should include the $d$: $(d\sin x)^{2}$ -- it is the differential
+$d\sin x$ that is of the second order. But as the examples in the
+Rogues' Gallery show -- see particularly (\ref{eq:eg3}) -- the
+inclination seems to be to do otherwise. This may be because one wants,
+in any case, to parenthesise the variable. A second, outer pair of
+parentheses then seems too fussy and detracts from comprehending the
+symbol `at a glance':
+\[
+\diff.wrapall.[2]{f(x)}{(1/x)}.
+\]
+
+Customary but illogical notations are familiar in mathematics --
+think of the position of the superscripts in an identity like $\sin^{2}\theta+\cos^{2}\theta=1$.
+But, like other features of the derivative, the manner of this wrapping
+in parentheses of long variables for \emph{higher order} derivatives
+is customisable; see §\ref{sec:Changing-defaults}.
+
+For first order derivatives, parenthesising does not occur. If you
+want the variable of differentiation to be parenthesised, you need
+to insert them yourself:
+\begin{centred}
+\verb`\[\diff {f(x)}{1/x}, \quad \diff {f(x)}{(1/x)}.\]` $\Longrightarrow$
+\[ \diff {f(x)}{1/x}, \quad\diff {f(x)}{(1/x)}.\]
+\end{centred}
+
+\section{Partial derivatives}
+
+\noindent \label{sec:Partial-derivatives}Partial derivatives follow
+the same pattern as ordinary derivatives, with some extensions. The
+command this time is \texttt{\textbackslash diffp}. Thus \texttt{\textbackslash diffp\{F\}\{x\}},
+or, with a saving on keystrokes,\texttt{ \textbackslash diffp Fx},
+produces $\diffp Fx$ in text style and
+\[
+\diffp{F}{x}
+\]
+in display style. (As for \texttt{\textbackslash diff}, the omission
+of braces is possible when the differentiand or the differentiation
+variable are single tokens.) As for \texttt{\textbackslash diff},
+there is a slash form, generally preferred for inline use, \texttt{\textbackslash diffp
+F/x}, displaying as $\diffp F/x$. Given that \texttt{\textbackslash partial}
+takes 8 keystrokes to type, the slash form \emph{does }economise on
+keystrokes for a partial derivative.
+
+With either the \verb`spaced` package option (see §\ref{subsec:Package-options})
+or the \verb`!` switch a space, defaulting to \verb`3 mu` with some
+stretch and shrink, can be inserted before the differentiand: \verb`\[ \diffp!{F(x,y)}x \]`
+$\Longrightarrow$ \[ \diffp!{F(x,y)}x. \]
+
+\noindent (But note that if the \verb`spaced` package option is used,
+the \verb`!` switch \emph{removes} any extra space.)
+
+Again an optional argument allows the specification of the order of
+differentiation which may be numeric or algebraic or a mix of the
+two:
+\begin{centred}
+\verb`\[ \diffp[3]F/x , \quad \diffp[n]F/x \]` $\Longrightarrow$
+\[\diffp[3]F/x , \quad \diffp[n]F/x\] \verb`\[ \diffp[n+1]Fx. \]`
+$\Longrightarrow$ \[ \diffp[n+1]Fx. \]
+\end{centred}
+
+\subsection{Variables held constant}
+
+In a subject like thermodynamics, there is a need to indicate which
+variables are held constant when the differentiation occurs. To show
+this, append a final square-bracketed optional argument and ensure
+that it follows \emph{immediately} on the preceding mandatory argument.
+A space here will detach the argument from the derivative and result
+in it being treated as a mathematical expression following the derivative.
+Thus to differentiate the entropy $S$ in temperature $T$ while holding
+the volume $V$ constant, write
+\begin{centred}
+\verb`\[ \diffp ST[V] \]` $\Longrightarrow$ \[ \diffp ST[V]. \]
+\end{centred}
+\noindent In slash form the same expression looks like
+\begin{centred}
+\noindent \verb`$ \diffp S/T[V] $` $\Longrightarrow$ $ \diffp S/T[V] $.
+\end{centred}
+This use of a parenthesised, subscripted form to indicate a variable
+or variables held constant, leaves open the question: how do we represent
+a point of evaluation? ISO 80000-2 makes no recommendation for \emph{partial}
+derivatives; presumably we follow the same practice as their recommendation
+for ordinary derivatives:
+\begin{example}
+\verb`\[ \diffp {F(x,y)}x[(0,0)] \]` $\Longrightarrow$ \[ \diffp {F(x,y)}x[(0,0)] \]
+\end{example}
+
+However, you may prefer (as many do) to use a vertical rule for this
+purpose:
+\[
+\diff.pvrule.{F(x,y)}x[(0,0)]
+\]
+Making this possibility available is discussed in §\ref{sec:Changing-defaults}.
+
+An empty final argument produces a parenthesised derivative with no
+subscript,
+\begin{centred}
+\verb`\[ \diffp yx[] \]` ${\displaystyle \Longrightarrow}$ \[ \diffp yx[] \]
+\end{centred}
+\noindent which can be useful sometimes. An instance is the writing
+of Lagrange's equations of motion in analytic mechanics:
+\begin{centred}
+\noindent \verb`\[ \diffp L{q_k}-\diff*{\diffp L{\dot{q}_k}[]}t = 0 \]`
+$\Longrightarrow$ \[ \diffp L{q_k}-\diff*{\diffp L{\dot{q}_k}[]}t = 0. \]
+\end{centred}
+
+\subsubsection{Text-style derivatives}
+
+The \texttt{diffcoeff} package assumes that derivatives formed as
+`numerator over denominator' will be used in display-style expressions,
+and that the slash form will be used for inline use (text style).
+This is the familiar practice in the literature. If one \emph{does}
+use the first form in an inline expression where a variable is held
+constant, say \texttt{\textbackslash diffp ST{[}V{]}} as here $\diffp ST[V]$,
+the result is unsatisfactory, the subscript too tight on the closing
+parenthesis and too much space between parentheses and derivative.
+The matter is easily resolved using `variant forms' -- see §\ref{subsec:Text-and-script-style}
+below -- giving, for our example, $\diff.ptxt.ST[V]$.
+
+\subsection{Appending the differentiand}
+
+\label{subsec:Partial-appending}For a long or awkward differentiand,
+it is generally better to \emph{append} it to a preceding differential
+operator, rather than create a fractional form with the long expression
+in the numerator. As with ordinary derivatives, this is achieved by
+adding an asterisk to (i.e. by starring) the \texttt{\textbackslash diffp}
+command.
+\begin{centred}
+\verb`\[ \diffp*[2]{\Phi(x,y,z)}x \]` $\Longrightarrow$ \[ \diffp*[2]{\Phi(x,y,z)}x. \]
+\end{centred}
+With the \verb`spaced` package option, or with the \verb`!` switch
+if the package option is not used (which is the case for this document),
+one gets
+\begin{centred}
+\verb`\[ \diffp*[2]!{\Phi(x,y,z)}x \]` $\Longrightarrow$ \[ \diffp*[2]!{\Phi(x,y,z)}x \]
+\end{centred}
+which is an improvement (to my eye).
+
+Alternatively you could leave the first mandatory argument empty and
+manually append the differentiand, but by deleting or inserting an
+asterisk, it is easy to compare the two forms, differentiand-in-the-numerator,
+differentiand-appended, and see which is preferable.
+
+In slash form, parentheses are automatically inserted around the differential
+operator when the differentiand is appended,
+\begin{centred}
+\verb`\[ \diffp*[n]{f(x)}/x \]` $\Longrightarrow$ \[ \diffp*[n]{f(x)}/x, \]
+\end{centred}
+\noindent although this behaviour can be changed (§\ref{sec:Changing-defaults}
+again).
+
+If you wish to both append the differentiand \emph{and} indicate variables
+held constant, then the starred form is much the easier way to achieve
+this. Thus, to express a relation in thermodynamics,
+\begin{centred}
+\verb`\[ \diffp*{\frac PT}U[V] = \diffp*{\frac 1T}V[U] \]` $\Longrightarrow$
+\[ \diffp*{\frac PT}U[V] = \diffp*{\frac 1T}V[U], \]
+\end{centred}
+\noindent where the starring automatically takes care of the parentheses
+and subscripts.
+
+\subsection{Iterated derivatives}
+
+Derivatives can be the differentiands of derivatives, as seen above
+when writing Lagrange's equations,
+\begin{centred}
+\noindent \verb`\[ \diffp L{q_k}-\diff*{\diffp L{\dot{q}_k}[]}t = 0 \]`
+$\Longrightarrow$ \[ \diffp L{q_k}-\diff*{\diffp L{\dot{q}_k}[]}t = 0. \]
+\end{centred}
+\noindent However, in versions of \texttt{diffcoeff} before version
+3.2, an ordinary derivative within a partial derivative rendered as
+a partial derivative. That is now corrected, the ordinary derivative
+rendering correctly:
+\begin{centred}
+\verb`\[ \diffp*{\diff{x^\mu}{\lambda}}{x^\sigma} \]` $\Longrightarrow$
+\[ \diffp*{\diff{x^\mu}{\lambda}}{x^\sigma}. \]
+\end{centred}
+
+\subsection{Mixed partial derivatives}
+
+The new thing with partial derivatives, not present with ordinary
+derivatives, is \emph{mixed} partial derivatives, where there is more
+than one variable of differentiation. If each variable is differentiated
+only to the first order, then it is easy to specify the derivative.
+Suppose $F$ is a function of three variables, $x$, $y$ and $z$.
+Then
+\begin{centred}
+\verb`\[ \diffp F{x,y,z} \]` $\Longrightarrow$ \[ \diffp F{x,y,z}, \]
+
+\verb`\[ \diffp !{F(x,y,z)}{x,y,z} \]` $\Longrightarrow$ \[ \diffp !{F(x,y,z)}{x,y,z}. \]
+\end{centred}
+In the second of these I have inserted space before the differentiand
+by using the \verb`!` switch. If the \verb`spaced` package option
+was being used, this would have been done automatically.
+
+The variables of differentiation are listed in order in a comma list
+forming the second mandatory argument. The total order of differentiation
+(3 in this example) is inserted automatically -- \texttt{diffcoeff}
+does the calculation. There is also a slash form:
+\begin{centred}
+\verb`$ \diffp F/{x,y,z} $` $\Longrightarrow$ $ \diffp F/{x,y,z}$.
+\end{centred}
+If we want to differentiate variables to higher order, then their
+orders need to be specified explicitly. To do so use a comma list
+for the optional argument:
+\begin{centred}
+\verb`\[ \diffp[2,3]F{x,y,z} \]` $\Longrightarrow$ \[ \diffp[2,3]F{x,y,z}. \]
+\end{centred}
+\noindent Notice that the overall order of the derivative -- 6 --
+is again automatically calculated and inserted as a superscript on
+the $\partial$ symbol in the numerator. In this example, the comma
+list of orders has only two members, even though there are three variables.
+It is assumed that the orders given in the comma list apply in sequence
+to the variables, the first order to the first variable, the second
+to the second variable, and so on, and that any subsequent orders
+not listed in the optional argument are, by default, 1. Thus we need
+to specify only 2 and 3 in the example; the order of differentiation
+of $z$ is 1 by default. But you \emph{cannot} use an order specification
+like \texttt{{[} , ,2{]}}. Instead write \texttt{{[}1,1,2{]}}.\textbf{
+}It is only the \emph{tail} of an order specification which can be
+omitted.
+
+\subsubsection{Minutiae of spacing (again)}
+
+\label{subsec:Minutiae-of-spacing}In Chapter 18 of the \emph{The\TeX book},
+Knuth suggests inserting a thin space, {\ttfamily\verb`\,`}
+(or {\ttfamily\verb`3 mu`}), between differentials in appropriate
+contexts, giving as an example $dx\,dy=r\,dr\,d\theta$. In the denominator
+of a derivative, however, that degree of extra spacing seems too great
+(to my eye), interfering with seeing the derivative `as a whole',
+\[
+\diff.pwide.F{x,y,z},
+\]
+especially for the slash-form of derivative: $\diff.pwide.F/{x,y,z}$.
+Some spacing is desirable, but less; by default \texttt{diffcoeff}
+inserts \verb`2 mu` between the differentials in the fraction form
+of derivative and \verb`1 mu`\texttt{ }in the slash form.
+
+Should a differentiation occur to higher order and so a variable acquire
+a superscript, an adjustment is made to the extra spacing. By default
+\verb`1 mu` is subtracted from the default spacing. Thus in
+\[
+\diffp[2]F{x,y,z},
+\]
+\verb`2 mu` of spacing is inserted between the $\partial y$ and
+$\partial z$, but because the superscript already provides some separation
+between them, only \verb`1 mu` is inserted between $\partial x^{2}$
+and $\partial y$.
+
+The values used for the spacing and its adjustment in the presence
+of a superscript can be changed by the user; see §\ref{sec:Changing-defaults}.
+Some other minutiae of spacing are discussed below in §\ref{subsec:Comma-list-of-vars}
+when the variables themselves are super- or subscripted (as happens
+in tensor calculus, for instance).
+
+Note that the \verb`!` switch, if used, is inserted \emph{immediately
+before} the differentiand. It is the placement of the differentiand,
+after all, that it is affecting:
+\begin{centred}
+\verb`\[ \diffp[2]!F{x,y,z} \]` $\Longrightarrow$ \[ \diffp[2]!F{x,y,z}. \]
+\end{centred}
+
+\subsubsection{Algebraic orders of differentiation}
+
+Calculation of the overall order of differentiation still occurs even
+when some or all of the individual orders are algebraic variables
+rather than numbers. For example, differentiating in three variables
+to orders \texttt{1, m+1, m-1},
+\begin{centred}
+\verb`\[ \diffp[1,m+1,m-1]{F(x,y,z)}{x,y,z} \]` $\Longrightarrow$
+\[ \diffp[1,m+1,m-1]{F(x,y,z)}{x,y,z}. \]
+\end{centred}
+
+\subsubsection{Error messages}
+
+Should you specify \emph{more} orders in the comma list of the order
+specification than there are variables, compilation will fail and
+an error message will be sent to the terminal and \LaTeX{} log . For
+example, if on (say) line 53 of my document I specify \texttt{{[}1,m-1,m+1,2{]}}
+for the orders of differentiation but list only \texttt{\{x,y,z\}}
+for the variables, the message will be
+\begin{lyxcode}
+!~Package~diffcoeff~Error:~4~orders~of~differentiation~
+
+specified~for~3~variables;~orders~{[}1,m+1,m-1,2{]}
+
+(on~line~53)~for~variables~x,y,z.
+\end{lyxcode}
+Should you try using a \emph{number} raised to a power in an order
+specification, it will cause an error. For example, if on line 53
+(say) of my document I try to form \texttt{\textbackslash diffp{[}2\textasciicircum 2{]}f\{x,y,z\}}
+compilation will fail with the message
+\begin{lyxcode}
+!~Package~diffcoeff~Error:~number~followed~by~\textasciicircum ~in~the~
+
+order~specification~{[}2\textasciicircum n,1,1{]}~on~line~53.~Diffcoeff~
+
+cannot~calculate~the~overall~order~of~differentiation~
+
+in~this~case.~Use~the~order-override~option~to~enter~
+
+the~overall~order.
+\end{lyxcode}
+The order-overide option mentioned here is discussed next. Similarly,
+you cannot use multiplication (\texttt{\textbackslash times} or \texttt{{*}})\texttt{
+}or division (\texttt{/} or \texttt{\textbackslash div}) signs after
+\emph{numbers} in an order specification; only \texttt{+} or \texttt{-}
+or a left parenthesis (see below) are allowed.
+
+\subsubsection{The order-override option}
+
+\noindent Perhaps the differentiations are to orders \texttt{{[}2km,m-1,m+1{]}}:
+\begin{centred}
+\noindent \verb`\[ \diffp[2km,m-1,m+1]{F(x,y,z)}{x,y,z} \]` $\Longrightarrow$
+\[ \diffp[2km,m-1,m+1]{F(x,y,z)}{x,y,z}. \]
+\end{centred}
+\noindent Here the overall order is presented as \texttt{2km+2m}.
+You might prefer this to be presented as \texttt{2m(k+1)}. Although
+\texttt{diffcoeff} takes some steps to present the overall order appropriately,
+it is not a computer algebra system and does not factorise expressions.
+If you want to present the order in a manner distinct from that presented
+by \texttt{diffcoeff}, use the \emph{order-override option}.
+
+This is a second optional argument immediately following the order
+specification. For our last example, filling the override option with
+\texttt{2m(k+1)} gives the desired result:
+\begin{centred}
+\verb`\[ \diffp[2km,m-1,m+1][2m(k+1)]{F(x,y,z)}{x,y,z} \]` $\Longrightarrow$
+\[ \diffp[2km,m-1,m+1][2m(k+1)]{F(x,y,z)}{x,y,z}. \]
+\end{centred}
+\noindent As another example, left to its own devices, \texttt{diffcoeff}
+produces
+\begin{centred}
+\noindent \verb`\[ \diffp[m/2+n/2,m/2,n/2]F{x,y,z} \]` $\Longrightarrow$
+\[ \diffp[m/2+n/2,m/2,n/2]F{x,y,z}, \]
+\end{centred}
+\noindent whereas we would like the total order to be presented as
+$m+n$. Using the override option,
+\begin{centred}
+\noindent \verb`\[ \diffp[m/2+n/2,m/2,n/2][m+n]F{x,y,z} \]` $\Longrightarrow$
+\[ \diffp[m/2+n/2,m/2,n/2][m+n]F{x,y,z}. \]
+\end{centred}
+The order-override option does exactly that: overrides the presentation
+of the calculated order with the manually given one. In fact the calculation
+algorithm does not get called at all when the override option is used
+so that one can in this way present the total order in whatever manner
+one wishes or, indeed, add essentially arbitrary material as a superscript
+to the $\partial$ symbol in the numerator.
+
+\subsubsection{Comma list of variables of differentiation}
+
+\label{subsec:Comma-list-of-vars}In tensor calculus the differentiations
+are almost always in terms of super- or subscripted coordinates. In
+many other contexts this is the case too -- the reciprocal of the
+temperature in thermodynamics or generalized coordinates in analytical
+mechanics. This is why a comma list is used in \texttt{diffcoeff}
+for specifying variables of differentiation for mixed partial derivatives.
+Although it would be nice to write the minimal \texttt{\{xy\}} rather
+than \texttt{\{x,y}\} when two variables $x$ and $y$ are involved,
+the extra writing is trivial and the comma list allows a simpler handling
+of multi-character variables. For instance in tensor calculus we get
+expressions like
+\begin{centred}
+\verb`\[ \diffp{A_i}{ x^j,x^k } \]` $\Longrightarrow$ \[ \diffp{A_i}{ x^j,x^k }. \]
+\end{centred}
+\noindent It is easier to write \texttt{\{x\textasciicircum j,x\textasciicircum k\}}
+here than, say, \texttt{\{\{x\textasciicircum j\}\{x\textasciicircum k\}\}}
+to distinguish the variables. It does mean that should the variable
+of differentiation include a comma then that comma needs to be enclosed
+in braces. There are plenty of instances of this out in the world
+(see, e.g., the last equation of (\ref{eq:eg1})) but it is overall
+a rare occurrence.
+
+\paragraph*{Minutiae of spacing (yet again):}
+
+In §\ref{subsec:Minutiae-of-spacing} above, I discussed a slight
+reduction in the space inserted between the terms occurring in the
+denominator of a mixed partial derivative when a higher order differentiation
+is involved. The superscript appearing on a differentiation variable
+in that case \emph{of itself} introduced a spacing adjustment between
+the terms. But the present discussion involves only first order differentiations
+and no such reduction is automatically made by \texttt{diffcoeff}.
+However it is still possible to explicitly make such an adjustment
+with the \texttt{\textbackslash negmu} command introduced earlier
+(§\ref{subsec:Spacing-commands}), which inserts \texttt{-1 mu} of
+spacing. For our example, in
+\begin{centred}
+\verb`\[ \diffp{A_i}{ x^j\negmu,x^k } \]` $\Longrightarrow$ \[ \diffp{A_i}{ x^j\negmu,x^k } \]
+\end{centred}
+\noindent the \texttt{\textbackslash negmu} decreases the spacing
+between the terms from the default \verb`2 mu` to \verb`1 mu`.
+
+\subsubsection{Overkill territory}
+
+Two previous examples illustrate limitations of the algorithm that
+calculates the overall order of differentiation: \texttt{2m/2+2n/2}
+is not simplified to \texttt{m+n} and \texttt{2km+2m} is not factorised
+to \texttt{2m(k+1)}. But there is much that the algorithm \emph{can}
+handle -- for instance, the simple use of parentheses:
+\begin{centred}
+\verb`\[ \diffp[2m-(k+1),2(k+1)-m]{F(x,y,z)}{x,y,z} \]` $\Longrightarrow$
+\[ \diffp[2m-(k+1),2(k+1)-m]{F(x,y,z)}{x,y,z}. \]
+\end{centred}
+
+\paragraph*{Dynamic use of parentheses}
+
+\noindent For parenthetic expressions to be evaluated as in this example
+-- the \emph{dynamic} use of parentheses -- the left parenthesis
+must be preceded at most by a sign or a number; the right parenthesis
+must be followed at most by a sign.
+
+If a right parenthesis is followed by a \emph{variable}, say by \texttt{m}
+as in the order spec. \texttt{{[}(2n+1)m,(2n-1)m{]}}, it will throw
+an error and halt compilation. A message will be sent to the terminal
+and the \LaTeX{} log like the following (which assumes the order spec.
+was on line 53 of the document):
+\begin{lyxcode}
+!~Package~diffcoeff~Error:~)~followed~by~m~in~the~
+
+order~specification~{[}(2n+1)m,(2n-1)m{]}~on~line~53.~
+
+Diffcoeff~cannot~calculate~the~overall~order~of~
+
+differentiation~in~this~case.~Use~the~order-override~
+
+option~to~enter~the~overall~order.
+\end{lyxcode}
+This is a limitation on the dynamic use of parentheses -- but they
+\emph{can} be nested.
+
+\paragraph*{Static use of parentheses}
+
+If a left parenthesis is preceded by a \emph{variable} (i.e., not
+a sign or a number) this signals to \texttt{diffcoeff} the \emph{static}
+use of parentheses, something like $f(k)$, `function of $k$'.
+No attempt is made to evaluate what is between them and they are treated
+simply as an extension of the variable. For example,
+\begin{centred}
+\verb`\[ \diffp[f(k+1)+1,f(k-1)-1]{F(x,y)}{x,y} \]` $\Longrightarrow$
+\[ \diffp[f(k+1)+1,f(k-1)-1]{F(x,y)}{x,y}. \]
+\end{centred}
+\noindent In the static case you \emph{can} follow the right parenthesis
+by a variable without generating an error.\emph{ }You can nest them,
+and you can include static parentheses within a dynamic pair; for
+example,
+\begin{centred}
+\noindent \verb`\[ \diffp[2(3+f(k))+1,1-3(f(k)-2)]{F(x,y)}{x,y} \]`
+$\Longrightarrow$ \[ \diffp[2(3+f(k))+1,1-3(f(k)-2)]{F(x,y)}{x,y}. \]
+\end{centred}
+\noindent However, the reverse is not possible: you can't have dynamic
+parentheses within a static pair.
+
+\paragraph*{Other refinements}
+
+Exponents and subscripts on a \emph{variable} are fine in an order
+specification, so long as the exponent or subscript consists of a
+\emph{single} token:
+\begin{centred}
+\verb`\[ \diffp[m^2+2(k-1),m^2-(k+1)]F{x,y,z,w} \]` $\Longrightarrow$
+\[ \diffp[m^2+2(k-1),m^2-(k+1)]F{x,y,z,w}. \]
+\end{centred}
+\noindent Braced arguments containing \emph{multiple} tokens as exponents
+or subscripts to variables will generally not halt compilation but
+will usually give nonsensical results, as will \emph{signs} treated
+as superscripts or subscripts. Neither circumstance is checked for
+by \texttt{diffcoeff}.
+
+\paragraph*{Override}
+
+There are limitations on what order specifications the \texttt{diffcoeff}
+package can `digest'; equally, it can digest a wide variety of such
+constructs, but it is \emph{not} a computer algebra system. In all
+those cases where it fails to calculate or present a correct total
+order, the order-override option is available. Yes, this is not as
+convenient as having the overall order calculated automatically but
+(let's remind ourselves) we are deep in overkill territory. Mixed
+partial derivatives are used far less often than the pure derivatives,
+and when they \emph{are} used it is nearly always to orders 1 or 2
+in the variables. Mixed partial derivatives to exotic orders of differentiation
+are rarely used, so that the limitations of the calculational algorithm
+are of little real moment -- and the override option is always available
+for such cases.
+
+\subsection{Parentheses around multi-character variables}
+
+In thermodynamics and statistical mechanics one may want to differentiate
+in the reciprocal of the temperature, $1/T$ (or $1/\Theta$):
+\begin{centred}
+\verb`\[ \diffp[2]q{\frac 1\Theta} \]` $\Longrightarrow$ \[ \diffp[2]q{\frac 1\Theta}. \]
+\end{centred}
+\noindent In this case and for other \emph{higher order} derivatives
+of multi-character variables of differentiation, the parentheses are
+inserted automatically by \texttt{diffcoeff}. Precisely where parentheses
+should be placed is moot. The placement in this example is not strictly
+logical, although it feels intuitive, but the placement can be customised
+(§\ref{sec:Changing-defaults}).
+
+Parentheses are automatically inserted like this only for higher order
+derivatives. When the differentiation is to first order, parenthesising
+is up to the user:
+\begin{centred}
+\verb`\[ \diffp q{(\frac 1\Theta),V} \]` $\Longrightarrow$ \[ \diffp q{(\frac 1\Theta),V}. \]
+\end{centred}
+
+\subsection{Jacobians}
+
+\texttt{diffcoeff} provides a command \texttt{\textbackslash jacob}
+for constructing Jacobians. For example
+\begin{centred}
+\verb`\[ \jacob{u,v,w}{x,y,z} \]` $\Longrightarrow$ \[ \jacob{u,v,w}{x,y,z}. \]
+\end{centred}
+The comma lists can contain any number of variables. \texttt{\textbackslash jacob}
+does \emph{not} check that the two arguments contain the same number
+of variables, so it is perfectly possible to form an object like \texttt{\textbackslash jacob\{u,v,w\}\{x,y\}}
+which as far as I know has no meaning.
+
+\section{Changing defaults; variant forms}
+
+\label{sec:Changing-defaults}To write the range of different examples
+displayed in the Rogues' Gallery (§\ref{sec:Rogues'-gallery}) I have
+had to make extensive use of forms of derivative other than the default.
+\texttt{diffcoeff} is built on the facilities offered by the \texttt{xtemplate}
+package (included in the \LaTeX 3 bundle \texttt{l3packages)}. These
+facilities are harnessed by means of a command, \texttt{\textbackslash diffdef},
+and a further optional argument of the \texttt{\textbackslash diff}
+command.\texttt{ }
+
+\subsection{Default values: ordinary derivatives}
+
+Table~\ref{tab:Ordinary-derivatives} lists the keys available for
+forming derivatives and the default values\footnote{Note that a mu is a `math unit', 1/18 of a quad.}
+they have been assigned. These default values have been chosen to
+coincide with those relevant for \emph{ordinary} derivatives -- apart
+from the keys \texttt{denom-term-sep}, \texttt{/-denom-term-sep},
+\texttt{term-sep-adjust} and \texttt{/-term-sep-adjust} which are
+ignored for ordinary derivatives but apply to the case of mixed partial
+derivatives when there is more than one variable of differentiation.
+Keys with an opening slash, /, apply only to the slash form of the
+derivative; keys with an opening asterisk, {*}, apply only when the
+differentiand is appended.
+
+Note that these settings are, in general, font dependent. The values
+given are (in the author's opinion) appropriate for the default \LaTeX{}
+math fonts. There are also likely to be variations required for whether
+a derivative is used in a display-style or text-style or script-style
+expression. That matter is discussed below in §\ref{subsec:Text-and-script-style}.
+All values specifying a space require the unit (\texttt{mu}) to be
+given; a number alone does not suffice.
+\noindent \begin{center}
+\begin{table}
+\centering
+\centering{}\caption{{\small Defaults (ordinary derivatives})\protect\label{tab:Ordinary-derivatives}}
+\begin{tabular}{lr}
+\toprule
+{\small key} & {\small default}\tabularnewline
+\midrule
+{\small op-symbol} & {\small\texttt{d}}\tabularnewline
+{\small op-symbol-alt} & {\small\texttt{op-symbol}}\tabularnewline
+{\small op-order-sep} & {\small\texttt{1 mu}}\tabularnewline
+{\small derivand-sep} & {\small\texttt{3 mu plus 1 mu minus 2 mu}}\tabularnewline
+{\small /-derivand-sep} & {\small\texttt{derivand-sep}}\tabularnewline
+{\small{*}-derivand-sep} & {\small\texttt{derivand-sep}}\tabularnewline
+{\small{*}/-derivand-sep} & {\small\texttt{/-derivand-sep}}\tabularnewline
+{\small denom-term-sep} & {\small\texttt{2 mu}}\tabularnewline
+{\small /-denom-term-sep} & {\small\texttt{1 mu}}\tabularnewline
+{\small term-sep-adjust} & {\small\texttt{-1 mu}}\tabularnewline
+{\small left-delim} & {\small\texttt{\textbackslash left .}}\tabularnewline
+{\small right-delim} & {\small\texttt{\textbackslash right |}}\tabularnewline
+{\small /-left-delim} & {\small\texttt{(}}\tabularnewline
+{\small /-right-delim} & {\small\texttt{)}}\tabularnewline
+{\small elbowroom} & {\small\texttt{0 mu}}\tabularnewline
+{\small /-elbowroom} & {\small\texttt{0 mu}}\tabularnewline
+{\small subscr-nudge} & {\small\texttt{0 mu}}\tabularnewline
+{\small /-subscr-nudge} & {\small\texttt{0 mu}}\tabularnewline
+{\small long-var-wrap} & {\small\texttt{d(v)}}\tabularnewline
+{\small{*}/-op-wrap} & {\small\texttt{true}}\tabularnewline
+{\small{*}-op-left} & {\small\texttt{false}}\tabularnewline
+{\small{*}-italic-nudge} & {\small\texttt{3 mu}}\tabularnewline
+\bottomrule
+\end{tabular}
+\end{table}
+\par\end{center}
+\begin{description}
+\item [{op-symbol}] the operator symbol; for ordinary derivatives, generally
+one of \texttt{d} or \texttt{\textbackslash mathrm\{d\}}, \texttt{D}
+or \texttt{\textbackslash mathrm\{D\}}, \texttt{\textbackslash delta}
+or \texttt{\textbackslash Delta}; for partial derivatives \texttt{\textbackslash partial};
+default = \texttt{d}
+\item [{op-symbol-alt}] if different from \textbf{op-symbol} then used
+in the denominator while \textbf{op-symbol} is used in the numerator;
+e.g. for $\diff.nabla.{v^{i}}t$, \texttt{op-symbol = \textbackslash nabla}
+and \texttt{op-symbol-alt = d}; otherwise (and usually) defaults to
+\textbf{op-symbol}
+\item [{op-order-sep}] extra horizontal space added between the op-symbol
+and the superscripted order of differentiation in higher order derivatives;
+for the math-italic forms compare $d^{2}$ with $d^{\mkern1mu 2}$,
+$\partial^{2}$ with $\partial^{\mkern1mu 2}$ where the first symbol
+in each case has no extra space and the second has an extra 1 mu;
+default = \texttt{1 mu}
+\item [{derivand-sep}] horizontal space added before the differentiand
+(derivand) if the \verb`spaced` package option is used, or by the
+\verb`!` switch if it is not; the default has some stretch and shrink;
+default = \verb`3mu plus 1mu minus 2mu`
+\item [{/-derivand-sep}] for the slash form of derivative, horizontal space
+added before the differentiand (derivand) if the \verb`spaced` package
+option is used, or by the \verb`!` switch if it is not; default =
+\verb`derivand-sep`
+\item [{{*}-derivand-sep}] when the derivand is appended, horizontal space
+added before the differentiand (derivand) if the \verb`spaced` package
+option is used, or by the \verb`!` switch if it is not; default =
+\verb`derivand-sep`
+\item [{{*}/-derivand-sep}] for the slash form of derivative when the derivand
+is appended, horizontal space added before the differentiand (derivand)
+if the \verb`spaced` package option is used, or by the \verb`!`
+switch if it is not; default = \verb`/-derivand-sep`
+\item [{denom-term-sep}] (mixed partial derivatives only) horizontal spacing
+inserted between the differentials in the denominator of a mixed partial
+derivative to avoid a solid cluster like $\partial x\partial y\partial z$;
+with the default 2 mu this is $\dl.p.x\dl.p.2y\dl.p.2z$; default
+= \texttt{2 mu}
+\item [{/-denom-term-sep}] (mixed partial derivatives only) horizontal
+spacing inserted between the differentials in the denominator of a
+slash-form mixed partial derivative; because a slash-form derivative
+is already spread out horizontally, the default spacing is less than
+for the \texttt{\textbackslash frac} form derivative; default = \texttt{1
+mu}
+\item [{term-sep-adjust}] (mixed partial derivatives only) adjustment (i.e.
+reduction) to \textbf{denom-term-sep} or \textbf{/-denom-term-sep}
+when differentiation in a variable occurs to an order other than 1;
+if, e.g., $\dl.p.x^{2}\dl.p.1y\dl.p.2z$ is the denominator of a mixed
+partial derivative in three variables, because of the superscript
+the spacing between $\partial x^{2}$ and $\partial y$ is reduced
+by\textbf{ term-sep-adjust} from the spacing between $\partial y$
+and $\partial z$; default = \texttt{-1 mu}
+\item [{left-delim}] the left member of a delimiter pair wrapping the derivative,
+the right member of which is subscripted to indicate a point of evaluation
+or variables held constant; default = \texttt{\textbackslash left
+.}
+\item [{right-delim}] the right member of a delimiter pair wrapping the
+derivative and subscripted to indicate a point of evaluation or variables
+held constant; default = \texttt{\textbackslash right |}
+\item [{/-left-delim}] for the slash form of derivative, the left member
+of a delimiter pair wrapping the derivative and subscripted to indicate
+a point of evaluation or variables held constant; default = \texttt{(}
+\item [{/-right-delim}] for the slash form of derivative, the right member
+of a delimiter pair wrapping the derivative, the right member of which
+is subscripted to indicate a point of evaluation or variables held
+constant; default = \texttt{)}
+\item [{elbowroom}] adjustment to the whitespace between the left and right
+delimiters and the enclosed derivative; negative values reduce the
+space; default = \texttt{0 mu}
+\item [{/-elbowroom}] adjustment to the whitespace between the left and
+right delimiters and the enclosed slash-form derivative; default =
+\texttt{0 mu}
+\item [{subscr-nudge}] horizontal adjustment of the subscript's placing
+relative to the \textbf{right-delim}iter, e.g., a negative value compensates
+for the curving inwards of a large right parenthesis; may be font
+dependent; default = \texttt{0 mu}
+\item [{/-subscr-nudge}] for the slash form of derivative, horizontal adjustment
+of the subscript's placing relative to the /-\textbf{right-delim}iter;
+may be font dependent; default = \texttt{0 mu}
+\item [{long-var-wrap}] to avoid ambiguity in higher order derivatives
+it may be advisable to wrap multi-token variables of differentiation
+in parentheses; default = \texttt{d(v)}; the choices are
+\begin{description}
+\item [{\texttt{dv}}] no wrapping, e.g. $dx_{i}^{2}$ or $d\frac{1}{\Theta}^{2}$,
+$\partial x_{i}^{2}$ or $\partial\frac{1}{\Theta}^{2}$,
+\item [{\texttt{d(v)}}] wrap the variable only, e.g. $d(x_{i})^{2}$ or
+$d(\frac{1}{\Theta})^{2}$, $\partial(x_{i})^{2}$ or $\partial(\frac{1}{\Theta})^{2}$
+\item [{\texttt{(dv)}}] wrap the op-symbol and variable, e.g. $(dx_{i})^{2}$
+or $(d\frac{1}{\Theta})^{2}$, $(\partial x_{i})^{2}$ or $(\partial\frac{1}{\Theta})^{2}$
+\end{description}
+\item [{{*}/-op-wrap}] a choice of \texttt{true} or \texttt{false} for
+slash forms of the derivative when the differentiand is appended,
+dictating whether the derivative is wrapped in parentheses, as here
+$\diffp*{F(x,y)}/x$, or not; default = \texttt{true}
+\item [{{*}-op-left}] a choice of \texttt{true} or \texttt{false} indicating
+whether the op-symbol is left-aligned or not when the differentiand
+is appended; generally it is centred; does not apply to slash forms
+of the derivative; default = \texttt{false}
+\item [{{*}-italic-nudge}] if \textbf{{*}-op-left} is \texttt{true}, makes
+an italic adjustment in the numerator, so that the op-symbols in numerator
+and denominator align in the same slanting column; for an upright
+\texttt{d} this would be set to \texttt{0 mu}; default = \texttt{3
+mu}
+\end{description}
+
+\subsection{ISO defaults}
+
+\label{subsec:ISO-defaults}\begin{wraptable}[10]{o}{0.4\columnwidth}%
+\centering{}\vspace{-5.35ex}
+ \caption{{\small ISO default changes}\protect\label{tab:ISO-setting-changes}}
+\abovetopsep=.5ex %
+\begin{tabular}{lr}
+\toprule
+{\small key} & {\small default}\tabularnewline
+\midrule
+{\small op-symbol} & {\small\texttt{\textbackslash mathrm\{d\}}}\tabularnewline
+{\small op-order-sep} & {\small\texttt{0 mu}}\tabularnewline
+{\small left-delim} & {\small\texttt{\textbackslash left (}}\tabularnewline
+{\small right-delim} & {\small\texttt{\textbackslash right )}}\tabularnewline
+{\small subscr-nudge} & {\small\texttt{-6 mu}}\tabularnewline
+\bottomrule
+\end{tabular}\end{wraptable}%
+You may not like the default settings that come with \texttt{diffcoeff}.
+The package does not follow ISO 80000-2 -- it does not use upright
+`d's nor does it wrap an ordinary differential coefficient in subscripted
+parentheses to indicate a point of evaluation. Both `defects' can
+be remedied by calling the package with the option \texttt{ISO}:\footnote{One can also use \texttt{ISO=true} to turn the option on and \texttt{ISO=false
+}to turn the option off. }
+\begin{lyxcode}
+\textbackslash usepackage{[}ISO{]}\{diffcoeff\}{[}=v4{]}
+\end{lyxcode}
+The uppercase is essential -- an option \texttt{iso} is not recognised.
+The \texttt{ISO} option results in changes to the default settings
+of Table~\ref{tab:Ordinary-derivatives} as listed in Table~\ref{tab:ISO-setting-changes}.
+Any settings not mentioned in Table~\ref{tab:ISO-setting-changes}
+retain the values presented in Table~\ref{tab:Ordinary-derivatives}.
+Note that the subscript nudge figure specified here is \emph{not}
+part of the standard, which makes no recommendation about the subscript's
+positioning. But: the \texttt{-6 mu} figure with a default or latin
+modern font gives a better representation of what is displayed in
+the standard than a zero figure.
+
+Because the `d' is upright with the \texttt{ISO} option, no extra
+space is required between the symbol and the superscript in a higher
+order derivative. Hence the zero value for the \texttt{op-order-sep}.
+ISO recommends subscripted parentheses to indicate a point of evaluation.
+Hence the other entries in the table. Because a large right parenthesis
+(penultimate setting) bends inwards, to the left, a negative value
+for the last entry ensures the subscript does not become detached
+from the derivative, looking lost in a sea of whitespace.
+
+Note that the \texttt{ISO} option will also produce upright `D's in
+derivatives formed from `D'; see §\ref{subsec:D-delta-Delta} below.
+
+\subsection{Partial derivatives}
+
+\begin{wraptable}{o}{0.4\columnwidth}%
+\centering{}\vspace{-5.35ex}
+ \caption{{\small Default changes for partial derivatives}\protect\label{tab:Partial-deriv-defaults}}
+\abovetopsep=.5ex %
+\begin{tabular}{lr}
+\toprule
+{\small key} & {\small default}\tabularnewline
+\midrule
+{\small op-symbol} & {\small\texttt{\textbackslash partial}}\tabularnewline
+{\small left-delim} & {\small\texttt{\textbackslash left (}}\tabularnewline
+{\small right-delim} & {\small\texttt{\textbackslash right )}}\tabularnewline
+{\small subscr-nudge} & {\small\texttt{-6 mu}}\tabularnewline
+\bottomrule
+\end{tabular}\end{wraptable}%
+The default values given in Table~\ref{tab:Ordinary-derivatives},
+when they are relevant, apply to \emph{ordinary} derivatives. For
+partial derivatives, some defaults change. These are listed in Table~\ref{tab:Partial-deriv-defaults}.
+All other keys take the default values of Table~\ref{tab:Ordinary-derivatives}.
+
+The last three entries here reflect the use of subscripted parentheses
+with partial derivatives to indicate variables held constant, for
+instance in the Maxwell relations of thermodynamics, one of which
+is
+\[
+\diffp SV[T]=\diffp PT[V]
+\]
+
+
+\subsection{Setting your own defaults: \texttt{\textbackslash diffdef}}
+
+\label{subsec:diffdef}Versions 2 and later of the \texttt{diffcoeff}
+package provide a command, \texttt{\textbackslash diffdef}, that
+enables users to set their own defaults.\texttt{ }For example, if
+you wish to use upright `d's but not follow ISO's use of subscripted
+parentheses to indicate a point of evaluation, enter in the preamble
+of your document the command
+\begin{lyxcode}
+\textbackslash diffdef~\{\}~~~~
+
+~~\{~~~~~~
+
+~~~~op-symbol~~~~=~\textbackslash mathrm\{d\},~~~~
+
+~~~~op-order-sep~=~0~mu
+
+~~\}
+\end{lyxcode}
+\noindent Since a list of settings, like this one, is a comma-\emph{separated}
+list, no comma is required for the last entry. That entry is a consequence
+of the first: upright symbols do not require any extra separation
+between the `d' and the superscript in a higher order derivative.
+
+The other point to note is the empty pair of braces after the \texttt{\textbackslash diffdef}
+command. \emph{They matter}. Their emptiness is what determines that
+it is the \emph{default} values that are changed. If they contain
+some content, then that content provides a \emph{name} for the particular
+set of values in the following list. The \texttt{diffcoeff} package
+exploits this facility to cope with the wide variety of forms displayed
+in the Rogues' Gallery of §\ref{sec:Rogues'-gallery}.
+
+\subsubsection{Space before the differentiand}
+
+\label{subsec:A-final-flourish}\begin{wraptable}{o}{0.6\columnwidth}%
+\begin{centering}
+\caption{Keys for spacing the derivand}
+\medskip{}
+\begin{tabular}{lr}
+\toprule
+{\small key} & {\small default}\tabularnewline
+\midrule
+{\small derivand-sep} & {\small\texttt{3mu plus 1mu minus 2mu}}\tabularnewline
+{\small{*}-derivand-sep} & {\small\texttt{derivand-sep}}\tabularnewline
+{\small /-derivand-sep} & {\small\texttt{derivand-sep}}\tabularnewline
+{\small{*}/-derivand-sep} & {\small\texttt{ /-derivand-sep}}\tabularnewline
+\bottomrule
+\end{tabular}
+\par\end{centering}
+\end{wraptable}%
+The insertion of a small space before the differentiand is effected
+by the \verb`!` key inserted immediately before the differentiand
+argument in the \verb`\diff` command. You may wish to make the insertion
+of this space the \emph{default} behaviour. This is done by using
+the \verb`spaced` package option (which makes the \verb`!` switch
+now reverse this new default and put \emph{no} extra space before
+the derivand). The amount of space inserted is, by default, \verb`3mu plus 1mu minus 2mu`,
+meaning the space is generally $3$mu but can stretch to $4$mu or
+shrink to $1$mu as \TeX{} strives to fit content in a line or on the
+page.
+
+Perhaps this doesn't suit. You may want a fixed space here, with no
+stretch or shrink. The key to change is \verb`derivand-sep`. By default,
+this setting applies not only to the fraction form of derivative,
+but also to the slash form and to when the derivand is appended.
+
+If you feel a little less space should be used for slash derivatives,
+then the key to change is \verb`/-deriv-sep`. This changed value
+will also be used for an appended derivand in a slash derivative.
+
+Thus to meet both wishes you might put in the preamble of your document
+something like
+\begin{lyxcode}
+\textbackslash diffdef~\{\}~~~~
+
+~~\{~~~~~~
+
+~~~~derivand-sep~~~=~3~mu,~~~~
+
+~~~~/-derivand-sep~=~2~mu
+
+~~\}
+\end{lyxcode}
+This will insert a fixed space of $3$mu before the differentiand
+in both the numerator and when appended in the fraction form of derivative,
+and a fixed space of $2$mu in the slash form of derivative, both
+in the numerator and when appended.
+
+If you want a different spacing when the derivand is appended, the
+keys to change are \verb`*-derivand-sep` and \verb`*/-derivand-sep`.
+
+\paragraph{Selective spacing}
+
+I have treated the \verb`spaced` package option thus far as if it
+were an \verb`ON/OFF` switch and, indeed, the presence of the package
+option \verb`spaced` behaves as \verb`ON` and its absence as \verb`OFF`.
+Internally, however, \verb`spaced` is equivalent to \verb`spaced=1`
+and its absence to \verb`spaced=0`. Entering \verb`spaced=n` in
+the package option where \verb`n` is a positive integer is equivalent
+to entering \verb`spaced=1` (and hence to simply entering \verb`spaced`),
+but if \verb`n` is a negative integer, a new effect is produced.
+
+Entering \verb`spaced=-1` (or any negative integer) as a package
+option will insert a space (by default \verb`3mu plus 1mu minus 2mu`)
+before the differentiand provided the differentiand\emph{ is longer
+than a single token} but will insert no space before single-token
+differentiands. The switch \verb`!` reverses this behaviour.
+
+\subsection{Variant forms}
+
+For this package I needed a number of variant forms to illustrate
+the wide variety of ways in which derivatives are displayed. The \texttt{\textbackslash diffdef}
+command in which the first argument is \emph{filled} provides one
+half of the means of doing this. I've given the single-letter name
+\texttt{p} to the following settings:
+\begin{lyxcode}
+\textbackslash diffdef~\{~p~\}
+
+~~\{
+
+~~~~op-symbol~~~~=~\textbackslash partial~,
+
+~~~~left-delim~~~=~\textbackslash left~(~~,
+
+~~~~right-delim~~=~\textbackslash right~)~,
+
+~~~~subscr-nudge~=~-6~mu
+
+~~\}
+\end{lyxcode}
+The second half of providing variant forms is to insert this name,
+\texttt{p}, between dots (periods, full stops) as the \emph{first}
+argument of the \texttt{\textbackslash diff} command. Thus, repeating
+an example at the end of §\ref{subsec:Partial-appending},
+\begin{centred}
+\verb`\[ \diff.p.*{\frac PT}U[V] = \diff.p.*{\frac 1T}V[U] \]` $\Longrightarrow$
+\[ \diff.p.*{\frac PT}U[V] = \diff.p.*{\frac 1T}V[U] \]
+\end{centred}
+\noindent The effect is exactly the same as previously, when the \texttt{\textbackslash diffp}
+command was used. Indeed, \texttt{diffcoeff} identifies \texttt{\textbackslash diffp}
+with \texttt{\textbackslash diff.p.}:
+\begin{lyxcode}
+\textbackslash NewDocumentCommand~\textbackslash diffp~\{~\}~\{~\textbackslash diff.p.~\}
+\end{lyxcode}
+Note that this identification of \texttt{\textbackslash diffp} with
+\texttt{\textbackslash diff.p.} means there is no equivalent dot-delimited
+argument available for \texttt{\textbackslash diffp}. The \emph{dot-delimited
+argument applies only to} \texttt{\textbackslash diff}.
+
+For example, to illustrate the upright-d form of derivative, without
+changing the default math-italic form (which I prefer), one might
+enter in the preamble
+\begin{lyxcode}
+\textbackslash diffdef~\{~up~\}~
+
+~~\{
+
+~~~~op-symbol~~~~=~\textbackslash mathrm\{d\},
+
+~~~~op-order-sep~=~0~mu
+
+~~\}
+\end{lyxcode}
+Apart from the \emph{key = value} settings, the critical feature here
+is the name, \texttt{up} (which is at your discretion and could equally
+be \texttt{upright} or \texttt{roman} or even \texttt{Fred} if you
+so fancied). This ensures that the changed settings apply only to
+this particular variant and do not `infect' the overall defaults.
+To use this variant, all that is needed is to add the name, between
+dots, to the \texttt{\textbackslash diff} command:
+\begin{centred}
+\verb`\[ \diff.up.yx \]` $\Longrightarrow$ \[ \diff.up.yx. \]
+\end{centred}
+\noindent Each variant derivative inherits all the default values
+that it does not explicitly countermand. Thus a point of evaluation
+is indicated by a vertical rule which is the \texttt{diffcoeff} default\footnote{\noindent But not the ISO recommendation.}:
+\begin{centred}
+\noindent \verb`\[ \diff.up.*{\frac{F(x)}{G(x)}}x[x=1] \]` $\Longrightarrow$
+\[ \diff.up.*{\frac{F(x)}{G(x)}}x[x=1] \]
+\end{centred}
+\noindent Dot-delimited arguments must always be the \emph{first}
+argument of the \texttt{\textbackslash diff} command, even preceding
+an asterisk (star) as in this example.
+
+As another example, suppose for the subscripted indication of variables
+held constant in a partial derivative that you want to see what things
+look like if the subscript is \emph{not }nudged in towards the right
+parenthesis. In that case define a variant form
+\begin{lyxcode}
+\textbackslash diffdef~\{~padrift~\}~\{~subscr-nudge~=~0~mu~\}
+\end{lyxcode}
+I have attached a name, \texttt{padrift},\texttt{ }to this setting,
+\begin{centred}
+\verb`\[ \diff.padrift.Fx[y] \]` $\Longrightarrow$ \[ \diff.padrift.Fx[y] \]
+\end{centred}
+\noindent since, to my eye, the subscript seems detached from the
+expression it qualifies -- is it perhaps a typo? -- and `adrift
+in a sea of whitespace'. This is to be compared with the default \verb`\[ \diffp Fx[y] \]`
+$\Longrightarrow$ \[ \diffp Fx[y] \]
+
+\noindent where the subscript is tucked in close to the right parenthesis
+and is clearly connected to it and the expression it delimits.
+
+Some might want to distinguish notationally a point of evaluation
+for a partial derivative from variables held constant, perhaps using
+a vertical rule for the former and (the default) parentheses for the
+latter. It would suffice then to add to the preamble
+\begin{centred}
+\verb`\diffdef { pvrule } { op-symbol = \partial }`
+\end{centred}
+This gives
+\begin{centred}
+\verb`\[ \diff.pvrule.{F(x,y)}x[x=1] \]`$\Longrightarrow$ \[ \diff.pvrule.{F(x,y)}x[x=1] \]
+\end{centred}
+
+\subsubsection{Text-style and script-style derivatives}
+
+\label{subsec:Text-and-script-style}As noted earlier, the \texttt{diffcoeff}
+package assumes that derivatives of fraction-like form will be used
+in display-style expressions and that the slash form will be used
+for inline use (text style). This is the usual practice. But if one
+does want to use the fraction form in an inline expression, say \texttt{\textbackslash diffp
+ST{[}V{]}} displaying as $\diffp ST[V]$, then some tweaking of settings
+is necessary: the subscript is obviously too close to the right parenthesis
+and, to my eye, there is too much `elbowroom' between the derivative
+and the enclosing parentheses. Hence define
+
+\noindent %
+\noindent\begin{minipage}[t]{1\columnwidth}%
+\begin{lyxcode}
+\textbackslash diffdef~\{~ptxt~\}~
+
+~~\{
+
+~~~~op-symbol~~~~~~=~\textbackslash partial,
+
+~~~~denom-term-sep~=~1~mu~~~~,
+
+~~~~left-delim~~~~~=~\textbackslash left~(~,
+
+~~~~right-delim~~~~=~\textbackslash right~),
+
+~~~~elbowroom~~~~~~=~-2~mu~~~,
+
+~~~~subscr-nudge~~~=~-3~mu~~~
+
+~~\}
+\end{lyxcode}
+%
+\end{minipage}
+
+We can now write, for the same example, \texttt{\textbackslash diff.ptxt.ST{[}V{]}}
+which displays as $\diff.ptxt.ST[V]$, where the subscript is better
+positioned and there is a better fit between parentheses and derivative.
+
+\subsubsection{Derivatives from D, \textbackslash delta, \textbackslash Delta}
+
+\label{subsec:D-delta-Delta}In addition to \texttt{\textbackslash diff.p.},\texttt{
+diffcoeff} has three other \emph{built-in} variant forms that are
+commonly used: \texttt{\textbackslash diff.D.}, \texttt{\textbackslash diff.delta.},
+and \texttt{\textbackslash diff.Delta.}, corresponding to derivatives
+formed from $D$, $\delta$ and $\Delta$ respectively.
+
+In fluid dynamics the \emph{material }or \emph{substantive} derivative
+uses an uppercase $D$ in place of $d$. For example, the continuity
+equation is,
+\begin{centred}
+\verb`\[ \diff.D.{\rho}t=\diffp\rho t + \mathbf{u\cdot}\nabla\rho \]`$\Longrightarrow$
+\[ \diff.D.{\rho}t=\diffp\rho t + \mathbf{u\cdot}\nabla\rho \]
+\end{centred}
+\noindent where \texttt{\textbackslash diff.D.} produces the D-derivative.
+If you want upright `D's, then the \texttt{ISO} package option will
+produce that effect. Alternatively,
+\begin{lyxcode}
+\textbackslash diffdef~\{~Up~\}~
+
+~~\{
+
+~~~~op-symbol~~~~=~\textbackslash mathrm\{D\},
+
+~~~~op-order-sep~=~0~mu
+
+~~\}
+\end{lyxcode}
+\noindent provides a variant with upright `D's.
+
+In introductory calculus texts the simple $\delta$-derivative is
+used. This is achieved with the \texttt{\textbackslash diff.delta.}
+command: \verb`\[ \diff.delta.yx \]` $\Longrightarrow$ \[ \diff.delta.yx. \]
+
+\noindent This form also features in analytical mechanics (in the
+Rogues' Gallery, the final example at (\ref{eq:eg6})).
+
+Similarly, \texttt{\textbackslash diff.Delta.} forms a derivative
+from $\Delta$:
+\begin{centred}
+\verb`$ \diff.Delta.y/x $` $\Longrightarrow$ $ \diff.Delta.y/x $
+\end{centred}
+\noindent where the slash form of the derivative is shown in this
+instance.
+
+Higher order forms of these derivatives, points of evaluation, appending
+the differentiand with a star argument, all follow exactly as for
+the `pure' \texttt{\textbackslash diff} command.
+
+\paragraph{The commands \textbackslash Diff, \textbackslash diffd, \textbackslash Diffd}
+
+For compatibility with version 1 of \texttt{diffcoeff}, the commands
+\texttt{\textbackslash Diff}, \texttt{\textbackslash diffd} and
+\texttt{\textbackslash Diffd} are available and also produce the
+$D$, $\delta$ and $\Delta$ derivatives. Just as \texttt{\textbackslash diffp}
+is identified with \texttt{\textbackslash diff.p.} for partial derivatives,
+these commands are identified with \texttt{\textbackslash diff.D.},
+\texttt{\textbackslash diff.delta.}, and \texttt{\textbackslash diff.Delta}
+through the commands
+\begin{lyxcode}
+\textbackslash NewDocumentCommand~\textbackslash Diff~\{\}~~\{\textbackslash diff.D.\}
+
+\textbackslash NewDocumentCommand~\textbackslash diffd~\{\}~\{\textbackslash diff.delta.\}
+
+\textbackslash NewDocumentCommand~\textbackslash Diffd~\{\}~\{\textbackslash diff.Delta.\}
+\end{lyxcode}
+Unless one is using such variant forms frequently, it seems simpler
+to remember that they are available as dot-delimited arguments to
+the \texttt{\textbackslash diff} command, using the obvious name
+in each case, rather than having to remember the precise camel-case
+form of name of the \texttt{\textbackslash Diff}, \texttt{\textbackslash diffd}
+and \texttt{\textbackslash Diffd} commands.
+
+\subsection{The \texttt{.def} file}
+
+\label{subsec:The-.def-file}This mechanism of variant formation is
+how I have been able to illustrate in the Rogues' Gallery, §\ref{sec:Rogues'-gallery},
+the wide variety of different usages culled from the literature. But
+the thought arises: if a variant is to be used only once or twice,
+isn't this a lot of bother? Why not just construct the variant derivative
+`by hand' out of \texttt{\textbackslash frac} and \texttt{\textbackslash mskip}
+for example? The reason for making such definitions is that they can
+be transferred from document to document. For instance, definitions
+placed in the preamble can be copied to the preamble of another document.
+
+But that is hardly optimal. Instead, \texttt{diffcoeff} allows such
+definitions to be placed in a text file with the the extension \texttt{.def}
+and a name of your choosing. For the present document the file is
+called \texttt{diffcoeff-doc.def} and should have been placed alongside
+the \verb`.sty` file in your \TeX{} distribution. The contents of
+this file can be seen at §To use these definitions, the \texttt{diffcoeff}
+package is called with the command
+\begin{lyxcode}
+\textbackslash usepackage{[}def-file=diffcoeff-doc{]}\{diffcoeff\}{[}=v4{]}
+\end{lyxcode}
+But even this process still means copying a definition file from directory
+to directory as one works on different documents. The solution is
+to make a definition file available for \emph{all} documents and the
+way to do that is by placing it in the texmf tree, preferably not
+the one created by your \TeX{} distribution (perhaps MiKTeX or TexLive),
+but your own \emph{personal} texmf tree.
+
+\texttt{\vspace{2ex}
+ }
+
+\noindent %
+\noindent\fbox{\begin{minipage}[t]{1\linewidth - 2\fboxsep - 2\fboxrule}%
+\textbf{Personal texmf tree? }
+
+This is a directory for `waifs and strays' of the \TeX{} system that
+are not included in standard distributions like MiK\TeX{} or \TeX Live.
+For instance, it is the place for personal packages designed for your
+own particular circumstances or preferences, and is structured like
+the standard MiK\TeX{} or \TeX Live hierarchy but placed in another
+location so that there is no chance of its being overwritten when
+MiK\TeX{} or \TeX Live are updated. However, those distributions need
+to be alerted to its existence. For MiK\TeX , open the MiK\TeX{} console,
+click on \textsf{Settings} and then the \textsf{Directories} tab.
+Click the \textsf{+} button and navigate to your personal texmf tree
+to add it to the MiK\TeX{} search path. Having added it, you will then
+need to refresh the filename database by clicking on the \textsf{Tasks}
+menu and selecting the obvious entry. I am not familiar with \TeX Live
+but presume an analogous process will apply there.%
+\end{minipage}}
+
+\medskip{}
+
+\noindent Provided your \LaTeX{} distribution knows about your personal
+texmf tree, then a \texttt{.def} file placed within it, will be accessible
+to all documents.
+
+\subsubsection{Structure of the \texttt{.def} file}
+
+The best way to see what a \texttt{.def} file looks like is to view
+\texttt{diffcoeff-doc.def }in a text editor.
+
+If you want your variant definitions to use defaults different from
+those supplied with the \texttt{diffcoeff} package, then the first
+definition in the \texttt{.def} file should be the one setting the
+new defaults, with an \emph{empty} first argument to the \texttt{\textbackslash diffdef}
+command:
+\begin{lyxcode}
+\textbackslash diffdef~\{\}~~~~
+
+~~\{~~~~~~
+
+~~~~key-1~=~value-1,~~~~
+
+~~~~key-2~=~value-2,
+
+~~~~...
+
+~~~~key-n~=~value-n
+
+~~\}
+\end{lyxcode}
+The key-value list is a comma-separated list; hence the last entry
+doesn't need to end with a comma. Nudge and separation values need
+to include the unit, \texttt{mu}; a numerical value alone will result
+in error.\texttt{ }Because a \texttt{.def} file\texttt{ }is a \LaTeX{}
+file, comments need to start with a \texttt{\%} character.
+
+\subsubsection{\texttt{diffcoeff.def}}
+
+Note that if the \texttt{diffcoeff} package is invoked without an
+explicit \texttt{def-file= <filename>} option statement, as here,
+\begin{lyxcode}
+\textbackslash usepackage\{diffcoeff\}{[}=v4{]}
+\end{lyxcode}
+then it will search in the texmf tree (the \LaTeX{} distribution's
+and your personal one) and the document directory for a file \texttt{diffcoeff.def}
+and if found will load that. This file should contain definitions
+of those variants you are likely to use in multiple documents. In
+my personal texmf tree (which I've put at \texttt{E:\textbackslash texmf\textbackslash}
+on a Windows machine) the file \texttt{diffcoeff.def} is located in
+the directory \texttt{E:\textbackslash texmf\textbackslash tex\textbackslash latex\textbackslash diffcoeff\textbackslash}.
+(The backslashes are replaced by forward slashes on linux machines.)
+
+Variants likely to be of value only to a specific document should
+be added to the preamble of that document. Alternatively, they could
+be added to \texttt{diffcoeff.def} but that added-to file saved to
+the document directory under a \emph{different} name -- e.g. I've
+saved the variants required for the present document under the name
+\texttt{diffcoeff-doc.def}. Many of these variants were created solely
+to illustrate points in the present document and I have no intention
+of using them in my own work. Consequently my \texttt{diffcoeff.def}
+file is smaller, containing only a selection from \texttt{diffcoeff-doc.def}.
+
+\section{Differentials in integrals, etc.}
+
+Forms like $dx$ occur not only in derivatives but also in other contexts,\footnote{I thank \noun{Sergio Callegari} for drawing my attention to this rather
+obvious point, and its omission from previous versions of \texttt{diffcoeff}.} for example, the expression for a total differential like
+\[
+\dl P=\diffp Px\dl x+\diffp Py\dl y+\diffp Pz\dl z,
+\]
+or an integral like $\int\sin x\dl2x$, or a multi-variable integral
+like
+\[
+\iiintop_{-\infty}^{\infty}V(x,y,z)\dl3x\dl2y\dl2z.
+\]
+Surely we want the `d's in these expressions to correspond to their
+form (upright or math italic) in derivatives? If, for instance, the
+\texttt{ISO} package option has been set, one doesn't want to be writing
+\texttt{\textbackslash mathrm\{d\}} in every (or indeed any) integral.
+To this end, \texttt{diffcoeff} provides a command \texttt{\textbackslash dl}
+to write the `d' in a differential in a manner consistent with the
+default form used in derivatives. In the present document, the default
+form is math-italic and so
+\begin{centred}
+\verb`$ \dl x $` $\Longrightarrow$ $ \dl x. $
+\end{centred}
+\noindent It is also possible\footnote{\noindent From version 3.1 of \texttt{diffcoeff}; version 3.0 of the
+package produced a \LaTeX{} error.} to use the command before, for instance, \texttt{\textbackslash mathbf\{x\}}
+or \texttt{\textbackslash vec\{x\}}:
+\begin{centred}
+\verb`$ \dl \vec{x} $` $\Longrightarrow$ $ \dl \vec{x} $,~~~~\verb`$ \dl \mathbf{x} $`
+$\Longrightarrow$$ \dl \mathbf{x}. $
+\end{centred}
+
+\subsection{Options}
+
+There are two options available with the differential command.
+
+The first is the dotted name option discussed in §\ref{sec:Changing-defaults}.
+Thus, to illustrate a differential with an upright `d', write
+\begin{centred}
+\verb`$ \dl.up.x $` $\Longrightarrow$ $ \dl.up.x. $
+\end{centred}
+\noindent This presumes that a variant derivative with upright `d's
+has been defined and the definition is available, either in the preamble
+or in an accessible \texttt{.def} file, as discussed in the previous
+section. Alternatively, if you have defined your default derivative
+to use upright `d's (perhaps with the \texttt{ISO} option) then
+\texttt{\textbackslash dl} alone will suffice to produce an upright
+`d'.
+
+\subsubsection{Partial differential}
+
+\label{subsec:Partial-differential}Since the variant \texttt{\textbackslash diff.p.}
+is defined in \texttt{diffcoeff4.sty} itself, \texttt{\textbackslash dl.p.}
+is always available and at 6 keystrokes offers a slightly shorter
+way of writing \texttt{\textbackslash partial} (8 keystrokes). However,
+there are sufficient contexts where expressions like \verb`\partial_x`
+are used, perhaps as a shortcut for a partial derivative, for it to
+be worthwhile to define an appropriate command for this variant. From
+version 4.0, \texttt{diffcoeff} therefore provides \verb`\dlp`, defined
+by
+\begin{lyxcode}
+\textbackslash NewDocumentCommand~\textbackslash dlp~\{\}~\{~\textbackslash dl.p.~\}
+\end{lyxcode}
+Thus, for instance, \verb`$ \dlp_x $` $\Longrightarrow$ $ \dlp_x $.
+
+\subsubsection{Spacing}
+
+This second option inserts spacing before the `d'. If \texttt{\textbackslash dl}
+is followed by a digit (0, 1, 2, ..., 9) it will insert a horizontal
+space of that number of mu before the `d'; (\texttt{\textbackslash dl0x}
+has the same effect as \texttt{\textbackslash dl x}.)\texttt{ }Thus,
+an alternative way of writing an example in Chapter~18 of \emph{The
+\TeX book} is
+\begin{centred}
+\verb`$ \dl x\dl3y=r\dl3r\dl3\theta $` $\Longrightarrow$ $ \dl x\dl3y=r\dl3r\dl3\theta. $
+\end{centred}
+\noindent To my eye this is too much space; I prefer
+\begin{centred}
+\noindent \verb`$ \dl x\dl2y=r\dl2r\dl2\theta $` $\Longrightarrow$
+$ \dl x\dl2y=r\dl2r\dl2\theta. $
+\end{centred}
+\noindent I used \texttt{\textbackslash dl3x\textbackslash dl2y\textbackslash dl2z}
+when writing the triple integral above, \emph{no} extra spacing when
+writing the total differential expression, since the differentials
+are already distinct from the preceding fraction forms $\diff.ptxt.Px$
+etc., and \texttt{\textbackslash dl2x} when writing $\int\sin x\dl2x$.
+
+Note that only \emph{one} digit can be used. If two are used, as here,
+\verb`$ \dl20x $` $\Longrightarrow$ $ \dl20x $, the effect is unlikely
+to be what is wanted.
+
+From version 3.2 of \texttt{diffcoeff} it is possible to also add
+\emph{negative} space before the differential, which might be useful
+in special contexts, perhaps to construct a symbol:
+\begin{centred}
+\verb`$ /\dl-9x $` $\Longrightarrow$ $ /\dl-9x. $
+\end{centred}
+\noindent For negative space before the differential, add a minus
+sign before the (single) digit.
+
+The spacing digit option \emph{follows} the dot-delimited name option.
+For example, earlier, in the denominator of a mixed partial derivative,
+I have used what is effectively \texttt{\textbackslash dlp x\textbackslash dlp2y\textbackslash dlp2z},
+and the variation to that spacing when a higher-order differentiation
+occurs:
+\begin{centred}
+\verb`$ \dlp x^2\dlp1y\dlp2z $` $\Longrightarrow$ $ \dlp x^2\dlp1y\dlp2z. $
+\end{centred}
+
+\subsection{Rationale}
+
+Version 1 of the \texttt{diffcoeff} package arose from a need to simplify
+the parsing of differential coefficients for another program I was
+working on which was struggling to `read' all the possible permutations
+of \texttt{\textbackslash frac} or \texttt{\textbackslash tfrac}
+or \texttt{\textbackslash dfrac} or slash forms of the derivative,
+of \texttt{d} or \texttt{\textbackslash mathrm\{d\}} or \texttt{\textbackslash partial}
+or \texttt{D} or \texttt{\textbackslash mathrm\{D\}} or \texttt{\textbackslash nabla},\texttt{
+}and of points of evaluation delimited by vertical rules or parentheses.\texttt{ }Although
+regular expressions coped with most of these cases, it was \emph{messy}.
+
+There are other packages which have commands for the derivative (e.g.,
+\texttt{bropd}, \texttt{commath},\texttt{ esdiff}, \texttt{physymb})
+but none quite gave what I wanted -- although they probably cope
+with most users' needs. \texttt{esdiff} came closest to what I was
+seeking but failed when it came to combining algebraic and numeric
+orders of differentation in a mixed partial derivative (and made heavier
+use of braces than I liked in that case too).
+
+\subsubsection{\texttt{diffcoeff.sty}}
+
+I have tried to make using \texttt{diffcoeff} intuitive. Looking at
+the other packages mentioned, writing something like \texttt{\textbackslash diff{[}n{]}\{f\}\{x\}}
+(which can be trimmed to \texttt{\textbackslash diff{[}n{]}fx} for
+single-token arguments) seems `natural' -- only \texttt{physymb}
+deviates from the pattern.
+\begin{itemize}
+\item It seems consistent with this pattern to use a comma list for specifying
+the orders of differentiation of the variables in a higher order mixed
+partial derivative (and its suppression when all are of order 1)
+\item Having specified the orders, surely the program itself should calculate
+the overall order? \texttt{esdiff} does this for numerical orders;
+\texttt{diffcoeff} does this for both numeric and algebraic orders,
+\end{itemize}
+\begin{centred}
+\verb`\[ \diffp[m-(k+1),m+(k-1)]{F(x,y,z)}{x,y,z} \]`
+\end{centred}
+\begin{example}
+$\Longrightarrow$ \[ \diffp[m-(k+1),m+(k-1)]{F(x,y,z)}{x,y,z} \]
+\end{example}
+
+\begin{itemize}
+\item and where it fails either to calculate at all or to present the result
+in a preferred form, offers the order-override option:
+\end{itemize}
+\begin{centred}
+\verb`\[ \diffp[m+(k+1),m+(k-1)][2(m+k+1)]{F(x,y,z,w)}{x,y,z,w} \]`
+\end{centred}
+\begin{example}
+$\Longrightarrow$ \[ \diffp[m+(k+1),m+(k-1)][2(m+k+1)]{F(x,y,z,w)}{x,y,z,w} \]
+\end{example}
+
+\begin{itemize}
+\item I wished to avoid the unnecessary writing of superscripts, subscripts
+and brace pairs. In the examples just given, no superscript tokens
+\texttt{\textasciicircum} are written by the user despite the higher-order
+differentiation in $x$ and $y$, and only the two inescapable brace
+pairs are required.
+\item The use of a comma list for the second mandatory argument in a partial
+derivative -- the list of variables -- makes differentiations in
+super- or subscripted symbols (as occurs prolifically in tensor calculus)
+easier to both write and read by avoiding unnecessary brace pairs.
+\end{itemize}
+\begin{centred}
+\verb`\[ \diffp{A_i}{ x^j,x^k } \]` $\Longrightarrow$ \[ \diffp{A_i}{ x^j,x^k } \]
+\end{centred}
+\begin{itemize}
+\item Should a point of evaluation or variables held constant be considered
+part of the derivative? Thermodynamic usage was decisive here. The
+partial derivative alone is ambiguous -- the parentheses and subscript
+are essential to understand what is being stated:
+\[
+\diffp ST[V]
+\]
+Hence provision for these extra elements was included in the derivative
+commands.
+\item Given the position of the subscripted symbol in the displayed derivative,
+it's positioning as the \emph{final} argument in the derivative command
+feels inevitable.
+\item Version 1 of \texttt{diffcoeff} used braces for this argument to avoid
+any possible confusion with a following mathematical expression. That
+use of braces is now deprecated in \texttt{xparse}, has been deprecated
+in \texttt{diffcoeff} since version 2, and is no longer compatible
+with version 4. Later versions of \texttt{diffcoeff} use square brackets,
+conforming with familiar \LaTeX{} practice. The only special remembering
+needed is avoidance of a space before the argument -- and if it does
+slip in, it won't cause a \LaTeX{} error. It will be treated as part
+of a following mathematical expression and displayed as such.
+\item The star option also prompted the question: is it needed? After all,
+one can always leave the first mandatory argument empty and append
+the differentiand `by hand'. But once the provision for points of
+evaluation or variables held constant was incorporated into the derivative
+commands, the star option became the simplest way of handling appended
+differentiands since the parentheses for a variable held constant
+must wrap around the differential operator \emph{and} differentiand.
+Once available, it provides a simple way of switching between (and
+comparing) the appearance of differentiand-in-the-numerator and differentiand-appended.
+\item The slash option was added to the derivative commands after seeing
+how widely such forms are used in texts at all levels. The placement
+of the slash, between the two mandatory arguments, seems more-or-less
+self-evident.
+\item A later option added to \texttt{\textbackslash diff} (and not present
+in version 1) was the dot-delimited name option. Once \texttt{xtemplate}
+was used as the basis of the package this seemed the most straightforward
+way of making available, ready to hand, the wealth of variants that
+\texttt{xtemplate} makes possible. (It's just a pity that the second
+dot is needed, and a single-dot naming scheme can't be used, but \texttt{xparse}
+forces my hand here.)
+\item Having added the dot-delimited name option, the use of a \texttt{def}
+file to store variants or preferred defaults is more-or-less forced,
+otherwise one is faced with making these definitions anew for each
+new document (or locating a previous document and copying from that
+to the new one).
+\item To handle possible differences between display-style and text-style
+(and script-style) derivatives (see §\ref{subsec:Text-and-script-style})
+I considered using \TeX 's \texttt{\textbackslash mathchoice} command.
+This command takes four arguments, corresponding to display-, text-,
+script- and scriptscript-styles and would require forming four derivatives
+each time a derivative is used, `just in case'. In fact fraction-form
+derivatives are used overwhelmingly in display-style expressions,
+the slash form being used for inline use. Given the ease of defining
+a fraction-form variant for text-style use, and the rareness of such
+use, employing variants seemed the way to go. It is the one adopted
+and avoids the computational burden associated with the use of \texttt{\textbackslash mathchoice}.
+\item After version 2 of the package appeared on CTAN, it was pointed out
+to me that there was an issue of consistency between the form of `d'
+used in a derivative (upright or math-italic) and the form used in
+an integral. I had overlooked this matter completely and in version
+3 of the package remedied the omission with the differential command
+\texttt{\textbackslash dl}. A spacing option for \texttt{\textbackslash dl}
+was almost inevitable. From version 4 the partial analogue \texttt{\textbackslash dlp}
+has been added.
+\item Space before the differentiand was requested by a user. Once considered
+it became clear that there are (at least) two ways of thinking of
+a derivative: as $\diff y/x$, a ratio of differentials where $\dl y$
+is a unit and it makes no sense to insert space between the `d'
+and the `y', and as
+\[
+\diff!{F(x)}x
+\]
+where the function $F(x)$ is being operated on by $\diff{}/x$ and
+it is natural to insert space between the `d' and the `F'. With
+that realisation came the need for a simple switch-like package option
+(\verb`spaced`) to turn spacing on or off, and a switch-like argument
+(\verb`!`) to countermand the package option in exceptional cases
+(version 4).
+\end{itemize}
+
+\section{Reference}
+
+\subsection{Commands}
+\begin{description}
+\item [{\texttt{\textbackslash diff}}] arguments (all optional unless
+otherwise indicated):
+\begin{enumerate}
+\item .\emph{name}. for the given settings
+\item {*} append-differentiand switch
+\item {[}\emph{order}{]} or {[}\emph{comma-list of orders}{]} of differentiation
+\item {[}\emph{order-override}{]}
+\item ! countermand before-differentiand spacing of the \verb`spaced` package
+option
+\item \{\emph{differentiand}\} (mandatory)
+\item / slash-form switch
+\item \{\emph{comma list of differentiation variables}\} (mandatory)
+\item {[}\emph{point of evaluation/variables held constant}{]}
+\end{enumerate}
+\item [{\texttt{\textbackslash diffdef}}] arguments (all mandatory):
+\begin{enumerate}
+\item \{\emph{name}\}
+\item \{\emph{key=value comma list}\}
+\end{enumerate}
+\item [{\texttt{\textbackslash diffp}}] \texttt{= \textbackslash diff.p.}
+\item [{\texttt{\textbackslash dl}}] arguments (all optional):
+\begin{enumerate}
+\item .\emph{name}. (as for \texttt{\textbackslash diff})
+\item \emph{minus sign} (optional, use only if negative spacing before the
+`d' is wanted)
+\item \emph{digit} (insert spacing of this number of mu before the `d')
+\end{enumerate}
+\item [{\texttt{\textbackslash dpl}}] \texttt{= \textbackslash dl.p.}
+\item [{\texttt{\textbackslash negmu}}] insert a $-1$ mu space
+\item [{\texttt{\textbackslash nilmu}}] insert a $0$ mu space
+\item [{\texttt{\textbackslash onemu}}] insert a $1$ mu space
+\item [{\texttt{\textbackslash twomu}}] insert a $2$ mu space
+\end{description}
+Deprecated (why try remembering the special names when the forms on
+the right are self-explanatory):
+\begin{description}
+\item [{\texttt{\textbackslash Diff}}] preferred form: \texttt{\textbackslash diff.D.}
+\item [{\texttt{\textbackslash diffd}}] preferred form \texttt{\textbackslash diff.delta.}
+\item [{\texttt{\textbackslash Diffd}}] preferred form\texttt{ \textbackslash diff.Delta.}
+\end{description}
+
+\subsection{The file \texttt{diffcoeff-doc.def}}
+
+\label{sec:diffcoeff-doc.def}The file \verb`diffcoeff-doc.def` contains
+the following definitions:
+\begin{verbatim}
+%%%%%%%%%% ordinary %%%%%%%%%%
+% ( ) for pt of eval.
+\diffdef { paren }
+ {
+ left-delim = \left ( ,
+ right-delim = \right ),
+ subscr-nudge = -6 mu
+ }
+
+% upright
+\diffdef { up }
+ {
+ op-symbol = \mathrm{d},
+ op-order-sep = 0 mu
+ }
+
+\diffdef { Up }
+ {
+ op-symbol = \mathrm{D},
+ op-order-sep = 0 mu
+ }
+
+% wrap long vars: (d longvar)
+\diffdef { wrapall } {long-var-wrap = (dv)}
+
+% nabla in numerator, d in denominator
+\diffdef { nabla }
+ {
+ op-symbol = \nabla,diffcoeff-doc.def
+ op-symbol-alt = d
+ }
+
+% align op left; no italic nudge
+\diffdef { left }
+ {
+ *-op-left = true,
+ *-italic-nudge = 0 mu
+ }
+
+% slash-form: vrule for pt of eval
+\diffdef { svrule }
+ {
+ /-left-delim = ,
+ /-right-delim = |
+ }
+
+%%%%%%%%%% partial %%%%%%%%%%
+% partial, vrule for pt of eval.
+\diffdef { pvrule } { op-symbol = \partial }
+
+% partial, no subscr nudge (adrift in a sea of white space)
+\diffdef { padrift }
+ {
+ op-symbol = \partial,
+ left-delim = \left ( ,
+ right-delim = \right ),
+ subscr-nudge = 0 mu
+ }
+
+% partial, [ ] for pt of eval.
+\diffdef { psqbra }
+ {
+ op-symbol = \partial,
+ left-delim = \left [ ,
+ right-delim = \right ],
+ subscr-nudge = 0 mu
+ }
+
+% Delta as partial deriv.
+\diffdef { pDelta }
+ {
+ op-symbol = \Delta ,
+ op-order-sep = 0 mu ,
+ left-delim = \left ( ,
+ right-delim = \right ),
+ subscr-nudge = -6 mu
+ }
+
+% align op left; italic nudge
+\diffdef { pleft }
+ {
+ op-symbol = \partial,
+ *-op-left = true ,
+ *-italic-nudge = 3 mu ,
+ left-delim = \left ( ,
+ right-delim = \right ),
+ subscr-nudge = -3 mu
+ }
+
+% partial, textstyle
+\diffdef { ptxt }
+ {
+ op-symbol = \partial,
+ denom-term-sep = 1 mu ,
+ left-delim = \left ( ,
+ right-delim = \right ),
+ elbowroom = -2 mu ,
+ subscr-nudge = -3 mu
+ }
+
+% partial, wide sep of terms
+\diffdef { pwide }
+ {
+ op-symbol = \partial,
+ denom-term-sep = 3 mu ,
+ /-denom-term-sep = 3 mu ,
+ left-delim = \left ( ,
+ right-delim = \right ),
+ subscr-nudge = -6 mu
+ }
+
+ %%%%%%%%%% differential %%%%%%%%%%
+ \diffdef { up }
+ { op-symbol = \mathrm{d} }
+\end{verbatim}
+
+
+\subsection{Version comparison}
+
+\label{sec:Version-comparison}Unlike version 1, version 2 and later
+are built on the the \texttt{xtemplate} package which makes certain
+facilities available which it would be silly not to exploit. Hence
+the coding in the later versions is completely different and there
+are consequences.
+\begin{enumerate}
+\item From version 2.0
+\begin{enumerate}
+\item The \texttt{\textbackslash diffset} command, formerly used to tweak
+the display of derivatives, has been superseded by the \texttt{\textbackslash diffdef}
+command. \texttt{\textbackslash diffset} now sends a message warning
+of its obsolescence to the terminal and \LaTeX{} log but is otherwise
+functionless. It should not interfere with the compilation of a document
+but any intended fine-tuning of the display by means of the \texttt{\textbackslash diffset}
+command\texttt{ }will not eventuate. The warning message is: \texttt{Obsolete
+command: \textbackslash diffset has been superseded by the \textbackslash diffdef
+command.} \texttt{See the diffcoeff} \texttt{doc\-umentation for
+further information.} The \texttt{\textbackslash diffdef} command
+is discussed in §\ref{subsec:diffdef};
+\item The optional trailing argument used to indicate a point of evaluation
+or variables held constant is now delimited by square brackets, \texttt{{[}}
+and \texttt{{]}}, as other optional arguments are. For compatibility
+with version 1, versions 2 and 3 still accepted braces to delimit
+this argument but from version 4 of \texttt{diffcoeff} only the square-bracket
+delimited argument is accepted. (The use of braces around \emph{optional}
+arguments while once accepted is now deprecated in \texttt{xparse}
+on which \texttt{diffcoeff} depends);
+\item The commands \texttt{\textbackslash Diff}, \texttt{\textbackslash diffd}
+and \texttt{\textbackslash Diffd} used to construct derivatives from
+$D$, $\delta$ and $\Delta$ in version 1, are still available but
+deprecated. A new optional argument in the \texttt{\textbackslash diff}
+command offers these and a host of other possibilities and is now
+the preferred method of forming such variants; see §\ref{subsec:D-delta-Delta}.
+\end{enumerate}
+\item Version 3.0
+\begin{enumerate}
+\item adds a command, \texttt{\textbackslash dl} (from \emph{d}ifferentia\emph{l})
+to write differentials like $dx$ that occur in integrals and in other
+contexts in a manner consistent with the form used in derivatives.
+After all, if one is using upright `d's in derivatives, similarly
+upright `d's should occur in these other contexts;\footnote{This rather obvious lack in version 2 was pointed out to me by Sergio
+Callegari.}
+\item provides some simple spacing commands that can be useful for tweaking
+standard spacing.
+\end{enumerate}
+\item Version 3.1 enables the differential command to be used before forms
+like \texttt{\textbackslash vec\{x\}} (an overlooked possibility
+causing an error in earlier versions).
+\item Version 3.2
+\begin{enumerate}
+\item allows negative spacing before the differential command \texttt{\textbackslash dl};
+\item fixes a bug in which an ordinary derivative as the differentiand of
+a partial derivative displayed as a partial derivativ\texttt{diffcoeff-doc.def}e.
+It now displays, as it should, as an ordinary derivative.
+\end{enumerate}
+\item Version 4.0
+\begin{enumerate}
+\item enables the insertion of a small space before the differentiand, either
+as the default behaviour (package option \verb`spaced`) or at explicit
+request (argument \verb`!` of the \verb`\diff` command); see §\ref{subsec:Spacing-before-derivand}.
+\item prevents the ligature $df$ that marred previous versions; this is
+now rendered $\dl f$.
+\item offers the document command \verb`\dlp` for the \emph{partial} differential;
+see §\ref{subsec:Partial-differential};
+\item no longer accepts \emph{the braced form} of the\emph{ }trailing optional
+argument specifying a point of evaluation or (for partial derivatives)
+variables held constant. This was a relic from version 1 of \texttt{diffcoeff},
+and has been deprecated since version 2.
+\end{enumerate}
+\item Version 4.1
+\begin{enumerate}
+\item changes the code for the \verb`long-var-wrap` setting to avoid a
+problem arising from a change in \verb`xtemplate`;
+\item improves spacing between operator and variable in \emph{denominators}
+of differential coefficients (e.g. prevents ligatures).
+\end{enumerate}
+\item Version 4.2
+\begin{enumerate}
+\item see the announcement at the start of this document.
+\end{enumerate}
+\end{enumerate}
+
+\end{document}
diff --git a/macros/latex/contrib/diffcoeff/diffcoeff5.def b/macros/latex/contrib/diffcoeff/diffcoeff5.def
new file mode 100644
index 0000000000..d61028a4a0
--- /dev/null
+++ b/macros/latex/contrib/diffcoeff/diffcoeff5.def
@@ -0,0 +1,136 @@
+% file `diffcoef5.def'
+% definitions for variant forms
+% 2023/01/03
+% Andrew Parsloe ajparsloe@gmail.com
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% material derivative
+\difdef { f, s } { D }
+ { op-symbol = \mathrm{D} }
+% math italic
+\difdef { f, s, c } { d' }
+ {
+ op-symbol = d,
+ op-order-nudge = 1 mu
+ }
+\difdef { f, s, c } { D' }
+ {
+ op-symbol = D,
+ op-order-nudge = 1 mu
+ }
+% Greek
+\difdef { f, s } { gd }
+ { op-symbol = \delta }
+\difdef { f, s } { gD }
+ { op-symbol = \Delta }
+% spaceless appending
+\difdef { f, fp } { *0 }
+ {
+ *derivand-sep = 0 mu ,
+ outer-Ldelim = \mleft ( ,
+ outer-Rdelim = \mright )
+ }
+% tfrac, nonscalable
+\difdef { f, fp } { t }
+ {
+ style = tfrac ,
+ derivand-sep = 1 mu plus 1 mu minus 1 mu,
+ multi-term-sep = 0 mu ,
+ term-sep-adjust = 0 mu ,
+ lvwrap-sup-nudge = 0 mu ,
+ outer-Ldelim = \bigl (,
+ outer-Rdelim = \bigr ),
+ elbowroom = -2 mu ,
+ sub-nudge = -3 mu
+ }
+% slash fractions: 0=scalable,
+% 1=big, 2=Big, 3=bigg, 4=Bigg
+% but > 1 gives eyesores
+\difdef { s, sp } { 0 }
+ {
+ style = auto ,
+ outer-Ldelim = \left [ ,
+ outer-Rdelim = \right ] ,
+ sub-nudge = 0 mu ,
+ *inner-Ldelim = \mleft ( ,
+ *inner-Rdelim = \mright ),
+ *outer-Ldelim = \left [ ,
+ *outer-Rdelim = \right ]
+ }
+\difdef { s, sp } { 1 }
+ {
+ style = big ,
+ outer-Ldelim = \bigl (,
+ outer-Rdelim = \bigr ),
+ sub-nudge = -2.5 mu,
+ *inner-Ldelim = \bigl (,
+ *inner-Rdelim = \bigr ),
+ *outer-Ldelim = \bigl [,
+ *outer-Rdelim = \bigr ]
+ }
+% vrule point of evaluation
+\difdef { f, fp, s, sp } { | }
+ {
+ outer-Ldelim = \left . ,
+ outer-Rdelim = \right |,
+ sub-nudge = 0 mu
+ }
+% sq. bracket pt of eval.
+\difdef { f, fp, s, sp } { ] }
+ {
+ outer-Ldelim = \left [ ,
+ outer-Rdelim = \right ],
+ elbowroom = 1 mu,
+ sub-nudge = 0 mu
+ }
+% long var wrap
+\difdef { f, fp } { (dv) }
+ { long-var-wrap = (dv) }
+\difdef { f, fp } { dv }
+ { long-var-wrap = dv }
+% compact, D operator
+\difdef { c } { D }
+ {
+ op-symbol = \mathrm{D},
+ op-sub-nudge = -2mu
+ }
+\difdef { c } { D' }
+ {
+ op-symbol = D,
+ op-sub-nudge = -2mu
+ }
+% bold
+\difdef { c } { bD }
+ {
+ op-symbol = \mathbf{D},
+ op-sub-nudge = -2mu
+ }
+% differential style
+\difdef { c, cp } { dl }
+ { style = dl }
+%%%%%%%%%%% differential %%%%%%%%%%
+% partial
+\difdef { l } { p }
+ { op-symbol = \partial }
+% bold
+\difdef { l } { b }
+ { op-symbol = \mathrm{d}\mathbf }
+
+% line elements: Pythagoras
+\difdef { l } { + }
+ {
+ multi-term-sep = 0 mu +,
+ term-sep-adjust = 0 mu ,
+ outer-Ldelim =
+ }
+% Minkowski
+\difdef { l } { - }
+ {
+ multi-term-sep = 0 mu -,
+ term-sep-adjust = 0 mu ,
+ outer-Ldelim =
+ }
+%%%%%%%%%% jacobian %%%%%%%%%%
+% slash fraction
+\difdef { j } { s }
+ { style = / } \ No newline at end of file
diff --git a/macros/latex/contrib/pythonimmediate/README b/macros/latex/contrib/pythonimmediate/README
index c164e2ca9b..be4026bf43 100644
--- a/macros/latex/contrib/pythonimmediate/README
+++ b/macros/latex/contrib/pythonimmediate/README
@@ -8,7 +8,7 @@ Report bugs at https://github.com/user202729/TeXlib
========
-Copyright 2022 user202729
+Copyright 2022-2023 user202729
This work may be distributed and/or modified under the conditions of the
LaTeX Project Public License (LPPL), either version 1.3c of this license or
@@ -21,4 +21,4 @@ This work has the LPPL maintenance status `maintained'.
The Current Maintainer of this work is user202729.
-This work consists of the files pythonimmediate.sty, pythonimmediate_script_pytotex.py, pythonimmediate_script_textopy.py.
+This work consists of the files pythonimmediate.sty.
diff --git a/macros/latex/contrib/pythonimmediate/pythonimmediate.pdf b/macros/latex/contrib/pythonimmediate/pythonimmediate.pdf
index 67bb6f1259..c9bf716c59 100644
--- a/macros/latex/contrib/pythonimmediate/pythonimmediate.pdf
+++ b/macros/latex/contrib/pythonimmediate/pythonimmediate.pdf
Binary files differ
diff --git a/macros/latex/contrib/pythonimmediate/pythonimmediate.sty b/macros/latex/contrib/pythonimmediate/pythonimmediate.sty
index 6ed72780bf..5a92dd88a6 100644
--- a/macros/latex/contrib/pythonimmediate/pythonimmediate.sty
+++ b/macros/latex/contrib/pythonimmediate/pythonimmediate.sty
@@ -1,5 +1,5 @@
% File: pythonimmediate.sty
-% Copyright 2022 user202729
+% Copyright 2022-2023 user202729
%
% This work may be distributed and/or modified under the conditions of the
% LaTeX Project Public License (LPPL), either version 1.3c of this license or
@@ -12,7 +12,7 @@
%
% The Current Maintainer of this work is user202729.
-\ProvidesExplPackage{pythonimmediate}{2022/12/23}{0.0.0}{Library to run Python code}
+\ProvidesExplPackage{pythonimmediate}{2023/01/09}{0.1.0}{Library to run Python code}
\RequirePackage{saveenv}
\RequirePackage{currfile}
@@ -29,110 +29,104 @@
\cs_generate_variant:Nn \str_if_in:nnF {VnF}
\cs_generate_variant:Nn \tl_build_put_right:Nn {NV}
-%\bench before~rescan.
-%\bench after~rescan.
+% some old commands e.g. \$, \^, \_, \~ require \set@display@protect to be robust.
+% ~ needs to be redefined directly.
+\precattl_exec:n {
+ \cs_new_protected:Npn \_pythonimmediate_begingroup_setup_estr: {
+ \begingroup
+ \escapechar=-1~
+ \cC{set@display@protect}
+ \let \cA\~ \relax
+ }
+}
-%\GenerateVariantsFile:n{\rescansynclastfilename}
+% use like this \__begingroup_setup_estr: ⟨some command⟩ \endgroup
+% e.g. \__begingroup_setup_estr: \exp_args:NNx \endgroup \__function:n {⟨text⟩}
+% will eventually execute to \__function:n {⟨estr-expansion of text⟩}
-\str_set:Nn \_pythonimmediate_outputdir{.}
-\tl_set:Nn \_pythonimmediate_textopy_script_path{}
-\str_set:Nn \_pythonimmediate_mode{multiprocessing-network}
+\str_set:Nn \_pythonimmediate_args{--mode=multiprocessing-network}
\str_set:Nn \_pythonimmediate_python_executable{python3}
+\str_set:Nn \_pythonimmediate_python_flags{}
\keys_define:nn{pythonimmediate}{
- outputdir.tl_set_x:N=\_pythonimmediate_outputdir,
- %outputdir.default:n={.}, % huh does not work?
-
- mode.tl_set:N=\_pythonimmediate_mode,
- scriptpath.tl_set_x:N=\_pythonimmediate_textopy_script_path,
-
- python-executable.tl_set:N=\_pythonimmediate_python_executable,
+ args.tl_gset:N =\_pythonimmediate_args,
+ python-executable.tl_gset:N=\_pythonimmediate_python_executable,
+ python-flags.tl_gset:N =\_pythonimmediate_python_flags,
+ child-process.bool_gset:N =\_pythonimmediate_child_process,
}
\ProcessKeysOptions{pythonimmediate}
-\str_set:NV \_pythonimmediate_outputdir \_pythonimmediate_outputdir
-\str_set:NV \_pythonimmediate_mode \_pythonimmediate_mode
-\str_set:NV \_pythonimmediate_textopy_script_path \_pythonimmediate_textopy_script_path
+\_pythonimmediate_begingroup_setup_estr:
+ \str_gset:Nx \_pythonimmediate_args { \_pythonimmediate_args }
+ \str_gset:Nx \_pythonimmediate_python_executable{ \_pythonimmediate_python_executable }
+ \str_gset:Nx \_pythonimmediate_python_flags { \_pythonimmediate_python_flags }
+\endgroup
-\msg_new:nnn {pythonimmediate} {shell-fail} {Shell~command~execution~failed!}
-\msg_new:nnn {pythonimmediate} {cannot-determine-script-path} {Cannot~determine~script~path!}
+\msg_new:nnn {pythonimmediate} {shell-fail} {Please~enable~unrestricted~shell~scape!}
\msg_new:nnn {pythonimmediate} {cannot-read-line} {Cannot~read~line!}
\msg_new:nnn {pythonimmediate} {internal-error} {Internal~error!}
-\msg_new:nnn {pythonimmediate} {invalid-mode} {Invalid~mode:~'#1'.}
-
-\bool_new:N \_pythonimmediate_mode_multiprocessing_network
-\bool_new:N \_pythonimmediate_mode_unnamed_pipe
-\str_if_eq:VnT \_pythonimmediate_mode {multiprocessing-network} {\bool_set_true:N \_pythonimmediate_mode_multiprocessing_network}
-\str_if_eq:VnT \_pythonimmediate_mode {unnamed-pipe} {\bool_set_true:N \_pythonimmediate_mode_unnamed_pipe}
-\bool_if:nF {\_pythonimmediate_mode_multiprocessing_network || \_pythonimmediate_mode_unnamed_pipe} {
- \msg_error:nnV {pythonimmediate} {invalid-mode} \_pythonimmediate_mode
+\sys_if_shell_unrestricted:F {
+ \msg_error:nn {pythonimmediate} {shell-fail}
}
-% we need to persistently open the file anyway, so using LaTeX3 stream reference counting doesn't help
-\newread \_pythonimmediate_read_file
-
+% note on \newread: we need to persistently open the file anyway, so using LaTeX3 stream reference counting doesn't help
+% ======== setup read file ========
-%\bench before~setup.
+\bool_if:NTF \_pythonimmediate_child_process {
+ % make read file read from stdin
+ % note that \ior_str_get:NN cannot be used here as it checks for \ifeof which breaks with terminal for some reason
+ \int_const:Nn \_pythonimmediate_read_file {-1}
+} {
+ \newread \_pythonimmediate_read_file
+ \openin \_pythonimmediate_read_file=|"\_pythonimmediate_python_executable \space \_pythonimmediate_python_flags \space -m ~ pythonimmediate.pytotex ~ \_pythonimmediate_args"~
+}
-\begingroup
- \endlinechar=-1~
- \tl_if_empty:NT \_pythonimmediate_textopy_script_path {
- % ======== first use kpsewhich to get the _pythonimmediate_script_path here ========
- % (abuse \_pythonimmediate_read_file variable for this purpose)
- \openin \_pythonimmediate_read_file=|"kpsewhich~ pythonimmediate_script_textopy.py"~
- \readline \_pythonimmediate_read_file to \_pythonimmediate_textopy_script_path
- %\bench after~get~textopy~path.
- \ifeof \_pythonimmediate_read_file
- \msg_error:nn {pythonimmediate} {cannot-determine-script-path}
- \fi
+% ======== copy of ior_str_get but does not check for file end ========
+\cs_generate_variant:Nn \use_ii_i:nn {o}
+\cs_new_protected:Npn \_pythonimmediate_str_get:N #1 {
+ \use_ii_i:on {\the\endlinechar\relax} {
+ \endlinechar=-1~
+ \readline \_pythonimmediate_read_file to #1
+ \endlinechar=
}
+}
+
- \str_if_eq:xnF {\str_range:Vnn \_pythonimmediate_textopy_script_path {-10} {-1}} {textopy.py} {
- \msg_error:nn {pythonimmediate} {cannot-determine-script-path}
- }
- \newwrite \_pythonimmediate_write_file
+% ======== setup write file ========
+\newwrite \_pythonimmediate_write_file
+\bool_if:NTF \_pythonimmediate_child_process {
+ %\immediate\openout \_pythonimmediate_write_file=symlink-to-stderr.txt~
+ % tried this method, it seems to work except that it's buffered when stderr is redirected to a file...
+ \immediate\openout \_pythonimmediate_write_file=|"\_pythonimmediate_python_executable \space \_pythonimmediate_python_flags \space -m ~ pythonimmediate.copy_to_stderr"~
+} {
+ \immediate\openout \_pythonimmediate_write_file=|"\_pythonimmediate_python_executable \space \_pythonimmediate_python_flags \space -m ~ pythonimmediate.textopy"~
+ % note that openout, even to shell, will append .tex if there's no dot in the command
+ % so we artificially add a dot here in `.textopy`
- %\bench before~openin.
+ % both processes must be before the \readline below so that the 2 Python processes are started "in parallel"
+ \_pythonimmediate_str_get:N \_pythonimmediate_line % read one line from pytotex half, forward to textopy half
- % ======== open persistent pipes to the child processes
- \bool_if:NTF \_pythonimmediate_mode_unnamed_pipe { % in this case make sure the pipe remains open...
- \openin \_pythonimmediate_read_file=|"sleep~ 0.5s|\_pythonimmediate_python_executable \space \str_range:Vnn \_pythonimmediate_textopy_script_path {1} {-11} pytotex.py \space \_pythonimmediate_mode"~ % we must use the primitive here to use the pipe file path
- % TODO sleep infinity causes some resource leak (the process will not exit after TeX exits). Need to fix
- % but sleep too little might be problematic that it exits before the setup is done
- % we can just assume machines are not that slow
- } {
- \openin \_pythonimmediate_read_file=|"\_pythonimmediate_python_executable \space \str_range:Vnn \_pythonimmediate_textopy_script_path {1} {-11} pytotex.py \space \_pythonimmediate_mode"~ % we must use the primitive here to use the pipe file path
+ \str_if_eq:VnT \_pythonimmediate_line {} {
+ \msg_error:nn {pythonimmediate} {cannot-read-line}
}
- %\bench after~openin.
+ \str_const:Nn \_pythonimmediate_engine_mark_pdftex {p}
+ \str_const:Nn \_pythonimmediate_engine_mark_ptex {P}
+ \str_const:Nn \_pythonimmediate_engine_mark_uptex {u}
- %\bench before~openout.
- \immediate\openout \_pythonimmediate_write_file=|"\_pythonimmediate_python_executable \space \_pythonimmediate_textopy_script_path \space \_pythonimmediate_mode"~
- % both processes must be before the \readline above so that the 2 Python processes are started "in parallel"
- %\bench after~openout.
+ \str_const:Nn \_pythonimmediate_engine_mark_xetex {x}
+ \str_const:Nn \_pythonimmediate_engine_mark_luatex {l}
- \readline \_pythonimmediate_read_file to \_pythonimmediate_dummy_line % endlinechar still -1
- %\bench after~read~line.
- \bool_if:NT \_pythonimmediate_mode_multiprocessing_network {
- \str_if_eq:VnF \_pythonimmediate_dummy_line {listener-setup-done} {
- \msg_error:nn {pythonimmediate} {cannot-read-line}
- }
- }
- \bool_if:NT \_pythonimmediate_mode_unnamed_pipe {
- \str_if_in:VnF \_pythonimmediate_dummy_line {pytotex_pid=} {
- \msg_error:nn {pythonimmediate} {cannot-read-line}
- }
+ \immediate\write\_pythonimmediate_write_file {
+ \use:c {_pythonimmediate_engine_mark_ \c_sys_engine_str}
+ \_pythonimmediate_line
}
- \bool_if:NT \_pythonimmediate_mode_unnamed_pipe {
- \immediate\write\_pythonimmediate_write_file {\_pythonimmediate_dummy_line} % which contains pytotex's pid
- }
-\endgroup
-
-%\bench after~setup.
+}
+% ======== bootstrap utility functions
% read one block of \TeX\ code from Python, store into the specified variable
% the block is delimited using |surround_delimiter()| in Python i.e. the first and last line are identical
@@ -149,9 +143,6 @@
\bool_do_until:nn {\tl_if_eq_p:NN \_pythonimmediate_delimiter \_pythonimmediate_line} {
\tl_build_gput_right:NV #1 \_pythonimmediate_line
- \ifeof \_pythonimmediate_read_file
- \msg_error:nn {pythonimmediate} {internal-error}
- \fi
\readline \_pythonimmediate_read_file to \_pythonimmediate_line
}
\tl_build_gend:N #1
@@ -176,8 +167,6 @@
\scantokens \expandafter{\_pythonimmediate_code}
} % trick described in https://tex.stackexchange.com/q/640274 to scantokens the code with \newlinechar=10
-% bootstrap code
-%\bench before~bootstrap.
+% ======== bootstrap code
\_pythonimmediate_run_block:
-%\bench after~bootstrap.
diff --git a/macros/latex/contrib/pythonimmediate/pythonimmediate.tex b/macros/latex/contrib/pythonimmediate/pythonimmediate.tex
index 877bc3a05e..eacffa24f6 100644
--- a/macros/latex/contrib/pythonimmediate/pythonimmediate.tex
+++ b/macros/latex/contrib/pythonimmediate/pythonimmediate.tex
@@ -1,4 +1,4 @@
-\ProvidesFile{pythonimmediate.tex}[2022/12/23 0.0.0 Library to run Python code]
+\ProvidesFile{pythonimmediate.tex}[2023/01/09 0.1.0 Library to run Python code]
\RequirePackage{fvextra}
\documentclass{l3doc}
\usepackage{tikz}
@@ -53,12 +53,25 @@ so you don't need to write a single line of \TeX\ code.
%You need to install Python \pkg{daemoniker} and \pkg{psutil} package.
-The package should work out of the box with no additional Python package needed.
+In addition to the \LaTeX\ package, you need the Python \pkg{pythonimmediate-tex} package,
+installation instruction can be found at \url{https://pypi.org/project/pythonimmediate-tex/}.
-\subsection{Installation on Overleaf}
+Note that not all \TeX\ package versions are compatible with all Python package versions.
+This \TeX\ package is compatible with Python package version |0.1.2|.
+
+Remember to enable unrestricted\footnote{
+ There's little point in supporting restricted mode, since it's possible to execute arbitrary shell commands in Python anyway.
+ If it's needed to execute untrusted \TeX\ code, separate sandboxing should be used.
+} shell-escape. (there's a guide on \TeX.SE if necessary: \url{https://tex.stackexchange.com/q/598818/250119})
+
+\subsection{Installation on Overleaf}\label{installation-on-overleaf}
At the point of writing, this package can be used on Overleaf.
+Nevertheless, you cannot use |pip| to install Python packages on Overleaf directly, instead it's possible to
+download |.zip| file, include it in your Overleaf project, and specify where the package can be found to Python
+using |PYTHONPATH| environment variable.
+
Instruction:
\begin{itemize}
@@ -67,14 +80,27 @@ Instruction:
\item \file{saveenv.sty}
\item \file{precattl.sty}
\item \file{pythonimmediate.sty}
- \item \file{pythonimmediate_script_textopy.py}
- \item \file{pythonimmediate_script_pytotex.py}
+ \item \file{pythonimmediate-tex-0.1.2.zip}
\end{itemize}
+ The |0.1.2| part should be replaced with the desired version
+ of the Python package.
+
+ The |.sty| files can be downloaded from CTAN at
+ \url{https://ctan.org/pkg/saveenv},
+ \url{https://ctan.org/pkg/precattl},
+ \url{https://ctan.org/pkg/pythonimmediate}
+ respectively.
+
+ The |.zip| file containing Python source code
+ can be downloaded from PyPI: \url{https://pypi.org/project/pythonimmediate-tex/\#files}.
+
\item Write the following in the preamble:
\begin{verbatim}
\usepackage[abspath]{currfile}
-\usepackage[mode=unnamed-pipe]{pythonimmediate}
+\usepackage[python-executable={PYTHONPATH=pythonimmediate-tex-0.1.2.zip/pythonimmediate-tex-0.1.2/ python3},args={--mode=unnamed-pipe}]{pythonimmediate}
\end{verbatim}
+As above, replace both occurrences of |0.1.2| with the downloaded version specified in the zip file above.
+
Refer to \ref{troubleshoot-source-file-not-found} for explanation of the |abspath| option.
\end{itemize}
@@ -84,32 +110,37 @@ so in that case consider writing |\errorstopmode|.
Refer to \ref{troubleshoot-Python-error} to read the error traceback in case of Python error.
+Some construct inside the |pycode| block might make the code editor on Overleaf report an error,
+even though the code is valid. Refer to \url{https://www.overleaf.com/learn/how-to/Code_Check#Code_Check_Limitations}.
+
\section{Usage}
\subsection{Package options}
-\DescribeOption{outputdir=}
-Specify the output directory if it's not the default value.
+Normally no options are required.
+If you're not sure what they do, just use the default options.
-\begin{texnote}
- The value will be |x|-expanded.
-\end{texnote}
-
-Using the \pkg{outputdir} package, it's possible to determine the output directory automatically, subject to restrictions.
-
-An usage example, if you invoked |pdflatex| with the command
+\DescribeOption{args=}
+Arguments to be passed to the Python component of the program. Run
\begin{verbatim}
-pdflatex --output-directory=/tmp/ a.tex
-\end{verbatim}
-then in the file \file{a.tex} you should have
-\begin{verbatim}
-\usepackage[outputdir=/tmp/]{pythonimmediate}
+python -m pythonimmediate.pytotex --help
\end{verbatim}
+on the command-line to view the available options.
+
+The documentation is also available at
+\url{https://pythonimmediate.readthedocs.io/en/latest/pythonimmediate.html#module-pythonimmediate.pytotex}.
-\DescribeOption{mode=}
-Method to communicate between \TeX\ and Python. Usually the method will be automatically detected.
+\DescribeOption{python-executable=}
+The name/path to the Python executable. Default to |python3|.
-Possible values include |multiprocessing-network| and |unnamed-pipe|.
+Can also be used to provide environment variables to the Python process.
+An example how to do that is explained in \ref{installation-on-overleaf}.
+
+\DescribeOption{python-flags=}
+Flags to be passed to the Python interpreter. For example pass |-O| to disable assertions.
+
+The documentations can be found by running |python --help| on the command-line,
+or visit \url{https://docs.python.org/3/using/cmdline.html}.
\subsection{\TeX\ interface}
@@ -226,16 +257,22 @@ The \TeX\ interface is only used to call Python. Apart from that, all the work c
All functions in this section should be imported from |pythonimmediate| package, unless specified otherwise.
+Currently, all the documentations are moved to the Python package documentation,
+see \url{https://pythonimmediate.readthedocs.io/}.
+
+Documentation of a few functions are still kept here for convenience, but \textbf{they might be outdated}.
+Always refer to the online documentation.
+
\subsubsection{Print to \TeX}\label{print-to-TeX}
-\DescribePython{.print()}
+\DescribePython{.print_TeX()}
\DescribePython{.file}
These functions are used in |\pyc| command or |pycode| environment.
Unlike most other packages, using |print()| function in Python will print to the console (\TeX\ standard output).
In order to print \TeX\ code to be executed, you can do one of
\begin{verbatim}
-pythonimmediate.print(...)
+pythonimmediate.print_TeX(...)
print(..., file=pythonimmediate.file)
with contextlib.redirect_stdout(pythonimmediate.file):
print(...)
@@ -286,7 +323,8 @@ This is an example of how the functions could be used. The name should be mostly
\usepackage{pythonimmediate}
\begin{document}
\begin{pycode}
-from pythonimmediate import newcommand, peek_next_char, get_next_char, get_arg_str, print
+from pythonimmediate import newcommand, peek_next_char, get_next_char, get_arg_str
+from pythonimmediate import print_TeX as print
@newcommand
def innerproduct():
s = get_arg_str() # in the example below this will have the value '\mathbf{a},\mathbf{b}'
@@ -334,7 +372,7 @@ Similar to some functions above, except that the argument is fully expanded and
similar to how |\py| command (\ref{py-command}) reads its arguments.
\DescribePython{.execute()}
-Takes a string and execute it immediately. (so that any |.execute()| will be executed before any |.print()|)
+Takes a string and execute it immediately. (so that any |.execute()| will be executed before any |.print_TeX()|)
Assuming \TeX\ is in errorstopmode (i.e. errors halt \TeX\ execution),
any error in \TeX\ will create an error in Python and the traceback should point to the correct line of code.
diff --git a/macros/latex/contrib/pythonimmediate/pythonimmediate_script_pytotex.py b/macros/latex/contrib/pythonimmediate/pythonimmediate_script_pytotex.py
deleted file mode 100755
index abb71a2631..0000000000
--- a/macros/latex/contrib/pythonimmediate/pythonimmediate_script_pytotex.py
+++ /dev/null
@@ -1,57 +0,0 @@
-#!/bin/python3
-"""
-======== Py-to-TeX half ========
-
-receive things that should be passed to TeX from TeX-to-Py half,
-then pass to TeX.
-
-the things that are sent should already be newline-terminated if necessary.
-
-user code are not executed here.
-"""
-
-import sys
-import signal
-signal.signal(signal.SIGINT, signal.SIG_IGN) # when the other half terminates this one will terminates "gracefully"
-
-#debug_file=open(Path(tempfile.gettempdir())/"pythonimmediate_debug_pytotex.txt", "w", encoding='u8', buffering=2)
-#debug=functools.partial(print, file=debug_file, flush=True)
-debug=lambda *args, **kwargs: None
-
-import argparse
-parser=argparse.ArgumentParser(formatter_class=argparse.ArgumentDefaultsHelpFormatter)
-parser.add_argument("mode", choices=["multiprocessing-network", "unnamed-pipe"])
-args=parser.parse_args()
-
-
-# ======== setup communication method. Just an infinite loop print whatever being sent.
-
-if args.mode=="multiprocessing-network":
- from multiprocessing.connection import Listener
-
- address=("localhost", 7348)
- #address="./pythonimmediate.socket"
- with Listener(address) as listener:
- print("listener-setup-done", flush=True)
- with listener.accept() as connection:
- debug("accepted a connection")
- while True:
- try:
- data=connection.recv_bytes()
- debug(" data=", data)
- sys.__stdout__.buffer.write(data) # will go to TeX
- sys.__stdout__.buffer.flush()
- except EOFError: break
-
-elif args.mode=="unnamed-pipe":
- import os
- sys.stdout.write("pytotex_pid=" + str(os.getpid()) + "\n")
- sys.stdout.flush()
- for line in sys.stdin:
- sys.stdout.write(line)
- sys.stdout.flush()
-
-else:
- assert False
-
-# ========
diff --git a/macros/latex/contrib/pythonimmediate/pythonimmediate_script_textopy.py b/macros/latex/contrib/pythonimmediate/pythonimmediate_script_textopy.py
deleted file mode 100755
index 7e4f4a7de9..0000000000
--- a/macros/latex/contrib/pythonimmediate/pythonimmediate_script_textopy.py
+++ /dev/null
@@ -1,2295 +0,0 @@
-#!/bin/python3
-"""
-======== TeX-to-Py half ========
-
-receive commands from TeX, then execute it here
-"""
-
-
-#from __future__ import annotations
-import sys
-import os
-import inspect
-import contextlib
-import io
-import functools
-from typing import Optional, Union, Callable, Any, Iterator, Protocol, Iterable, Sequence, Type, Tuple, List, Dict
-import typing
-from abc import ABC, abstractmethod
-from pathlib import Path
-from dataclasses import dataclass
-import tempfile
-import signal
-import traceback
-import re
-import collections
-import enum
-
-
-def user_documentation(x: Union[Callable, str])->Any:
- return x
-
-
-
-#debug=functools.partial(print, file=sys.stderr, flush=True) # unfortunately this is async ... or so it seems...?
-#debug_file=open(Path(tempfile.gettempdir())/"pythonimmediate_debug_textopy.txt", "w", encoding='u8', buffering=2)
-#debug=functools.partial(print, file=debug_file, flush=True)
-debug=lambda *args, **kwargs: None
-
-
-import argparse
-parser=argparse.ArgumentParser(formatter_class=argparse.ArgumentDefaultsHelpFormatter)
-parser.add_argument("mode", choices=["multiprocessing-network", "unnamed-pipe"])
-args=parser.parse_args()
-
-expansion_only_can_call_Python=False # normally. May be different in LuaTeX etc.
-
-# ======== setup communication method. Requires raw_readline() and send_raw() methods.
-
-if True:
- sys.stdin=None # type: ignore
- # avoid user mistakenly read
-
- raw_readline=sys.__stdin__.readline # raw_readline() should return "⟨line⟩\n" or "" (if EOF) on each call
-
-if args.mode=="multiprocessing-network":
- address=("localhost", 7348) # this must be identical to that of the other half-script
- #address="./pythonimmediate.socket"
-
- from multiprocessing.connection import Client
- connection=Client(address)
- debug("connected")
-
- def send_raw(s: str)->None: # send_raw() should get pass the s = "⟨line⟩\n"
- global connection
- connection.send_bytes(s.encode('u8'))
-
-elif args.mode=="unnamed-pipe":
- pytotex_pid_line=raw_readline()
- match_=re.fullmatch("pytotex_pid=(\d+)\n", pytotex_pid_line)
- assert match_
- pytotex_pid=int(match_[1])
-
- connection_=open("/proc/" + str(pytotex_pid) + "/fd/0", "w", encoding='u8',
- buffering=1 # line buffering
- )
-
- def send_raw(s: str)->None:
- global connection_
- connection_.write(s)
- connection_.flush() # just in case
-
-else:
- assert False
-
-# ======== done.
-
-# https://stackoverflow.com/questions/5122465/can-i-fake-a-package-or-at-least-a-module-in-python-for-testing-purposes
-from types import ModuleType
-pythonimmediate: Any=ModuleType("pythonimmediate")
-pythonimmediate.__file__="pythonimmediate.py"
-sys.modules["pythonimmediate"]=pythonimmediate
-
-pythonimmediate.debugging=True
-
-def export_function_to_module(f: Callable)->Callable:
- """
- the functions decorated with this decorator are accessible from user code with
-
- import pythonimmediate
- pythonimmediate.⟨function name⟩(...)
- """
- setattr(pythonimmediate, f.__name__, f)
- return f
-
-action_done=False
-
-
-def check_not_finished()->None:
- global action_done
- if action_done:
- raise RuntimeError("can only do one action per block!")
-
-def send_finish(s: str)->None:
- check_not_finished()
- global action_done
- action_done=True
- send_raw(s)
-
-
-import random
-def surround_delimiter(block: str)->str:
- while True:
- delimiter=str(random.randint(0, 10**12))
- if delimiter not in block: break
- return delimiter + "\n" + block + "\n" + delimiter + "\n"
-
-bootstrap_code: Optional[str]=""
-def mark_bootstrap(code: str)->None:
- global bootstrap_code
- assert bootstrap_code is not None
- bootstrap_code+=code
-
-def substitute_private(code: str)->str:
- return (code
- #.replace("\n", ' ') # because there are comments in code, cannot
- .replace("__", "_" + "pythonimmediate" + "_")
- )
-
-def send_bootstrap_code()->None:
- global bootstrap_code
- assert bootstrap_code is not None
- send_raw(surround_delimiter(substitute_private(bootstrap_code)))
- bootstrap_code = None
-
-# ========
-
-
-# as the name implies, this reads one "command" from Python side and execute it.
-# the command might do additional tasks e.g. read more \TeX\ code.
-#
-# e.g. if `block' is read from the communication channel, run |\__run_block:|.
-
-mark_bootstrap(
-r"""
-\cs_new_protected:Npn \__read_do_one_command: {
- \begingroup
- \endlinechar=-1~
- \readline \__read_file to \__line
- \expandafter
- \endgroup % also this will give an error instead of silently do nothing when command is invalid
- \csname __run_ \__line :\endcsname
-}
-
-% read documentation of |_peek| commands for details what this command does.
-\cs_new_protected:Npn \pythonimmediatecontinue #1 {
- \immediate\write \__write_file {r #1}
- \__read_do_one_command:
-}
-
-\cs_new_protected:Npn \pythonimmediatecontinuenoarg {
- \pythonimmediatecontinue {}
-}
-
-% internal function. Just send an arbitrary block of data to Python.
-\cs_new_protected:Npn \__send_block:e #1 {
- \immediate\write \__write_file {
- #1 ^^J
- pythonimm?""" + '"""' + r"""?'''? % following character will be newline
- }
-}
-
-\cs_new_protected:Npn \__send_block:n #1 {
- \__send_block:e {\unexpanded{#1}}
-}
-
-\AtEndDocument{
- \immediate\write \__write_file {r}
-}
-""")
-
-
-# ========
-
-# when 'i⟨string⟩' is sent from TeX to Python, the function with index ⟨string⟩ in this dict is called
-TeX_handlers: Dict[str, Callable[[], None]]={}
-
-TeXToPyObjectType=Optional[str]
-
-def run_main_loop()->TeXToPyObjectType:
- while True:
- line=readline()
- if not line: return None
-
- if line[0]=="i":
- TeX_handlers[line[1:]]()
- elif line[0]=="r":
- return line[1:]
- else:
- raise RuntimeError("Internal error: unexpected line "+line)
-
-def run_main_loop_get_return_one()->str:
- line=readline()
- assert line[0]=="r"
- return line[1:]
-
-
-
-user_documentation(
-"""
-All exported functions can be accessed through the module as |import pythonimmediate|.
-
-The |_finish| functions are internal functions, which must be called \emph{at most} once in each
-|\pythonimmediate:n| call from \TeX\ to tell \TeX\ what to do.
-
-The |_local| functions simply execute the code. These functions will only return when
-the \TeX\ code finishes executing; nevertheless, the \TeX\ code might recursively execute some Python code
-inside it.
-
-A simple example is |pythonimmediate.run_block_local('123')| which simply typesets |123|.
-
-The |_peek| functions is the same as above; however, the \TeX\ code must contain an explicit command
-|\pythonimmediatecontinue{...}|.
-
-The argument of |\pythonimmediatecontinue| will be |e|-expanded
-by |\write| (note that the written content must not contain any newline character,
-otherwise the behavior is undefined), then returned as a string by the Python code.
-The Python function will only return when |\pythonimmediatecontinue| is called.
-
-In other words, |run_*_local(code)| is almost identical to |run_*_peek(code + "\pythonimmediatecontinue {}")|.
-""")
-
-@export_function_to_module
-def run_block_finish(block: str)->None:
- send_finish("block\n" + surround_delimiter(block))
-
-
-@user_documentation
-@export_function_to_module
-def execute(block: str)->None:
- """
- Run a block of \TeX\ code (might consist of multiple lines).
- Catcode-changing commands are allowed inside.
-
- A simple example is |pythonimmediate.run_block_local('123')| which simply typesets |123|.
-
- A more complicated example is |pythonimmediate.run_block_local(r'\verb+%+')|.
- """
- run_block_local(block)
-
-def check_line(line: str, *, braces: bool, newline: bool, continue_: Optional[bool])->None:
- """
- check user-provided line before sending to TeX for execution
- """
- if braces:
- assert line.count("{") == line.count("}")
- if newline:
- assert '\n' not in line
- assert '\r' not in line # this is not the line separator but just in case
- if continue_==True: assert "pythonimmediatecontinue" in line
- elif continue_==False: assert "pythonimmediatecontinue" not in line
-
-
-
-
-do_run_error_finish=True
-
-
-
-
-
-user_scope: Dict[str, Any]={} # consist of user's local variables etc.
-
-def readline()->str:
- line=raw_readline()
- if not line:
- sys.stderr.write("\n\nTraceback (most recent call last):\n")
- traceback.print_stack(file=sys.stderr)
- sys.stderr.write("RuntimeError: Fatal irrecoverable TeX error\n\n")
- os._exit(1)
-
-
- assert line[-1]=='\n'
- line=line[:-1]
- debug("======== saw line", line)
- return line
-
-block_delimiter: str="pythonimm?\"\"\"?'''?"
-
-def read_block()->str:
- """
- Internal function to read one block sent from \TeX\ (including the final delimiter line,
- but the delimiter line is not returned)
- """
- lines: List[str]=[]
- while True:
- line=readline()
- if line==block_delimiter:
- return '\n'.join(lines)
- else:
- lines.append(line)
-
-
-@export_function_to_module
-class NToken(ABC):
- """
- Represent a possibly-notexpanded token.
- For convenience, a notexpanded token is called a blue token.
- It's not always possible to determine the notexpanded status of a following token in the input stream.
- Remark: Token objects must be frozen.
- """
-
- @abstractmethod
- def __str__(self)->str: ...
-
- @abstractmethod
- def repr1(self)->str: ...
-
- @property
- @abstractmethod
- def assignable(self)->bool: ...
-
- def assign(self, other: "NToken")->None:
- assert self.assignable
- NTokenList([T.let, self, C.other("="), C.space(' '), other]).execute()
-
- def assign_future(self)->None:
- assert self.assignable
- futurelet_(PTTBalancedTokenList(BalancedTokenList([self.no_blue])))
-
- def assign_futurenext(self)->None:
- assert self.assignable
- futureletnext_(PTTBalancedTokenList(BalancedTokenList([self.no_blue])))
-
- def meaning_str(self)->str:
- """
- get the meaning of this token as a string.
- """
- return NTokenList([T.meaning, self]).expand_x().str()
-
- @property
- @abstractmethod
- def blue(self)->"BlueToken": ...
-
- @property
- @abstractmethod
- def no_blue(self)->"Token": ...
-
- def meaning_equal(self, other: "Token")->bool:
- return NTokenList([T.ifx, self, other, Catcode.other("1"), T["else"], Catcode.other("0"), T.fi]).expand_x().bool()
-
- def str(self)->str:
- """
- self must represent a character of a TeX string. (i.e. equal to itself when detokenized)
- return the string content.
-
- default implementation below. Not necessarily correct.
- """
- raise ValueError("Token does not represent a string!")
-
- def degree(self)->int:
- """
- return the imbalance degree for this token ({ -> 1, } -> -1, everything else -> 0)
-
- default implementation below. Not necessarily correct.
- """
- return 0
-
-
-@export_function_to_module
-class Token(NToken):
- """
- Represent a TeX token, excluding the notexpanded possibility.
- See also documentation of NToken.
- """
-
- @abstractmethod
- def serialize(self)->str: ...
-
- @property
- def blue(self)->"BlueToken": return BlueToken(self)
-
- @property
- def no_blue(self)->"Token": return self
-
- def __repr__(self)->str:
- return f"<Token: {self.repr1()}>"
-
- @staticmethod
- def deserialize(s: str)->"Token":
- t=TokenList.deserialize(s)
- assert len(t)==1
- return t[0]
-
- @staticmethod
- def get_next()->"Token":
- """
- Get the following token.
-
- Note: in LaTeX3 versions without the commit |https://github.com/latex3/latex3/commit/24f7188904d6|
- sometimes this may error out.
-
- Note: because of the internal implementation of |\peek_analysis_map_inline:n|, this may
- tokenize up to 2 tokens ahead (including the returned token),
- as well as occasionally return the wrong token in unavoidable cases.
- """
- return Token.deserialize(str(get_next_()[0]))
-
- @staticmethod
- def peek_next()->"Token":
- """
- Get the following token without removing it from the input stream.
-
- Equivalent to get_next() then put_next() immediately. See documentation of get_next() for some notes.
- """
- return Token.deserialize(
- typing.cast(Callable[[], TTPLine], Python_call_TeX_local(
- r"""
- \cs_new_protected:Npn \__peek_next_callback: #1 {
- \immediate\write \__write_file { r^^J #1 }
- \expandafter % expand the ##1 in (*)
- \__read_do_one_command:
- }
-
- \cs_new_protected:Npn %name% {
- \peek_analysis_map_inline:n {
- \peek_analysis_map_break:n {
- \__tlserialize_char_unchecked:nnNN {##1}{##2}##3 \__peek_next_callback: ##1 % (*)
- }
- }
- }
- """, recursive=False))()
- )
-
- def put_next(self)->None:
- d=self.degree()
- if d==0:
- BalancedTokenList([self]).put_next()
- else:
- assert isinstance(self, CharacterToken)
- if d==1:
- put_next_bgroup(PTTInt(self.index))
- else:
- assert d==-1
- put_next_egroup(PTTInt(self.index))
-
-
-
-
-
-
-"""
-TeX code for serializing and deserializing a token list.
-Convert a token list from/to a string.
-"""
-
-
-mark_bootstrap(
-r"""
-\precattl_exec:n {
-
-% here #1 is the target token list to store the result to, #2 is a string with the final '.'.
-\cs_new_protected:Npn \__tldeserialize_dot:Nn #1 #2 {
- \begingroup
- \tl_set:Nn \__tmp {#2}
- \tl_replace_all:Nnn \__tmp {~} {\cO\ }
-
- \def \start ##1 { \csname ##1 \endcsname }
-
- \def \> ##1 ##2 \cO\ { \csname ##1 \endcsname ##2 \cU\ }
- \def \\ ##1 \cO\ ##2 { \expandafter \noexpand \csname ##1 \endcsname \csname ##2 \endcsname }
- \def \1 ##1 ##2 { \char_generate:nn {`##1} {1} \csname ##2 \endcsname }
- \def \2 ##1 ##2 { \char_generate:nn {`##1} {2} \csname ##2 \endcsname }
- \def \3 ##1 ##2 { \char_generate:nn {`##1} {3} \csname ##2 \endcsname }
- \def \4 ##1 ##2 { \char_generate:nn {`##1} {4} \csname ##2 \endcsname }
- \def \6 ##1 ##2 { #### \char_generate:nn {`##1} {6} \csname ##2 \endcsname }
- \def \7 ##1 ##2 { \char_generate:nn {`##1} {7} \csname ##2 \endcsname }
- \def \8 ##1 ##2 { \char_generate:nn {`##1} {8} \csname ##2 \endcsname }
- \def \A ##1 ##2 { \char_generate:nn {`##1} {10} \csname ##2 \endcsname }
- \def \B ##1 ##2 { \char_generate:nn {`##1} {11} \csname ##2 \endcsname }
- \def \C ##1 ##2 { \char_generate:nn {`##1} {12} \csname ##2 \endcsname }
- \def \D ##1 ##2 { \expandafter \expandafter \expandafter \noexpand \char_generate:nn {`##1} {13} \csname ##2 \endcsname }
- \def \R ##1 { \cFrozenRelax \csname ##1 \endcsname }
-
- \let \. \empty
-
- \exp_args:NNNx
- \endgroup \tl_set:Nn #1 {\expandafter \start \__tmp}
-}
-
-\cs_new_protected:Npn \__tlserialize_char_unchecked:nnNN #1 #2 #3 #4 {
- % #1=token, #2=char code, #3=catcode, #4: callback (will be called exactly once and with nothing following the input stream)
- \int_compare:nNnTF {#2} = {-1} {
- % token is control sequence
- \tl_if_eq:onTF {#1} {\cFrozenRelax} {
- #4 {\cStr{ R }}
- } {
- \tl_if_eq:onTF {#1} { \cC{} } {
- #4 {\cStr{ \\\ }}
- } {
- \tl_set:Nx \__name { \expandafter \cs_to_str:N #1 }
- \exp_args:Nx #4 { \prg_replicate:nn {\str_count_spaces:N \__name} {>} \cStr\\ \__name \cStr\ }
- }
- }
- } {
- % token is not control sequence
- % (hex catcode) (character) (or escape sequence with that character)
- \exp_args:Nx #4 { #3 \expandafter \string #1 }
- }
-}
-
-}
-
-% deserialize as above but #2 does not end with '.'.
-\cs_new_protected:Npn \__tldeserialize_nodot:Nn #1 #2 {
- \__tldeserialize_dot:Nn #1 {#2 .}
-}
-
-% serialize token list in #2 store to #1.
-\cs_new_protected:Npn \__tlserialize_nodot_unchecked:Nn #1 #2 {
- \tl_build_begin:N #1
- \tl_set:Nn \__tlserialize_callback { \tl_build_put_right:Nn #1 }
- \tl_analysis_map_inline:nn {#2} {
- \__tlserialize_char_unchecked:nnNN {##1}{##2}##3 \__tlserialize_callback
- }
- \tl_build_end:N #1
-}
-
-% serialize token list in #2 store to #1. Call T or F branch depends on whether serialize is successful.
-% #1 must be different from \__tlserialize_tmp.
-\cs_new_protected:Npn \__tlserialize_nodot:NnTF #1 #2 {
- \__tlserialize_nodot_unchecked:Nn #1 {#2}
- \__tldeserialize_nodot:NV \__tlserialize_nodot_tmp #1
-
- \tl_if_eq:NnTF \__tlserialize_nodot_tmp {#2} % dangling
-}
-
-\cs_new_protected:Npn \__tlserialize_nodot:NnF #1 #2 {
- \__tlserialize_nodot:NnTF #1 {#2} {} % dangling
-}
-
-\cs_new_protected:Npn \__tlserialize_nodot:NnT #1 #2 #3 { \__tlserialize_nodot:NnTF #1 {#2} {#3} {} }
-
-\msg_new:nnn {pythonimmediate} {cannot-serialize} {Token~list~cannot~be~serialized}
-
-\cs_new_protected:Npn \__tlserialize_nodot:Nn #1 #2{
- \__tlserialize_nodot:NnF #1 {#2} {
- \msg_error:nn {pythonimmediate} {cannot-serialize}
- }
-}
-
-\cs_generate_variant:Nn \__tldeserialize_dot:Nn {NV}
-\cs_generate_variant:Nn \__tldeserialize_nodot:Nn {NV}
-\cs_generate_variant:Nn \__tlserialize_nodot:Nn {NV}
-""")
-
-
-class ControlSequenceTokenMaker:
- """
- shorthand to create control sequence objects in Python easier.
- """
- def __init__(self, prefix: str)->None:
- self.prefix=prefix
- def __getattribute__(self, a: str)->"ControlSequenceToken":
- return ControlSequenceToken(object.__getattribute__(self, "prefix")+a)
- def __getitem__(self, a: str)->"ControlSequenceToken":
- return ControlSequenceToken(object.__getattribute__(self, "prefix")+a)
-
-
-@export_function_to_module
-@dataclass(repr=False, frozen=True)
-class ControlSequenceToken(Token):
- make=typing.cast(ControlSequenceTokenMaker, None) # some interference makes this incorrect. Manually assign below
- csname: str
- @property
- def assignable(self)->bool:
- return True
- def __str__(self)->str:
- if self.csname=="": return r"\csname\endcsname"
- return "\\"+self.csname
- def serialize(self)->str:
- return ">"*self.csname.count(" ") + "\\" + self.csname + " "
- def repr1(self)->str:
- return f"\\{self.csname}"
-
-
-ControlSequenceToken.make=ControlSequenceTokenMaker("")
-
-T=ControlSequenceToken.make
-P=ControlSequenceTokenMaker("_pythonimmediate_") # create private tokens
-
-@export_function_to_module
-class Catcode(enum.Enum):
- begin_group=bgroup=1
- end_group=egroup=2
- math_toggle=math=3
- alignment=4
- parameter=param=6
- math_superscript=superscript=7
- math_subscript=subscript=8
- space=10
- letter=11
- other=12
- active=13
-
- escape=0
- end_of_line=paragraph=line=5
- ignored=9
- comment=14
- invalid=15
-
- @property
- def for_token(self)->bool:
- """
- Return whether a token may have this catcode.
- """
- return self not in (Catcode.escape, Catcode.line, Catcode.ignored, Catcode.comment, Catcode.invalid)
-
- def __call__(self, ch: Union[str, int])->"CharacterToken":
- """
- Shorthand:
- Catcode.letter("a") = Catcode.letter(97) = CharacterToken(index=97, catcode=Catcode.letter)
- """
- if isinstance(ch, str): ch=ord(ch)
- return CharacterToken(ch, self)
-
-C=Catcode
-
-@export_function_to_module
-@dataclass(repr=False, frozen=True) # must be frozen because bgroup and egroup below are reused
-class CharacterToken(Token):
- index: int
- catcode: Catcode
- @property
- def chr(self)->str:
- return chr(self.index)
- def __post_init__(self)->None:
- assert self.catcode.for_token
- def __str__(self)->str:
- return self.chr
- def serialize(self)->str:
- return f"{self.catcode.value:X}{self.chr}"
- def repr1(self)->str:
- cat=str(self.catcode.value).translate(str.maketrans("0123456789", "â‚€â‚₂₃₄₅₆₇₈₉"))
- return f"{self.chr}{cat}"
- @property
- def assignable(self)->bool:
- return self.catcode==Catcode.active
- def degree(self)->int:
- if self.catcode==Catcode.bgroup:
- return 1
- elif self.catcode==Catcode.egroup:
- return -1
- else:
- return 0
- def str(self)->str:
- catcode=Catcode.space if self.index==32 else Catcode.other
- if catcode!=self.catcode:
- raise ValueError("this CharacterToken does not represent a string!")
- return self.chr
-
-class FrozenRelaxToken(Token):
- def __str__(self)->str:
- return r"\relax"
- def serialize(self)->str:
- return "R"
- def repr1(self)->str:
- return r"[frozen]\relax"
- @property
- def assignable(self)->bool:
- return False
-
-frozen_relax_token=FrozenRelaxToken()
-pythonimmediate.frozen_relax_token=frozen_relax_token
-
-# other special tokens later...
-
-bgroup=Catcode.bgroup("{")
-egroup=Catcode.egroup("}")
-space=Catcode.space(" ")
-
-
-
-@export_function_to_module
-@dataclass(frozen=True)
-class BlueToken(NToken):
- token: Token
-
- @property
- def blue(self)->"BlueToken": return self
-
- @property
- def no_blue(self)->"Token": return self.token
-
- def __str__(self)->str: return str(self.token)
-
- def repr1(self)->str: return "notexpanded:"+self.token.repr1()
-
- @property
- def assignable(self)->bool: return self.token.assignable
-
- def put_next(self)->None:
- put_next_blue(PTTBalancedTokenList(BalancedTokenList([self.token])))
-
-
-doc_catcode_table: Dict[int, Catcode]={}
-doc_catcode_table[ord("{")]=Catcode.begin_group
-doc_catcode_table[ord("}")]=Catcode.end_group
-doc_catcode_table[ord("$")]=Catcode.math_toggle
-doc_catcode_table[ord("&")]=Catcode.alignment
-doc_catcode_table[ord("#")]=Catcode.parameter
-doc_catcode_table[ord("^")]=Catcode.math_superscript
-doc_catcode_table[ord("_")]=Catcode.math_subscript
-doc_catcode_table[ord(" ")]=Catcode.space
-doc_catcode_table[ord("~")]=Catcode.active
-for ch in range(ord('a'), ord('z')+1): doc_catcode_table[ch]=Catcode.letter
-for ch in range(ord('A'), ord('Z')+1): doc_catcode_table[ch]=Catcode.letter
-doc_catcode_table[ord("\\")]=Catcode.escape
-doc_catcode_table[ord("%")]=Catcode.comment
-
-e3_catcode_table=dict(doc_catcode_table)
-e3_catcode_table[ord("_")]=Catcode.letter
-e3_catcode_table[ord(":")]=Catcode.letter
-e3_catcode_table[ord(" ")]=Catcode.ignored
-e3_catcode_table[ord("~")]=Catcode.space
-
-
-TokenListType = typing.TypeVar("TokenListType", bound="TokenList")
-
-if typing.TYPE_CHECKING:
- TokenListBaseClass = collections.UserList[Token]
-else: # Python 3.8 compatibility
- TokenListBaseClass = collections.UserList
-
-@export_function_to_module
-class TokenList(TokenListBaseClass):
- @staticmethod
- def force_token_list(a: Iterable)->Iterable[Token]:
- for x in a:
- if isinstance(x, Token):
- yield x
- elif isinstance(x, Sequence):
- yield bgroup
- child=BalancedTokenList(x)
- assert child.is_balanced()
- yield from child
- yield egroup
- else:
- raise RuntimeError(f"Cannot make TokenList from object {x} of type {type(x)}")
-
- def is_balanced(self)->bool:
- """
- check if this is balanced.
- """
- degree=0
- for x in self:
- degree+=x.degree()
- if degree<0: return False
- return degree==0
-
- def check_balanced(self)->None:
- """
- ensure that this is balanced.
- """
- if not self.is_balanced():
- raise ValueError("Token list is not balanced")
-
- def balanced_parts(self)->"List[Union[BalancedTokenList, Token]]":
- """
- split this TokenList into a list of balanced parts and unbalanced {/}tokens
- """
- degree=0
- min_degree=0, 0
- for i, token in enumerate(self):
- degree+=token.degree()
- min_degree=min(min_degree, (degree, i+1))
- min_degree_pos=min_degree[1]
-
- left_half: List[Union[BalancedTokenList, Token]]=[]
- degree=0
- last_pos=0
- for i in range(min_degree_pos):
- d=self[i].degree()
- degree+=d
- if degree<0:
- degree=0
- if last_pos!=i:
- left_half.append(BalancedTokenList(self[last_pos:i]))
- left_half.append(self[i])
- last_pos=i+1
- if min_degree_pos!=last_pos:
- left_half.append(BalancedTokenList(self[last_pos:min_degree_pos]))
-
- right_half: List[Union[BalancedTokenList, Token]]=[]
- degree=0
- last_pos=len(self)
- for i in range(len(self)-1, min_degree_pos-1, -1):
- d=self[i].degree()
- degree-=d
- if degree<0:
- degree=0
- if i+1!=last_pos:
- right_half.append(BalancedTokenList(self[i+1:last_pos]))
- right_half.append(self[i])
- last_pos=i
- if min_degree_pos!=last_pos:
- right_half.append(BalancedTokenList(self[min_degree_pos:last_pos]))
-
- return left_half+right_half[::-1]
-
- def put_next(self)->None:
- for part in reversed(self.balanced_parts()): part.put_next()
-
- @property
- def balanced(self)->"BalancedTokenList":
- """
- return a BalancedTokenList containing the content of this object.
- it must be balanced.
- """
- return BalancedTokenList(self)
-
- def __init__(self, a: Iterable=())->None:
- super().__init__(TokenList.force_token_list(a))
-
- @staticmethod
- def iterable_from_string(s: str, get_catcode: Callable[[int], Catcode])->Iterable[Token]:
- """
- refer to documentation of from_string() for details.
- """
- i=0
- while i<len(s):
- ch=s[i]
- i+=1
- cat=get_catcode(ord(ch))
- if cat==Catcode.space:
- yield space
- # special case: collapse multiple spaces into one but only if character code is space
- if get_catcode(32) in (Catcode.space, Catcode.ignored):
- while i<len(s) and s[i]==' ':
- i+=1
- elif cat.for_token:
- yield cat(ch)
- elif cat==Catcode.ignored:
- continue
- else:
- assert cat==Catcode.escape, f"cannot create TokenList from string containing catcode {cat}"
- cat=get_catcode(ord(s[i]))
- if cat!=Catcode.letter:
- yield ControlSequenceToken(s[i])
- i+=1
- else:
- csname=s[i]
- i+=1
- while i<len(s) and get_catcode(ord(s[i]))==Catcode.letter:
- csname+=s[i]
- i+=1
- yield ControlSequenceToken(csname)
- # special case: remove spaces after control sequence but only if character code is space
- if get_catcode(32) in (Catcode.space, Catcode.ignored):
- while i<len(s) and s[i]==' ':
- i+=1
-
- @classmethod
- def from_string(cls: Type[TokenListType], s: str, get_catcode: Callable[[int], Catcode])->TokenListType:
- """
- convert a string to a TokenList approximately.
- The tokenization algorithm is slightly different from TeX's in the following respect:
-
- * multiple spaces are collapsed to one space, but only if it has character code space (32).
- * spaces with character code different from space (32) after a control sequence is not ignored.
- * ^^ syntax are not supported. Use Python's escape syntax as usual.
- """
- return cls(TokenList.iterable_from_string(s, get_catcode))
-
- @classmethod
- def e3(cls: Type[TokenListType], s: str)->TokenListType:
- """
- approximate tokenizer in expl3 catcode, implemented in Python.
- refer to documentation of from_string() for details.
- """
- return cls.from_string(s, lambda x: e3_catcode_table.get(x, Catcode.other))
-
- @classmethod
- def doc(cls: Type[TokenListType], s: str)->TokenListType:
- """
- approximate tokenizer in document catcode, implemented in Python.
- refer to documentation of from_string() for details.
- """
- return cls.from_string(s, lambda x: doc_catcode_table.get(x, Catcode.other))
-
- def serialize(self)->str:
- return "".join(t.serialize() for t in self)
-
- @classmethod
- def deserialize(cls: Type[TokenListType], data: str)->TokenListType:
- result: List[Token]=[]
- i=0
- cs_skip_space_count=0
- while i<len(data):
- if data[i]==">":
- cs_skip_space_count+=1
- i+=1
- elif data[i]=="\\":
- j=data.index(' ', i+1)
- for __ in range(cs_skip_space_count):
- j=data.index(' ', j+1)
- cs_skip_space_count=0
- result.append(ControlSequenceToken(data[i+1:j]))
- i=j+1
- elif data[i]=="R":
- result.append(frozen_relax_token)
- i+=1
- else:
- result.append(CharacterToken(index=ord(data[i+1]), catcode=Catcode(int(data[i], 16))))
- i+=2
- return cls(result)
-
- def __repr__(self)->str:
- return '<' + type(self).__name__ + ': ' + ' '.join(t.repr1() for t in self) + '>'
-
- def execute(self)->None:
- NTokenList(self).execute()
-
- def expand_x(self)->"BalancedTokenList":
- return NTokenList(self).expand_x()
-
- def bool(self)->bool:
- return NTokenList(self).bool()
-
- def str(self)->str:
- return NTokenList(self).str()
-
-
-
-@export_function_to_module
-class BalancedTokenList(TokenList):
- """
- Represents a balanced token list.
- Note that runtime checking is not strictly enforced,
- use `is_balanced()` method explicitly if you need to check.
- """
-
- def __init__(self, a: Iterable=())->None:
- """
- constructor. This must check for balanced-ness as balanced() method depends on this.
- """
- super().__init__(a)
- self.check_balanced()
-
- def expand_o(self)->"BalancedTokenList":
- return BalancedTokenList(expand_o_(PTTBalancedTokenList(self))[0]) # type: ignore
- def expand_x(self)->"BalancedTokenList":
- return BalancedTokenList(expand_x_(PTTBalancedTokenList(self))[0]) # type: ignore
- def execute(self)->None:
- execute_(PTTBalancedTokenList(self))
-
- def put_next(self)->None:
- put_next_tokenlist(PTTBalancedTokenList(self))
-
- @staticmethod
- def get_next()->"BalancedTokenList":
- """
- get an (undelimited) argument from the TeX input stream.
- """
- return BalancedTokenList(get_argument_tokenlist_()[0]) # type: ignore
-
-
-
-if typing.TYPE_CHECKING:
- NTokenListBaseClass = collections.UserList[NToken]
-else: # Python 3.8 compatibility
- NTokenListBaseClass = collections.UserList
-
-@export_function_to_module
-class NTokenList(NTokenListBaseClass):
- @staticmethod
- def force_token_list(a: Iterable)->Iterable[NToken]:
- for x in a:
- if isinstance(x, NToken):
- yield x
- elif isinstance(x, Sequence):
- yield bgroup
- child=NTokenList(x)
- assert child.is_balanced()
- yield from child
- yield egroup
- else:
- raise RuntimeError(f"Cannot make NTokenList from object {x} of type {type(x)}")
-
- def __init__(self, a: Iterable=())->None:
- super().__init__(NTokenList.force_token_list(a))
-
- def is_balanced(self)->bool:
- return TokenList(self).is_balanced() # a bit inefficient (need to construct a TokenList) but good enough
-
- def simple_parts(self)->List[Union[BalancedTokenList, Token, BlueToken]]:
- """
- Split this NTokenList into a list of balanced non-blue parts, unbalanced {/} tokens, and blue tokens.
- """
- parts: List[Union[TokenList, BlueToken]]=[TokenList()]
- for i in self:
- if isinstance(i, BlueToken):
- parts+=i, TokenList()
- else:
- assert isinstance(i, Token)
- last_part=parts[-1]
- assert isinstance(last_part, TokenList)
- last_part.append(i)
- result: List[Union[BalancedTokenList, Token, BlueToken]]=[]
- for large_part in parts:
- if isinstance(large_part, BlueToken):
- result.append(large_part)
- else:
- result+=large_part.balanced_parts()
- return result
-
- def put_next(self)->None:
- for part in reversed(self.simple_parts()): part.put_next()
-
- def execute(self)->None:
- """
- Execute self.
- """
- parts=self.simple_parts()
- if len(parts)==1:
- x=parts[0]
- if isinstance(x, BalancedTokenList):
- x.execute()
- return
- NTokenList([*self, T.pythonimmediatecontinue, []]).put_next()
- continue_until_passed_back()
-
- def expand_x(self)->BalancedTokenList:
- """
- x-expand self. The result must be balanced.
- """
- NTokenList([T.edef, P.tmp, bgroup, *self, egroup]).execute()
- return BalancedTokenList([P.tmp]).expand_o()
-
- def str(self)->str:
- """
- self must represent a TeX string. (i.e. equal to itself when detokenized)
- return the string content.
- """
- return "".join(t.str() for t in self)
-
- def bool(self)->bool:
- s=self.str()
- return {"0": False, "1": True}[s]
-
-
-class TeXToPyData(ABC):
- @staticmethod
- @abstractmethod
- def read()->"TeXToPyData":
- ...
- @staticmethod
- @abstractmethod
- def send_code(arg: str)->str:
- pass
- @staticmethod
- @abstractmethod
- def send_code_var(var: str)->str:
- pass
-
-# tried and failed
-#@typing.runtime_checkable
-#class TeXToPyData(Protocol):
-# @staticmethod
-# def read()->"TeXToPyData":
-# ...
-#
-# #send_code: str
-#
-# #@staticmethod
-# #@property
-# #def send_code()->str:
-# # ...
-
-
-class TTPLine(TeXToPyData, str):
- send_code=r"\immediate \write \__write_file {{\unexpanded{{ {} }}}}".format
- send_code_var=r"\immediate \write \__write_file {{\unexpanded{{ {} }}}}".format
- @staticmethod
- def read()->"TTPLine":
- return TTPLine(readline())
-
-# some old commands e.g. \$, \^, \_, \~ require \set@display@protect to be robust.
-# ~ needs to be redefined directly.
-mark_bootstrap(
-r"""
-\precattl_exec:n {
- \cs_new_protected:Npn \__begingroup_setup_estr: {
- \begingroup
- \escapechar=-1~
- \cC{set@display@protect}
- \let \cA\~ \relax
- }
-}
-""")
-
-class TTPELine(TeXToPyData, str):
- """
- Same as TTPEBlock, but for a single line only.
- """
- send_code=r"\__begingroup_setup_estr: \immediate \write \__write_file {{ {} }} \endgroup".format
- send_code_var=r"\__begingroup_setup_estr: \immediate \write \__write_file {{ {} }} \endgroup".format
- @staticmethod
- def read()->"TTPELine":
- return TTPELine(readline())
-
-class TTPEmbeddedLine(TeXToPyData, str):
- @staticmethod
- def send_code(self)->str:
- raise RuntimeError("Must be manually handled")
- @staticmethod
- def send_code_var(self)->str:
- raise RuntimeError("Must be manually handled")
- @staticmethod
- def read()->"TTPEmbeddedLine":
- raise RuntimeError("Must be manually handled")
-
-class TTPBlock(TeXToPyData, str):
- send_code=r"\__send_block:n {{ {} }}".format
- send_code_var=r"\__send_block:V {}".format
- @staticmethod
- def read()->"TTPBlock":
- return TTPBlock(read_block())
-
-class TTPEBlock(TeXToPyData, str):
- """
- A kind of argument that interprets "escaped string" and fully expand anything inside.
- For example, {\\} sends a single backslash to Python, {\{} sends a single '{' to Python.
- Done by fully expand the argument in \escapechar=-1 and convert it to a string.
- Additional precaution is needed, see the note above.
- """
- send_code=r"\__begingroup_setup_estr: \__send_block:e {{ {} }} \endgroup".format
- send_code_var=r"\__begingroup_setup_estr: \__send_block:e {} \endgroup".format
- @staticmethod
- def read()->"TTPEBlock":
- return TTPEBlock(read_block())
-
-class TTPBalancedTokenList(TeXToPyData, BalancedTokenList):
- send_code=r"\__tlserialize_nodot:Nn \__tmp {{ {} }} \immediate \write \__write_file {{\unexpanded\expandafter{{ \__tmp }}}}".format
- send_code_var=r"\__tlserialize_nodot:NV \__tmp {} \immediate \write \__write_file {{\unexpanded\expandafter{{ \__tmp }}}}".format
- @staticmethod
- def read()->"TTPBalancedTokenList":
- return TTPBalancedTokenList(BalancedTokenList.deserialize(readline()))
-
-
-class PyToTeXData(ABC):
- @staticmethod
- @abstractmethod
- def read_code(var: str)->str:
- ...
- @abstractmethod
- def write(self)->None:
- ...
-
-@dataclass
-class PTTVerbatimLine(PyToTeXData):
- """
- Represents a line to be tokenized verbatim. Internally the |\readline| primitive is used, as such, any trailing spaces are stripped.
- The trailing newline is not included, i.e. it's read under |\endlinechar=-1|.
- """
- data: str
- read_code=r"\ior_str_get:NN \__read_file {} ".format
- def write(self)->None:
- assert "\n" not in self.data
- assert self.data.rstrip()==self.data, "Cannot send verbatim line with trailing spaces!"
- send_raw(self.data+"\n")
-
-@dataclass
-class PTTInt(PyToTeXData):
- data: int
- read_code=PTTVerbatimLine.read_code
- def write(self)->None:
- PTTVerbatimLine(str(self.data)).write()
-
-@dataclass
-class PTTTeXLine(PyToTeXData):
- """
- Represents a line to be tokenized in \TeX's current catcode regime.
- The trailing newline is not included, i.e. it's tokenized under |\endlinechar=-1|.
- """
- data: str
- read_code=r"\ior_get:NN \__read_file {} ".format
- def write(self)->None:
- assert "\n" not in self.data
- send_raw(self.data+"\n")
-
-@dataclass
-class PTTBlock(PyToTeXData):
- data: str
- read_code=r"\__read_block:N {}".format
- def write(self)->None:
- send_raw(surround_delimiter(self.data))
-
-@dataclass
-class PTTBalancedTokenList(PyToTeXData):
- data: BalancedTokenList
- read_code=r"\ior_str_get:NN \__read_file {0} \__tldeserialize_dot:NV {0} {0}".format
- def write(self)->None:
- PTTVerbatimLine(self.data.serialize()+".").write()
-
-
-# ======== define TeX functions that execute Python code ========
-# ======== implementation of |\py| etc. Doesn't support verbatim argument yet. ========
-
-import itertools
-import string
-
-def random_identifiers()->Iterator[str]: # do this to avoid TeX hash collision while keeping the length short
- for len_ in itertools.count(0):
- for value in range(1<<len_):
- for initial in string.ascii_letters:
- yield initial + f"{value:0{len_}b}".translate({ord("0"): "a", ord("1"): "b"})
-
-random_identifier_iterable=random_identifiers()
-
-def get_random_identifier()->str:
- return next(random_identifier_iterable)
-
-
-def define_TeX_call_Python(f: Callable[..., None], name: Optional[str]=None, argtypes: Optional[List[Type[TeXToPyData]]]=None, identifier: Optional[str]=None)->str:
- """
- This function setups some internal data structure, and
- returns the \TeX\ code to be executed on the \TeX\ side to define the macro.
-
- f: the Python function to be executed.
- It should take some arguments and eventually (optionally) call one of the |_finish| functions.
-
- name: the macro name on the \TeX\ side. This should only consist of letter characters in |expl3| catcode regime.
-
- argtypes: list of argument types. If it's None it will be automatically deduced from the function |f|'s signature.
-
- Returns: some code (to be executed in |expl3| catcode regime) as explained above.
- """
- if argtypes is None: argtypes=[p.annotation for p in inspect.signature(f).parameters.values()]
- if name is None: name=f.__name__
-
- if identifier is None: identifier=get_random_identifier()
- assert identifier not in TeX_handlers
-
- @functools.wraps(f)
- def g()->None:
- assert argtypes is not None
- args=[argtype.read() for argtype in argtypes]
-
-
- global action_done
- old_action_done=action_done
-
- action_done=False
- try:
- f(*args)
- except:
- if action_done:
- # error occurred after 'finish' is called, cannot signal the error to TeX, will just ignore (after printing out the traceback)...
- pass
- else:
- # TODO what should be done here? What if the error raised below is caught
- action_done=True
- raise
- finally:
- if not action_done:
- run_none_finish()
-
- action_done=old_action_done
-
-
- TeX_handlers[identifier]=g
-
- TeX_argspec = ""
- TeX_send_input_commands = ""
- for i, argtype in enumerate(argtypes):
- if isinstance(argtype, str):
- raise RuntimeError("string annotation or `from __future__ import annotations' not yet supported")
- if not issubclass(argtype, TeXToPyData):
- raise RuntimeError(f"Argument type {argtype} is incorrect, should be a subclass of TeXToPyData")
- arg = f"#{i+1}"
- TeX_send_input_commands += argtype.send_code(arg)
- TeX_argspec += arg
-
- return """
- \\cs_new_protected:Npn \\""" + name + TeX_argspec + """ {
- \immediate \write \__write_file { i """ + identifier + """ }
- """ + TeX_send_input_commands + """
- \__read_do_one_command:
- }
- """
-
-
-def define_internal_handler(f: Callable)->Callable:
- mark_bootstrap(define_TeX_call_Python(f))
- return f
-
-
-import linecache
-
-# https://stackoverflow.com/questions/47183305/file-string-traceback-with-line-preview
-def exec_or_eval_with_linecache(code: str, globals: dict, mode: str)->Any:
- sourcename: str="<usercode>"
- i=0
- while sourcename in linecache.cache:
- sourcename="<usercode" + str(i) + ">"
- i+=1
-
- lines=code.splitlines(keepends=True)
- linecache.cache[sourcename] = len(code), None, lines, sourcename
-
- compiled_code=compile(code, sourcename, mode)
- return (exec if mode=="exec" else eval)(compiled_code, globals)
-
- #del linecache.cache[sourcename]
- # we never delete the cache, in case some function is defined here then later are called...
-
-def exec_with_linecache(code: str, globals: Dict[str, Any])->None:
- exec_or_eval_with_linecache(code, globals, "exec")
-
-def eval_with_linecache(code: str, globals: Dict[str, Any])->Any:
- return exec_or_eval_with_linecache(code, globals, "eval")
-
-
-@define_internal_handler
-def py(code: TTPEBlock)->None:
- pythonimmediate.run_block_finish(str(eval_with_linecache(code, user_scope))+"%")
-
-@define_internal_handler
-def pyfile(filename: TTPELine)->None:
- with open(filename, "r") as f:
- source=f.read()
- exec(compile(source, filename, "exec"), user_scope)
-
-def print_TeX(*args, **kwargs)->None:
- if not hasattr(pythonimmediate, "file"):
- raise RuntimeError("Internal error: attempt to print to TeX outside any environment!")
- if pythonimmediate.file is not None:
- functools.partial(print, file=pythonimmediate.file)(*args, **kwargs) # allow user to override `file` kwarg
-pythonimmediate.print=print_TeX
-
-class RedirectPrintTeX:
- def __init__(self, t)->None:
- self.t=t
-
- def __enter__(self)->None:
- if hasattr(pythonimmediate, "file"):
- self.old=pythonimmediate.file
- pythonimmediate.file=self.t
-
- def __exit__(self, exc_type, exc_value, tb)->None:
- if hasattr(self, "old"):
- pythonimmediate.file=self.old
- else:
- del pythonimmediate.file
-
-def run_code_redirect_print_TeX(f: Callable[[], Any])->None:
- with io.StringIO() as t:
- with RedirectPrintTeX(t):
- result=f()
- if result is not None:
- t.write(str(result)+"%")
- content=t.getvalue()
- if content.endswith("\n"):
- content=content[:-1]
- else:
- #content+=r"\empty" # this works too
- content+="%"
- pythonimmediate.run_block_finish(content)
-
-@define_internal_handler
-def pyc(code: TTPEBlock)->None:
- run_code_redirect_print_TeX(lambda: exec_with_linecache(code, user_scope))
-
-@define_internal_handler
-def pycq(code: TTPEBlock)->None:
- with RedirectPrintTeX(None):
- exec_with_linecache(code, user_scope)
- run_none_finish()
-
-mark_bootstrap(
-r"""
-\NewDocumentCommand\pyv{v}{\py{#1}}
-\NewDocumentCommand\pycv{v}{\pyc{#1}}
-""")
-
-# ======== implementation of |pycode| environment
-mark_bootstrap(
-r"""
-\NewDocumentEnvironment{pycode}{}{
- \saveenvreinsert \__code {
- \exp_last_unbraced:Nx \__pycodex {{\__code} {\the\inputlineno} {
- \ifdefined\currfilename \currfilename \fi
- } {
- \ifdefined\currfileabspath \currfileabspath \fi
- }}
- }
-}{
- \endsaveenvreinsert
-}
-""")
-
-def normalize_lines(lines: List[str])->List[str]:
- return [line.rstrip() for line in lines]
-
-@define_internal_handler
-def __pycodex(code: TTPBlock, lineno_: TTPLine, filename: TTPLine, fileabspath: TTPLine)->None:
- if not code: return
-
- lineno=int(lineno_)
- # find where the code comes from... (for easy meaningful traceback)
- target_filename: Optional[str] = None
-
- code_lines_normalized=normalize_lines(code.splitlines(keepends=True))
-
- for f in (fileabspath, filename):
- if not f: continue
- p=Path(f)
- if not p.is_file(): continue
- file_lines=p.read_text().splitlines(keepends=True)[lineno-len(code_lines_normalized)-1:lineno-1]
- if normalize_lines(file_lines)==code_lines_normalized:
- target_filename=f
- break
-
- if not target_filename:
- raise RuntimeError("Source file not found! (attempted {})".format((fileabspath, filename)))
-
- with io.StringIO() as t:
- with RedirectPrintTeX(t):
- if target_filename:
- code_=''.join(file_lines) # restore missing trailing spaces
- code_="\n"*(lineno-len(code_lines_normalized)-1)+code_
- if target_filename:
- compiled_code=compile(code_, target_filename, "exec")
- exec(compiled_code, user_scope)
- else:
- exec(code_, user_scope)
- pythonimmediate.run_block_finish(t.getvalue())
-
-# ======== Python-call-TeX functions
-# ======== additional functions...
-
-user_documentation(
-r"""
-These functions get an argument in the input stream and returns it detokenized.
-
-Which means, for example, |#| are doubled, multiple spaces might be collapsed into one, spaces might be introduced
-after a control sequence.
-
-It's undefined behavior if the message's "string representation" contains a "newline character".
-""")
-
-def template_substitute(template: str, pattern: str, substitute: Union[str, Callable[[re.Match], str]], optional: bool=False)->str:
- """
- pattern is a regex
- """
- if not optional:
- #assert template.count(pattern)==1
- assert len(re.findall(pattern, template))==1
- return re.sub(pattern, substitute, template)
-
-#typing.TypeVarTuple(PyToTeXData)
-
-#PythonCallTeXFunctionType=Callable[[PyToTeXData], Optional[Tuple[TeXToPyData, ...]]]
-
-class PythonCallTeXFunctionType(Protocol): # https://stackoverflow.com/questions/57658879/python-type-hint-for-callable-with-variable-number-of-str-same-type-arguments
- def __call__(self, *args: PyToTeXData)->Optional[Tuple[TeXToPyData, ...]]: ...
-
-class PythonCallTeXSyncFunctionType(PythonCallTeXFunctionType, Protocol): # https://stackoverflow.com/questions/57658879/python-type-hint-for-callable-with-variable-number-of-str-same-type-arguments
- def __call__(self, *args: PyToTeXData)->Tuple[TeXToPyData, ...]: ...
-
-
-@dataclass(frozen=True)
-class Python_call_TeX_data:
- TeX_code: str
- recursive: bool
- finish: bool
- sync: Optional[bool]
-
-@dataclass(frozen=True)
-class Python_call_TeX_extra:
- ptt_argtypes: Tuple[Type[PyToTeXData], ...]
- ttp_argtypes: Union[Type[TeXToPyData], Tuple[Type[TeXToPyData], ...]]
-
-Python_call_TeX_defined: Dict[Python_call_TeX_data, Tuple[Python_call_TeX_extra, Callable]]={}
-
-def Python_call_TeX_local(TeX_code: str, *, recursive: bool=True, sync: Optional[bool]=None, finish: bool=False)->Callable:
- data=Python_call_TeX_data(
- TeX_code=TeX_code, recursive=recursive, sync=sync, finish=finish
- )
- return Python_call_TeX_defined[data][1]
-
-def build_Python_call_TeX(T: Type, TeX_code: str, *, recursive: bool=True, sync: Optional[bool]=None, finish: bool=False)->None:
- assert T.__origin__ == typing.Callable[[], None].__origin__ # type: ignore
- # might be typing.Callable or collections.abc.Callable depends on Python version
- data=Python_call_TeX_data(
- TeX_code=TeX_code, recursive=recursive, sync=sync, finish=finish
- )
-
- tmp: Any = T.__args__[-1]
- ttp_argtypes: Union[Type[TeXToPyData], Tuple[Type[TeXToPyData], ...]]
- if tmp is type(None):
- ttp_argtypes = ()
- elif isinstance(tmp, type) and issubclass(tmp, TeXToPyData):
- # special case, return a single object instead of a tuple of length 1
- ttp_argtypes = tmp
- else:
- ttp_argtypes = tmp.__args__ # type: ignore
-
- extra=Python_call_TeX_extra(
- ptt_argtypes=T.__args__[:-1],
- ttp_argtypes=ttp_argtypes
- ) # type: ignore
- if data in Python_call_TeX_defined:
- assert Python_call_TeX_defined[data][0]==extra
- else:
- if isinstance(ttp_argtypes, type) and issubclass(ttp_argtypes, TeXToPyData):
- # special case, return a single object instead of a tuple of length 1
- code, result1=define_Python_call_TeX(TeX_code=TeX_code, ptt_argtypes=[*extra.ptt_argtypes], ttp_argtypes=[ttp_argtypes],
- recursive=recursive, sync=sync, finish=finish,
- )
- def result(*args):
- [tmp]=result1(*args)
- return tmp
- else:
- code, result=define_Python_call_TeX(TeX_code=TeX_code, ptt_argtypes=[*extra.ptt_argtypes], ttp_argtypes=[*ttp_argtypes],
- recursive=recursive, sync=sync, finish=finish,
- )
- mark_bootstrap(code)
- Python_call_TeX_defined[data]=extra, result
-
-def scan_Python_call_TeX(filename: str)->None:
- """
- scan the file in filename for occurrences of typing.cast(T, Python_call_TeX_local(...)), then call build_Python_call_TeX(T, ...) for each occurrence.
-
- Don't use on untrusted code.
- """
- import ast
- from copy import deepcopy
- for node in ast.walk(ast.parse(Path(filename).read_text(), mode="exec")):
- try:
- if isinstance(node, ast.Call):
- if (
- isinstance(node.func, ast.Attribute) and
- isinstance(node.func.value, ast.Name) and
- node.func.value.id == "typing" and
- node.func.attr == "cast"
- ):
- T = node.args[0]
- if isinstance(node.args[1], ast.Call):
- f_call = node.args[1]
- if isinstance(f_call.func, ast.Name):
- if f_call.func.id == "Python_call_TeX_local":
- f_call=deepcopy(f_call)
- assert isinstance(f_call.func, ast.Name)
- f_call.func.id="build_Python_call_TeX"
- f_call.args=[T]+f_call.args
- eval(compile(ast.Expression(body=f_call), "<string>", "eval"))
- except:
- print("======== error on line", node.lineno, "========", file=sys.stderr)
- raise
-
-def define_Python_call_TeX(TeX_code: str, ptt_argtypes: List[Type[PyToTeXData]], ttp_argtypes: List[Type[TeXToPyData]],
- *,
- recursive: bool=True,
- sync: Optional[bool]=None,
- finish: bool=False,
- )->Tuple[str, PythonCallTeXFunctionType]:
- r"""
- |TeX_code| should be some expl3 code that defines a function with name |%name%| that when called should:
- * run some \TeX\ code (which includes reading the arguments, if any)
- * do the following if |sync|:
- * send |r| to Python (equivalently write %sync%)
- * send whatever needed for the output (as in |ttp_argtypes|)
- * call |\__read_do_one_command:| iff not |finish|.
-
- This is allowed to contain the following:
- * %name%: the name of the function to be defined as explained above.
- * %read_arg0(\var_name)%, %read_arg1(...)%: will be expanded to code that reads the input.
- * %send_arg0(...)%, %send_arg1(...)%: will be expanded to code that sends the content.
- * %send_arg0_var(\var_name)%, %send_arg1_var(...)%: will be expanded to code that sends the content in the variable.
- * %optional_sync%: expanded to code that writes |r| (to sync), if |sync| is True.
-
- ptt_argtypes: list of argument types to be sent from Python to TeX (i.e. input of the TeX function)
-
- ttp_argtypes: list of argument types to be sent from TeX to Python (i.e. output of the TeX function)
-
- recursive: whether the TeX_code might call another Python function. Default to True.
- It does not hurt to always specify True, but performance would be a bit slower.
-
- sync: whether the Python function need to wait for the TeX function to finish.
- Required if |ttp_argtypes| is not empty.
- This should be left to be the default None most of the time. (which will make it always sync if |debugging|,
- otherwise only sync if needed i.e. there's some output)
-
- finish: Include this if and only if |\__read_do_one_command:| is omitted.
- Normally this is not needed, but it can be used as a slight optimization; and it's needed internally to implement
- |run_none_finish| among others.
- For each TeX-call-Python layer, \emph{exactly one} |finish| call can be made. If the function itself doesn't call
- any |finish| call (which happens most of the time), then the wrapper will call |run_none_finish|.
-
- Return some TeX code to be executed, and a Python function object that when called will call the TeX function
- and return the result.
-
- Possible optimizations:
- * the |r| is not needed if not recursive and |ttp_argtypes| is nonempty
- (the output itself tells Python when the \TeX\ code finished)
- * the first line of the output may be on the same line as the |r| itself (done, use TTPEmbeddedLine type, although a bit hacky)
- """
- if ttp_argtypes!=[]:
- assert sync!=False
- sync=True
-
- if sync is None:
- sync=pythonimmediate.debugging
-
- TeX_code=template_substitute(TeX_code, "%optional_sync%",
- lambda _: r'\immediate\write\__write_file { r }' if sync else '',)
-
- TeX_code=template_substitute(TeX_code, "%sync%",
- lambda _: r'\immediate\write\__write_file { r }' if sync else '', optional=True)
-
- assert sync is not None
- if ttp_argtypes: assert sync
- assert ttp_argtypes.count(TTPEmbeddedLine)<=1
- identifier=get_random_identifier() # TODO to be fair it isn't necessary to make the identifier both ways distinct, can reuse
-
- TeX_code=template_substitute(TeX_code, "%name%", lambda _: r"\__run_" + identifier + ":")
-
- for i, argtype_ in enumerate(ptt_argtypes):
- TeX_code=template_substitute(TeX_code, r"%read_arg" + str(i) + r"\(([^)]*)\)%",
- lambda match: argtype_.read_code(match[1]),
- optional=True)
-
- for i, argtype in enumerate(ttp_argtypes):
- TeX_code=template_substitute(TeX_code, f"%send_arg{i}" + r"\(([^)]*)\)%",
- lambda match: argtype.send_code(match[1]),
- optional=True)
- TeX_code=template_substitute(TeX_code, f"%send_arg{i}_var" + r"\(([^)]*)\)%",
- lambda match: argtype.send_code_var(match[1]),
- optional=True)
-
- def f(*args)->Optional[Tuple[TeXToPyData, ...]]:
- assert len(args)==len(ptt_argtypes)
-
- # send function header
- check_not_finished()
- if finish:
- global action_done
- action_done=True
- send_raw(identifier+"\n")
-
- # send function args
- for arg, argtype in zip(args, ptt_argtypes):
- assert isinstance(arg, argtype)
- arg.write()
-
- if not sync: return None
-
- # wait for the result
- if recursive:
- result_=run_main_loop()
- else:
- result_=run_main_loop_get_return_one()
-
- result: List[TeXToPyData]=[]
- if TTPEmbeddedLine not in ttp_argtypes:
- assert not result_
- for argtype_ in ttp_argtypes:
- if argtype_==TTPEmbeddedLine:
- result.append(TTPEmbeddedLine(result_))
- else:
- result.append(argtype_.read())
- return tuple(result)
-
- return TeX_code, f
-
-scan_Python_call_TeX(__file__)
-
-def define_Python_call_TeX_local(*args, **kwargs)->PythonCallTeXFunctionType:
- """
- used to define "local" handlers i.e. used by this library.
- The code will be included in mark_bootstrap().
- """
- code, result=define_Python_call_TeX(*args, **kwargs)
- mark_bootstrap(code)
- return result
-
-# essentially this is the same as the above, but just that the return type is guaranteed to be not None to satisfy type checkers
-def define_Python_call_TeX_local_sync(*args, **kwargs)->PythonCallTeXSyncFunctionType:
- return define_Python_call_TeX_local(*args, **kwargs, sync=True) # type: ignore
-
-run_none_finish=define_Python_call_TeX_local(
-r"""
-\cs_new_eq:NN %name% \relax
-""", [], [], finish=True, sync=False)
-
-
-"""
-|run_error_finish| is fatal to TeX, so we only run it when it's fatal to Python.
-
-We want to make sure the Python traceback is printed strictly before run_error_finish() is called,
-so that the Python traceback is not interleaved with TeX error messages.
-"""
-run_error_finish=define_Python_call_TeX_local(
-r"""
-\msg_new:nnn {pythonimmediate} {python-error} {Python~error.}
-\cs_new_protected:Npn %name% {
- %read_arg0(\__data)%
- \wlog{^^JPython~error~traceback:^^J\__data^^J}
- \msg_error:nn {pythonimmediate} {python-error}
-}
-""", [PTTBlock], [], finish=True, sync=False)
-
-
-put_next_blue=define_Python_call_TeX_local(
-r"""
-\cs_new_protected:Npn \__put_next_blue_tmp {
- %optional_sync%
- \expandafter \__read_do_one_command: \noexpand
-}
-\cs_new_protected:Npn %name% {
- %read_arg0(\__target)%
- \expandafter \__put_next_blue_tmp \__target
-}
-"""
- , [PTTBalancedTokenList], [], recursive=False)
-
-
-put_next_tokenlist=define_Python_call_TeX_local(
-r"""
-\cs_new_protected:Npn \__put_next_tmp {
- %optional_sync%
- \__read_do_one_command:
-}
-\cs_new_protected:Npn %name% {
- %read_arg0(\__target)%
- \expandafter \__put_next_tmp \__target
-}
-"""
- , [PTTBalancedTokenList], [], recursive=False)
-
-get_next_=define_Python_call_TeX_local_sync(
-r"""
-\cs_new_protected:Npn %name% {
- \peek_analysis_map_inline:n {
- \peek_analysis_map_break:n {
- \__tlserialize_char_unchecked:nnNN {##1}{##2}##3 \pythonimmediatecontinue
- }
- }
-}
-""", [], [TTPEmbeddedLine], recursive=False)
-
-put_next_bgroup=define_Python_call_TeX_local_sync(
-r"""
-\cs_new_protected:Npn %name% {
- %read_arg0(\__index)%
- \expandafter \expandafter \expandafter \pythonimmediatecontinuenoarg
- \char_generate:nn {\__index} {1}
-}
-""", [PTTInt], [], recursive=False)
-
-put_next_egroup=define_Python_call_TeX_local_sync(
-r"""
-\cs_new_protected:Npn %name% {
- %read_arg0(\__index)%
- \expandafter \expandafter \expandafter \pythonimmediatecontinuenoarg
- \char_generate:nn {\__index} {2}
-}
-""", [PTTInt], [], recursive=False)
-
-
-get_argument_tokenlist_=define_Python_call_TeX_local_sync(
-r"""
-\cs_new_protected:Npn %name% #1 {
- %sync%
- %send_arg0(#1)%
- \__read_do_one_command:
-}
-""", [], [TTPBalancedTokenList], recursive=False)
-
-
-run_tokenized_line_local_=define_Python_call_TeX_local(
-r"""
-\cs_new_protected:Npn %name% {
- %read_arg0(\__data)%
- \__data
- %optional_sync%
- \__read_do_one_command:
-}
-""", [PTTTeXLine], [])
-
-@export_function_to_module
-def run_tokenized_line_local(line: str, *, check_braces: bool=True, check_newline: bool=True, check_continue: bool=True)->None:
- check_line(line, braces=check_braces, newline=check_newline, continue_=(False if check_continue else None))
- run_tokenized_line_local_(PTTTeXLine(line))
-
-
-
-@export_function_to_module
-def run_tokenized_line_peek(line: str, *, check_braces: bool=True, check_newline: bool=True, check_continue: bool=True)->str:
- check_line(line, braces=check_braces, newline=check_newline, continue_=(True if check_continue else None))
- return typing.cast(
- Callable[[PTTTeXLine], Tuple[TTPEmbeddedLine]],
- Python_call_TeX_local(
- r"""
- \cs_new_protected:Npn %name% {
- %read_arg0(\__data)%
- \__data
- }
- """)
- )(PTTTeXLine(line))[0]
-
-
-run_block_local_=define_Python_call_TeX_local(
-r"""
-\cs_new_protected:Npn %name% {
- %read_arg0(\__data)%
- \begingroup \newlinechar=10~ \expandafter \endgroup
- \scantokens \expandafter{\__data}
- % trick described in https://tex.stackexchange.com/q/640274 to scantokens the code with \newlinechar=10
-
- %optional_sync%
- \__read_do_one_command:
-}
-""", [PTTBlock], [])
-
-@export_function_to_module
-def run_block_local(block: str)->None:
- run_block_local_(PTTBlock(block))
-
-expand_o_=define_Python_call_TeX_local_sync(
-r"""
-\cs_new_protected:Npn %name% {
- %read_arg0(\__data)%
- \exp_args:NNV \tl_set:No \__data \__data
- %sync%
- %send_arg0_var(\__data)%
- \__read_do_one_command:
-}
-""", [PTTBalancedTokenList], [TTPBalancedTokenList], recursive=expansion_only_can_call_Python)
-
-expand_x_=define_Python_call_TeX_local_sync(
-r"""
-\cs_new_protected:Npn %name% {
- %read_arg0(\__data)%
- \tl_set:Nx \__data {\__data}
- %sync%
- %send_arg0_var(\__data)%
- \__read_do_one_command:
-}
-""", [PTTBalancedTokenList], [TTPBalancedTokenList], recursive=expansion_only_can_call_Python)
-
-execute_=define_Python_call_TeX_local(
-r"""
-\cs_new_protected:Npn %name% {
- %read_arg0(\__data)%
- \__data
- %optional_sync%
- \__read_do_one_command:
-}
-""", [PTTBalancedTokenList], [])
-
-futurelet_=define_Python_call_TeX_local_sync(
-r"""
-\cs_new_protected:Npn %name% {
- %read_arg0(\__data)%
- \expandafter \futurelet \__data \pythonimmediatecontinuenoarg
-}
-""", [PTTBalancedTokenList], [])
-
-futureletnext_=define_Python_call_TeX_local_sync(
-r"""
-\cs_new_protected:Npn %name% {
- %read_arg0(\__data)%
- \afterassignment \pythonimmediatecontinuenoarg \expandafter \futurelet \__data
-}
-""", [PTTBalancedTokenList], [])
-
-continue_until_passed_back_=define_Python_call_TeX_local_sync(
-r"""
-\cs_new_eq:NN %name% \relax
-""", [], [TTPEmbeddedLine])
-
-@export_function_to_module
-def continue_until_passed_back_str()->str:
- """
- Usage:
-
- First put some tokens in the input stream that includes |\pythonimmediatecontinue{...}|
- (or |%sync% \__read_do_one_command:|), then call |continue_until_passed_back()|.
-
- The function will only return when the |\pythonimmediatecontinue| is called.
- """
- return str(continue_until_passed_back_()[0])
-
-@export_function_to_module
-def continue_until_passed_back()->None:
- """
- Same as |continue_until_passed_back_str()| but nothing can be returned from TeX to Python.
- """
- result=continue_until_passed_back_str()
- assert not result
-
-
-@export_function_to_module
-def expand_once()->None:
- typing.cast(Callable[[], None], Python_call_TeX_local(
- r"""
- \cs_new_protected:Npn %name% { \expandafter \pythonimmediatecontinuenoarg }
- """, recursive=False, sync=True))()
-
-
-@export_function_to_module
-@user_documentation
-def get_arg_str()->str:
- """
- Get a mandatory argument.
- """
- return typing.cast(Callable[[], TTPEmbeddedLine], Python_call_TeX_local(
- r"""
- \cs_new_protected:Npn %name% #1 {
- \immediate\write\__write_file { \unexpanded {
- r #1
- }}
- \__read_do_one_command:
- }
- """, recursive=False))()
-
-get_arg_estr_=define_Python_call_TeX_local_sync(
-r"""
-\cs_new_protected:Npn %name% #1 {
- %sync%
- %send_arg0(#1)%
- \__read_do_one_command:
-}
-""", [], [TTPEBlock], recursive=False)
-@export_function_to_module
-@user_documentation
-def get_arg_estr()->str:
- return str(get_arg_estr_()[0])
-
-
-get_optional_argument_detokenized_=define_Python_call_TeX_local_sync(
-r"""
-\NewDocumentCommand %name% {o} {
- \immediate\write \__write_file {
- r ^^J
- \IfNoValueTF {#1} {
- 0
- } {
- \unexpanded{1 #1}
- }
- }
- \__read_do_one_command:
-}
-""", [], [TTPLine], recursive=False)
-@export_function_to_module
-@user_documentation
-def get_optional_arg_str()->Optional[str]:
- """
- Get an optional argument.
- """
- [result]=get_optional_argument_detokenized_()
- result_=str(result)
- if result_=="0": return None
- assert result_[0]=="1", result_
- return result_[1:]
-
-
-get_optional_arg_estr_=define_Python_call_TeX_local_sync(
-r"""
-\NewDocumentCommand %name% {o} {
- %sync%
- \IfNoValueTF {#1} {
- %send_arg0(0)%
- } {
- %send_arg0(1 #1)%
- }
- \__read_do_one_command:
-}
-""", [], [TTPEBlock], recursive=False)
-
-@export_function_to_module
-@user_documentation
-def get_optional_arg_estr()->Optional[str]:
- [result]=get_optional_arg_estr_()
- result_=str(result)
- if result_=="0": return None
- assert result_[0]=="1", result_
- return result_[1:]
-
-
-get_verbatim_argument_=define_Python_call_TeX_local_sync(
-r"""
-\NewDocumentCommand %name% {v} {
- \immediate\write\__write_file { \unexpanded {
- r ^^J
- #1
- }}
- \__read_do_one_command:
-}
-""", [], [TTPLine], recursive=False)
-@export_function_to_module
-@user_documentation
-def get_verb_arg()->str:
- """
- Get a verbatim argument. Since it's verbatim, there's no worry of |#| being doubled,
- but it can only be used at top level.
- """
- return str(get_verbatim_argument_()[0])
-
-get_multiline_verbatim_argument_=define_Python_call_TeX_local_sync(
-r"""
-\NewDocumentCommand %name% {+v} {
- \immediate\write\__write_file { r }
- \begingroup
- \newlinechar=13~ % this is what +v argument type in xparse uses
- \__send_block:n { #1 }
- \endgroup
- \__read_do_one_command:
-}
-""", [], [TTPBlock], recursive=False)
-@export_function_to_module
-@user_documentation
-def get_multiline_verb_arg()->str:
- """
- Get a multi-line verbatim argument.
- """
- return str(get_multiline_verbatim_argument_()[0])
-
-newcommand2=define_Python_call_TeX_local(
-r"""
-\cs_new_protected:Npn %name% {
- \begingroup
- \endlinechar=-1~
- %read_arg0(\__line)%
- %read_arg1(\__identifier)%
- \cs_new_protected:cpx {\__line} {
- \unexpanded{\immediate\write \__write_file} { i \__identifier }
- \unexpanded{\__read_do_one_command:}
- }
- \endgroup
- %optional_sync%
- \__read_do_one_command:
-}
-""", [PTTVerbatimLine, PTTVerbatimLine], [], recursive=False)
-
-renewcommand2=define_Python_call_TeX_local(
-r"""
-\cs_new_protected:Npn %name% {
- \begingroup
- \endlinechar=-1~
- \readline \__read_file to \__line
- \readline \__read_file to \__identifier
- \exp_args:Ncx \renewcommand {\__line} {
- \unexpanded{\immediate\write \__write_file} { i \__identifier }
- \unexpanded{\__read_do_one_command:}
- }
- \exp_args:Nc \MakeRobust {\__line} % also make the command global
- \endgroup
- %optional_sync%
- \__read_do_one_command:
-}
-""", [PTTVerbatimLine, PTTVerbatimLine], [], recursive=False)
-
-def check_function_name(name: str)->None:
- if not re.fullmatch("[A-Za-z]+", name) or (len(name)==1 and ord(name)<=0x7f):
- raise RuntimeError("Invalid function name: "+name)
-
-def newcommand_(name: str, f: Callable)->Callable:
- identifier=get_random_identifier()
-
- newcommand2(PTTVerbatimLine(name), PTTVerbatimLine(identifier))
-
- _code=define_TeX_call_Python(
- lambda: run_code_redirect_print_TeX(f),
- name, argtypes=[], identifier=identifier)
- # ignore _code, already executed something equivalent in the TeX command
- return f
-
-def renewcommand_(name: str, f: Callable)->Callable:
- identifier=get_random_identifier()
-
- renewcommand2(PTTVerbatimLine(name), PTTVerbatimLine(identifier))
- # TODO remove the redundant entry from TeX_handlers (although technically is not very necessary, just cause slight memory leak)
- #try: del TeX_handlers["u"+name]
- #except KeyError: pass
-
- _code=define_TeX_call_Python(
- lambda: run_code_redirect_print_TeX(f),
- name, argtypes=[], identifier=identifier)
- # ignore _code, already executed something equivalent in the TeX command
- return f
-
-
-
-@export_function_to_module
-def newcommand(x: Union[str, Callable, None]=None, f: Optional[Callable]=None)->Callable:
- """
- Define a new \TeX\ command.
- If name is not provided, it's automatically deduced from the function.
- """
- if f is not None: return newcommand(x)(f)
- if x is None: return newcommand # weird design but okay (allow |@newcommand()| as well as |@newcommand|)
- if isinstance(x, str): return functools.partial(newcommand_, x)
- return newcommand_(x.__name__, x)
-
-@export_function_to_module
-def renewcommand(x: Union[str, Callable, None]=None, f: Optional[Callable]=None)->Callable:
- """
- Redefine a \TeX\ command.
- If name is not provided, it's automatically deduced from the function.
- """
- if f is not None: return newcommand(x)(f)
- if x is None: return newcommand # weird design but okay (allow |@newcommand()| as well as |@newcommand|)
- if isinstance(x, str): return functools.partial(renewcommand_, x)
- return renewcommand_(x.__name__, x)
-
-
-# ========
-
-put_next_TeX_line=define_Python_call_TeX_local(
-r"""
-\cs_new_protected:Npn \__put_next_tmpa {
- %optional_sync%
- \__read_do_one_command:
-}
-\cs_new_protected:Npn %name% {
- %read_arg0(\__target)%
- \expandafter \__put_next_tmpa \__target
-}
-"""
- , [PTTTeXLine], [], recursive=False)
-
-@export_function_to_module
-@user_documentation
-def put_next(arg: Union[str, Token, BalancedTokenList])->None:
- """
- Put some content forward in the input stream.
-
- arg: has type |str| (will be tokenized in the current catcode regime, must be a single line),
- or |BalancedTokenList|.
- """
- if isinstance(arg, str): put_next_TeX_line(PTTTeXLine(arg))
- else: arg.put_next()
-
-
-
-# TODO I wonder which one is faster. Need to benchmark...
-@export_function_to_module
-@user_documentation
-def peek_next_meaning()->str:
- """
- Get the meaning of the following token, as a string, using the current |\escapechar|.
-
- This is recommended over |peek_next_token()| as it will not tokenize an extra token.
-
- It's undefined behavior if there's a newline (|\newlinechar| or |^^J|, the latter is OS-specific)
- in the meaning string.
- """
- return typing.cast(Callable[[], TTPEmbeddedLine], Python_call_TeX_local(
- r"""
- \cs_new_protected:Npn \__peek_next_meaning_callback: {
-
- \edef \__tmp {\meaning \__tmp} % just in case |\__tmp| is outer, |\write| will not be able to handle it
- %\immediate\write \__write_file { r \unexpanded\expandafter{\__tmp} }
- \immediate\write \__write_file { r \__tmp }
-
- \__read_do_one_command:
- }
- \cs_new_protected:Npn %name% {
- \futurelet \__tmp \__peek_next_meaning_callback:
- }
- """, recursive=False))()
-
-
-if 0:
- peek_next_char_=define_Python_call_TeX_local_sync(
-
- # first attempt. Slower than peek_next_meaning.
- r"""
- \cs_new_protected:Npn \__peek_next_char_callback: {
- \edef \__tmpb { \expandafter\str_item:nn\expandafter{\meaning \__tmp} {-1} } % \expandafter just in case \__tmp is \outer
- \if \noexpand\__tmp \__tmpb % is a character
- \immediate\write \__write_file { r^^J \__tmpb . }
- \else % is not?
- \immediate\write \__write_file { r^^J }
- \fi
- \__read_do_one_command:
- }
- \cs_new_protected:Npn %name% {
- \futurelet \__tmp \__peek_next_char_callback:
- }
- """
-
- # second attempt. Faster than before but still slower than peek_next_meaning.
- #r"""
- #\cs_new_protected:Npn %name% {
- # \futurelet \__tmp \__peek_next_char_callback:
- #}
- #
- #\cs_new_protected:Npn \__peek_next_char_callback: {
- # %\if \noexpand\__tmp \c_space_token % there's also this case and that \__tmp is some TeX primitive conditional...
- # \expandafter \__peek_next_char_callback_b: \meaning \__tmp \relax
- #}
- #
- #\cs_new_protected:Npn \__peek_next_char_callback_b: #1 #2 {
- # \ifx #2 \relax
- # \if \noexpand\__tmp #1 % is a character
- # \immediate\write \__write_file { r^^J #1 }
- # \else % is not?
- # \immediate\write \__write_file { r^^J }
- # \fi
- # \expandafter \__read_do_one_command:
- # \else
- # \expandafter \__peek_next_char_callback_b: \expandafter #2
- # \fi
- #}
- #
- #"""
-
- , [], [TTPLine], recursive=False)
-
-
-
-meaning_str_to_catcode: Dict[str, Catcode]={
- "begin-group character ": Catcode.bgroup,
- "end-group character ": Catcode.egroup,
- "math shift character ": Catcode.math,
- "alignment tab character ": Catcode.alignment,
- "macro parameter character ": Catcode.parameter,
- "superscript character ": Catcode.superscript,
- "subscript character ": Catcode.subscript,
- "blank space ": Catcode.space,
- "the letter ": Catcode.letter,
- "the character ": Catcode.other,
- }
-
-def parse_meaning_str(s: str)->Optional[Tuple[Catcode, str]]:
- if s and s[:-1] in meaning_str_to_catcode:
- return meaning_str_to_catcode[s[:-1]], s[-1]
- return None
-
-@export_function_to_module
-@user_documentation
-def peek_next_char()->str:
- """
- Get the character of the following token, or empty string if it's not a character.
- Will also return nonempty if the next token is an implicit character token.
-
- Uses peek_next_meaning() under the hood to get the meaning of the following token. See peek_next_meaning() for a warning on undefined behavior.
- """
-
- #return str(peek_next_char_()[0])
- # too slow (marginally slower than peek_next_meaning)
-
- r=parse_meaning_str(peek_next_meaning())
- if r is None:
- return ""
- return r[1]
-
-@export_function_to_module
-def get_next_char()->str:
- result=Token.get_next()
- assert isinstance(result, CharacterToken), "Next token is not a character!"
- return result.chr
-
-# ========
-
-try:
- send_bootstrap_code()
- run_main_loop() # if this returns cleanly TeX has no error. Otherwise some readline() will reach eof and print out a stack trace
- assert not raw_readline(), "Internal error: TeX sends extra line"
-
-except:
- # see also documentation of run_error_finish.
- sys.stderr.write("\n")
- traceback.print_exc(file=sys.stderr)
-
- if do_run_error_finish:
- action_done=False # force run it
- run_error_finish(PTTBlock("".join(traceback.format_exc())))
-
- os._exit(0)
-
diff --git a/macros/latex/contrib/sagetex/PKG-INFO b/macros/latex/contrib/sagetex/PKG-INFO
index 628c7e2da9..6cc7afeaa0 100644
--- a/macros/latex/contrib/sagetex/PKG-INFO
+++ b/macros/latex/contrib/sagetex/PKG-INFO
@@ -1,12 +1,15 @@
-Metadata-Version: 1.0
+Metadata-Version: 2.1
Name: sagetex
-Version: 3.5
+Version: 3.6.1
Summary: Embed Sage code and plots into LaTeX
Home-page: https://github.com/sagemath/sagetex
-Author: SageMath developers
-Author-email: sage-devel@googlegroups.com
+Author: Dan Drake
+Author-email: dr.dan.drake@gmail.com
+Maintainer: SageMath developers
+Maintainer-email: sage-devel@googlegroups.com
License: GPLv2+
-Description: The SageTeX package allows you to embed code,
- results of computations, and plots from the Sage mathematics
- software suite (http://sagemath.org) into LaTeX documents.
-Platform: UNKNOWN
+License-File: LICENSE
+
+The SageTeX package allows you to embed code,
+ results of computations, and plots from the Sage mathematics
+ software suite (http://sagemath.org) into LaTeX documents.
diff --git a/macros/latex/contrib/sagetex/README.md b/macros/latex/contrib/sagetex/README.md
index f6e75ac061..2864569f39 100644
--- a/macros/latex/contrib/sagetex/README.md
+++ b/macros/latex/contrib/sagetex/README.md
@@ -8,7 +8,7 @@ computations, and plots from the Sage mathematics software suite
SageTeX is included with Sage, so to use it, you only need to make the
file sagetex.sty known to TeX; that file will be in
-SAGE_ROOT/local/share/texmf/tex/latex/sagetex, along with
+SAGE_ROOT/venv/share/texmf/tex/latex/sagetex, along with
documentation and examples. See the Sage tutorial at
https://doc.sagemath.org/html/en/tutorial/sagetex.html
for a quick usage introduction, and for complete installation
@@ -23,14 +23,14 @@ the SAGE_ROOT/... directory mentioned above.
If you want to extract any of SageTeX's files from the .dtx sources, you
can do
- 0. Run `latex sagetex.ins'
+ 0. Run `latex sagetex.ins`
To regenerate the documentation, do
- 1. Run `latex sagetex.dtx'
- 2. Run `sage sagetex.sage'
+ 1. Run `latex sagetex.dtx`
+ 2. Run `sage sagetex.sage`
3. Run the indexing commands that the .ins file told you about.
- 4. Run `latex sagetex.dtx' again.
+ 4. Run `latex sagetex.dtx` again.
You can skip step 3 if you don't care about the index. You will need the
pgf and tikz packages installed to typeset the figures.
diff --git a/macros/latex/contrib/sagetex/example.pdf b/macros/latex/contrib/sagetex/example.pdf
index af815f0b56..2f8c9347d5 100644
--- a/macros/latex/contrib/sagetex/example.pdf
+++ b/macros/latex/contrib/sagetex/example.pdf
Binary files differ
diff --git a/macros/latex/contrib/sagetex/py-and-sty.dtx b/macros/latex/contrib/sagetex/py-and-sty.dtx
index 49bf5cd05e..acd92c08e2 100644
--- a/macros/latex/contrib/sagetex/py-and-sty.dtx
+++ b/macros/latex/contrib/sagetex/py-and-sty.dtx
@@ -29,7 +29,7 @@
% and |listings| for the |sagecommandline| environment.
% \begin{macrocode}
\RequirePackage{listings}
-\RequirePackage{color}
+\RequirePackage{xcolor}
\lstdefinelanguage{Sage}[]{Python}
{morekeywords={False,sage,True},sensitive=true}
\lstdefinelanguage{SageOutput}[]{}
@@ -68,9 +68,9 @@
\lstdefinestyle{SageOutput}{
style=DefaultSageOutput,
}
-\definecolor{dbluecolor}{rgb}{0.01,0.02,0.7}
-\definecolor{dgreencolor}{rgb}{0.2,0.4,0.0}
-\definecolor{dgraycolor}{rgb}{0.30,0.3,0.30}
+\providecolor{dbluecolor}{rgb}{0.01,0.02,0.7}
+\providecolor{dgreencolor}{rgb}{0.2,0.4,0.0}
+\providecolor{dgraycolor}{rgb}{0.30,0.3,0.30}
% \end{macrocode}
% Unsurprisingly, the |\sageplot| command works poorly without graphics
% support.
@@ -1243,7 +1243,7 @@ http://doc.sagemath.org/html/en/tutorial/sagetex.html.""".format(jobname,
raise SyntaxError(""" SageTeX no longer supports "..." for line continuation in sagexample and
sagecommandline environments. Use "....:", which matches what the Sage
interpreter uses. See the documentation and example file in
-SAGE_ROOT/local/share/doc/sagetex.""")
+SAGE_ROOT/venv/share/doc/sagetex.""")
if has_cont:
cmd.append(line[has_cont.end():])
ret.append((start, end, '\n'.join(cmd)))
@@ -1521,9 +1521,9 @@ SAGE_ROOT/local/share/doc/sagetex.""")
% \begin{center}
% \verb+egrep -v '^( _st_.goboom| ?_st_.current_tex_line|print(.SageT)' filename.sage | md5sum+
% \end{center}
-% in a shell. The included |run-sagetex-if-necessary| uses this
+% in a shell. The included |sagetex-run| uses this
% mechanism to, well, only run Sage when necessary; see
-% \autoref{sec:run-sagetex-if-necessary}.
+% \autoref{sec:sagetex-run}.
% \begin{macrocode}
def endofdoc(self):
sagef = open(self.filename + '.sagetex.sage', 'r')
diff --git a/macros/latex/contrib/sagetex/sagetex.dtx b/macros/latex/contrib/sagetex/sagetex.dtx
index b5598d990e..e028698816 100644
--- a/macros/latex/contrib/sagetex/sagetex.dtx
+++ b/macros/latex/contrib/sagetex/sagetex.dtx
@@ -30,10 +30,10 @@
%<latex>\ProvidesPackage{sagetex}
%<python>__version__ = """
%<*latex|python>
- [2020/08/12 v3.5 embedding Sage into LaTeX documents]
+ [2022/08/21 v3.6.1 embedding Sage into LaTeX documents]
%</latex|python>
%<python>""".strip()
-%<latex>\newcommand{\ST@ver}{2020/08/12 v3.5}
+%<latex>\newcommand{\ST@ver}{2022/08/21 v3.6.1}
%<*driver>
\documentclass{ltxdoc}
\usepackage{sagetex}
@@ -261,9 +261,9 @@ suggestions.
% |sage.plot.plot?| and look for |ticks| and |tick_formatter|.)
%
% Till Tantau has some good commentary on the use of graphics in the
-% \href{http://www.ctan.org/tex-archive/help/Catalogue/entries/pgf.html}{``Guidelines
+% \href{https://pgf-tikz.github.io/pgf/pgfmanual.pdf}{``Guidelines
% on Graphics'' section of the \textsc{pgf} manual} (chapter 7 of the
-% manual for version 2.10). You should always give careful thought and
+% manual for version 3.1.9). You should always give careful thought and
% attention to creating graphics for your document; I have in mind that
% a good workflow for using \ST for plotting is something like this:
%
@@ -539,7 +539,7 @@ suggestions.
% ``\percent'' inside such an environment will get written, uh, verbatim
% to the |.sage| file.
%
-% \paragraph{Arguments with side effects}
+% \subsubsection{Arguments with side effects}
%
% Be careful when feeding |\sage| and |\sagestr| arguments that have
% side effects, since in some situations they can get evaluated more
@@ -763,7 +763,7 @@ suggestions.
% indented when typeset. You can change this length however you like
% with |\setlength|: do |\setlength{\sagetexindent}{6ex}| or whatever.
%
-% \DescribeEnv{sageexample} This environment allow you to include
+% \DescribeEnv{sageexample} This environment allows you to include
% doctest-like snippets in your document that will be nicely typeset.
% For example,
% \begin{quote}
@@ -811,7 +811,7 @@ suggestions.
% Thi\'ery.\\
%
% \DescribeEnv{sagecommandline} This environment is similar to the
-% sageexample environment in that it allow you to use \ST as a
+% sageexample environment in that it allows you to use \ST as a
% pretty-printing command line, or to include doctest-like snippets in
% your document. The difference is that the output is typeset as text,
% much like running Sage on the command line, using the
@@ -839,7 +839,7 @@ suggestions.
% You have a choice of either explicitly providing the Sage output or
% leaving it up to the computer to fill in the blanks. Above, the output
% for $t$ was provided, but the output for the |factor()| command
-% wasn't. Moreover, any Sage comment that starts with a ``at'' sign is
+% wasn't. Moreover, any Sage comment that starts with an ``at'' sign is
% escaped to \LTX. In particular, you can use |\label| to mark line
% numbers in order to |\ref|erence and |\pageref|erence them as usual.
% See the example file to see this mechanism in action.
@@ -960,8 +960,8 @@ suggestions.
% the typesetting engine dropdown menu and then typeset.
%
% (You can also replace "|sage|" above with the
-% |run-sagetex-if-necessary| script---see
-% \autoref{sec:run-sagetex-if-necessary}.)
+% |sagetex-run| script---see
+% \autoref{sec:sagetex-run}.)
%
% \subsection{Using Beamer}
%
@@ -1054,11 +1054,11 @@ suggestions.
%
% \subsubsection{The 21st century way}
%
-% The SageMathCloud
-% (\href{http://cloud.sagemath.com}{\texttt{cloud.sagemath.com}}) service has
+% CoCalc
+% (\href{https://cocalc.com/}{\texttt{cocalc.com/}}) has
% full support for \ST, is free to use, and has many fantastic
% collaboration features. If you somehow want to collaborate on a
-% \ST-enabled \TeX document with a colleague, using SageMathCloud is one
+% \ST-enabled \TeX document with a colleague, using CoCalc is one
% of the best and easiest ways to do it. You and your collaborators
% simply create an account, then make a project for your collaboration,
% and add all the collaborators to the project. Then you can all enjoy
@@ -1066,7 +1066,7 @@ suggestions.
%
% \subsubsection{The $N$th century way, for $N < 21$}
%
-% Using anything other than SageMathCloud, |git|, or similar tools these
+% Using anything other than CoCalc, |git|, or similar tools these
% days seems pretty primitive. If emailing |.tex| files back and forth
% seems perfectly reasonable to you, or if you have to send a file to a
% journal, the easiest way is to simply include with your document the
diff --git a/macros/latex/contrib/sagetex/sagetex.ins b/macros/latex/contrib/sagetex/sagetex.ins
index dd8dabb80a..bbbbe1388a 100644
--- a/macros/latex/contrib/sagetex/sagetex.ins
+++ b/macros/latex/contrib/sagetex/sagetex.ins
@@ -84,7 +84,6 @@ with this program. If not, see <http://www.gnu.org/licenses/>.
\from{py-and-sty.dtx}{python}}}
\generate{\file{sagetexparse.py}{\from{scripts.dtx}{parsermod}}}
-
\usedir{scripts/sagetex}
% Now define a new preamble with the shebang line at the top.
@@ -92,10 +91,10 @@ with this program. If not, see <http://www.gnu.org/licenses/>.
\def\envpypreamble{\hash!/usr/bin/env python^^J\pypreamble}
\usepreamble\envpypreamble
-\generate{\file{run-sagetex-if-necessary.py}{\from{scripts.dtx}{ifnecessaryscript}}}
-\generate{\file{makestatic.py}{\from{scripts.dtx}{staticscript}}}
-\generate{\file{extractsagecode.py}{\from{scripts.dtx}{extractscript}}}
-\generate{\file{remote-sagetex.py}{\from{remote-sagetex.dtx}{remotesagetex}}}
+\generate{\file{sagetex-run.py}{\from{scripts.dtx}{ifnecessaryscript}}}
+\generate{\file{sagetex-makestatic.py}{\from{scripts.dtx}{staticscript}}}
+\generate{\file{sagetex-extract.py}{\from{scripts.dtx}{extractscript}}}
+\generate{\file{sagetex-remote.py}{\from{remote-sagetex.dtx}{remotesagetex}}}
\obeyspaces
\Msg{******************************************************************}
diff --git a/macros/latex/contrib/sagetex/sagetex.pdf b/macros/latex/contrib/sagetex/sagetex.pdf
index 4ad0f319e8..66f93e8add 100644
--- a/macros/latex/contrib/sagetex/sagetex.pdf
+++ b/macros/latex/contrib/sagetex/sagetex.pdf
Binary files differ
diff --git a/macros/latex/contrib/sagetex/scripts.dtx b/macros/latex/contrib/sagetex/scripts.dtx
index 8f7048dcef..988f9732dc 100644
--- a/macros/latex/contrib/sagetex/scripts.dtx
+++ b/macros/latex/contrib/sagetex/scripts.dtx
@@ -1,27 +1,26 @@
% \section{Included Python scripts}
% \label{sec:included-scripts}
%
-% Here we describe the Python code for |run-sagetex-if-necessary|, and
-% also |makestatic.py|, which removes \ST commands to produce a
-% ``static'' file, and |extractsagecode.py|, which extracts all the Sage
-% code from a |.tex| file.
+% Here we describe the Python code for \ST scripts, for running
+% Sage only if necessary, substituting in Sage outputs to produce
+% a ``static'' file, and extracting all Sage code from a |.tex| file.
%
-% \subsection{run-sagetex-if-necessary}
-% \label{sec:run-sagetex-if-necessary}
+% \subsection{\texttt{sagetex-run}}
+% \label{sec:sagetex-run}
% \iffalse
%<*ifnecessaryscript>
% \fi
%
% When working on a document that uses \ST, running Sage every time you
% typeset your document may take too long, especially since it often
-% won't be necessary. This script is a drop-in replacement for Sage:
+% is not necessary. This script is a drop-in replacement for Sage:
% instead of
% \begin{center}
% |sage document.sagetex.sage|
% \end{center}
% you can do
% \begin{center}
-% |run-sagetex-if-necessary.py document.sagetex.sage|
+% |sagetex-run document.sagetex.sage|
% \end{center}
% and it will use the MD5 mechanism described in the |endofdoc| macro
% (page~{\pageref{macro:endofdoc}). With this, you can set up your editor
@@ -29,105 +28,114 @@
% that does
% \begin{quote}
% |pdflatex $1|\\
-% |run-sagetex-if-necessary.py $1|
+% |sagetex-run $1|
% \end{quote}
% which will only, of course, run Sage when necessary.
% \begin{macrocode}
-
-# given a filename f, examines f.sagetex.sage and f.sagetex.sout and
-# runs Sage if necessary.
+"""
+Given a filename f, examines f.sagetex.sage and f.sagetex.sout and
+runs Sage if necessary.
+"""
import hashlib
import sys
import os
import re
import subprocess
-from six import PY3
-
-# CHANGE THIS AS APPROPRIATE
-path_to_sage = os.path.expanduser('~/bin/sage')
-# or try to auto-find it:
-# path_to_sage = subprocess.check_output(['which', 'sage']).strip()
-# or just tell me:
-# path_to_sage = '/usr/local/bin/sage'
-
-if sys.argv[1].endswith('.sagetex.sage'):
- src = sys.argv[1][:-13]
-else:
- src = os.path.splitext(sys.argv[1])[0]
-
-usepackage = r'usepackage(\[.*\])?{sagetex}'
-uses_sagetex = False
-
-# if it does not use sagetex, obviously running sage is unnecessary
-with open(src + '.tex') as texf:
- for line in texf:
- if line.strip().startswith(r'\usepackage') and re.search(usepackage, line):
- uses_sagetex = True
- break
-
-if not uses_sagetex:
- print(src + ".tex doesn't seem to use SageTeX, exiting.")
- sys.exit(0)
-
-# if something goes wrong, assume we need to run Sage
-run_sage = True
-ignore = r"^( _st_.goboom|print\('SageT| ?_st_.current_tex_line)"
-
-try:
- with open(src + '.sagetex.sage', 'r') as sagef:
- h = hashlib.md5()
- for line in sagef:
- if not re.search(ignore, line):
- if PY3:
- h.update(bytearray(line,'utf8'))
- else:
- h.update(bytearray(line))
-except IOError:
- print('{0}.sagetex.sage not found, I think you need to typeset {0}.tex first.'.format(src))
- sys.exit(1)
-
-try:
- with open(src + '.sagetex.sout', 'r') as outf:
- for line in outf:
- m = re.match('%([0-9a-f]+)% md5sum', line)
- if m:
- print('computed md5:', h.hexdigest())
- print('sagetex.sout md5:', m.group(1))
- if h.hexdigest() == m.group(1):
- run_sage = False
+import shutil
+import argparse
+
+def argparser():
+ p = argparse.ArgumentParser(description=__doc__.strip())
+ p.add_argument('--sage', action='store', default=find_sage(),
+ help="Location of the Sage executable")
+ p.add_argument('src', help="Input file name (basename or .sagetex.sage)")
+ return p
+
+def find_sage():
+ return shutil.which('sage') or 'sage'
+
+def run(args):
+ src = args.src
+ path_to_sage = args.sage
+
+ if src.endswith('.sagetex.sage'):
+ src = src[:-13]
+ else:
+ src = os.path.splitext(src)[0]
+
+ # Ensure results are output in the same directory as the source files
+ os.chdir(os.path.dirname(src))
+ src = os.path.basename(src)
+
+ usepackage = r'usepackage(\[.*\])?{sagetex}'
+ uses_sagetex = False
+
+ # If it does not use sagetex, obviously running sage is unnecessary.
+ if os.path.isfile(src + '.tex'):
+ with open(src + '.tex') as texf:
+ for line in texf:
+ if line.strip().startswith(r'\usepackage') and re.search(usepackage, line):
+ uses_sagetex = True
break
-except IOError:
- pass
-
-if run_sage:
- print('Need to run Sage on {0}.'.format(src))
- sys.exit(subprocess.call([path_to_sage, src + '.sagetex.sage']))
-else:
- print('Not necessary to run Sage on {0}.'.format(src))
+ else:
+ # The .tex file might not exist if LaTeX output was put to a different
+ # directory, so in that case just assume we need to build.
+ uses_sagetex = True
+
+ if not uses_sagetex:
+ print(src + ".tex doesn't seem to use SageTeX, exiting.", file=sys.stderr)
+ sys.exit(1)
+
+ # if something goes wrong, assume we need to run Sage
+ run_sage = True
+ ignore = r"^( _st_.goboom|print\('SageT| ?_st_.current_tex_line)"
+
+ try:
+ with open(src + '.sagetex.sage', 'r') as sagef:
+ h = hashlib.md5()
+ for line in sagef:
+ if not re.search(ignore, line):
+ h.update(bytearray(line,'utf8'))
+ except IOError:
+ print('{0}.sagetex.sage not found, I think you need to typeset {0}.tex first.'
+ ''.format(src), file=sys.stderr)
+ sys.exit(1)
+
+ try:
+ with open(src + '.sagetex.sout', 'r') as outf:
+ for line in outf:
+ m = re.match('%([0-9a-f]+)% md5sum', line)
+ if m:
+ print('computed md5:', h.hexdigest())
+ print('sagetex.sout md5:', m.group(1))
+ if h.hexdigest() == m.group(1):
+ run_sage = False
+ break
+ except IOError:
+ pass
+
+ if run_sage:
+ print('Need to run Sage on {0}.'.format(src))
+ sys.exit(subprocess.call([path_to_sage, src + '.sagetex.sage']))
+ else:
+ print('Not necessary to run Sage on {0}.'.format(src))
+
+if __name__ == "__main__":
+ run(argparser().parse_args())
% \end{macrocode}
%
-% \subsection{makestatic.py}
-% \label{sec:makestatic}
+% \subsection{\texttt{sagetex-makestatic}}
+% \label{sec:sagetex-makestatic}
% \iffalse
%</ifnecessaryscript>
%<*staticscript>
% \fi
%
-% Now the |makestatic.py| script. It's about the most basic, generic
-% Python script taking command-line arguments that you'll find. The
-% |#!/usr/bin/env python| line is provided for us by the |.ins| file's
-% preamble, so we don't put it here.
+% Now the |sagetex-makestatic|:
+%
% \begin{macrocode}
-import sys
-import time
-import getopt
-import os.path
-from sagetexparse import DeSageTex
-
-def usage():
- print("""Usage: %s [-h|--help] [-o|--overwrite] inputfile [outputfile]
-
+"""
Removes SageTeX macros from `inputfile' and replaces them with the
Sage-computed results to make a "static" file. You'll need to have run
Sage on `inputfile' already.
@@ -136,53 +144,61 @@ Sage on `inputfile' already.
`outputfile', the results will be written to a file of that name.
Specify `-o' or `--overwrite' to overwrite the file if it exists.
-See the SageTeX documentation for more details.""" % sys.argv[0])
-
-try:
- opts, args = getopt.getopt(sys.argv[1:], 'ho', ['help', 'overwrite'])
-except getopt.GetoptError as err:
- print(str(err))
- usage()
- sys.exit(2)
-
-overwrite = False
-for o, a in opts:
- if o in ('-h', '--help'):
- usage()
- sys.exit()
- elif o in ('-o', '--overwrite'):
- overwrite = True
-
-if len(args) == 0 or len(args) > 2:
- print('Error: wrong number of arguments. Make sure to specify options first.\n')
- usage()
- sys.exit(2)
-
-if len(args) == 2 and (os.path.exists(args[1]) and not overwrite):
- print('Error: %s exists and overwrite option not specified.' % args[1])
- sys.exit(1)
-
-src, ext = os.path.splitext(args[0])
+See the SageTeX documentation for more details.
+"""
+import sys
+import time
+import os.path
+import argparse
+
+from sagetexparse import DeSageTex
+
+def argparser():
+ p = argparse.ArgumentParser(description=__doc__.strip())
+ p.add_argument('inputfile', help="Input file name (basename or .tex)")
+ p.add_argument('outputfile', nargs='?', default=None, help="Output file name")
+ p.add_argument('-o', '--overwrite', action="store_true", default=False,
+ help="Overwrite output file if it exists")
+ p.add_argument('-s', '--sout', action="store", default=None,
+ help="Location of the .sagetex.sout file")
+ return p
+
+def run(args):
+ src, dst, overwrite = args.inputfile, args.outputfile, args.overwrite
+
+ if dst is not None and (os.path.exists(dst) and not overwrite):
+ print('Error: %s exists and overwrite option not specified.' % dst,
+ file=sys.stderr)
+ sys.exit(1)
+
+ src, ext = os.path.splitext(src)
+ texfn = src + '.tex'
+ soutfn = args.sout if args.sout is not None else src + '.sagetex.sout'
% \end{macrocode}
% All the real work gets done in the line below. Sorry it's not more
% exciting-looking.
% \begin{macrocode}
-desagetexed = DeSageTex(src)
+ desagetexed = DeSageTex(texfn, soutfn)
% \end{macrocode}
% This part is cool: we need double percent signs at the beginning of
% the line because Python needs them (so they get turned into single
% percent signs) \emph{and} because \textsf{Docstrip} needs them (so the
% line gets passed into the generated file). It's perfect!
% \begin{macrocode}
-header = "%% SageTeX commands have been automatically removed from this file and\n%% replaced with plain LaTeX. Processed %s.\n" % time.strftime('%a %d %b %Y %H:%M:%S', time.localtime())
+ header = ("%% SageTeX commands have been automatically removed from this file and\n"
+ "%% replaced with plain LaTeX. Processed %s.\n"
+ "" % time.strftime('%a %d %b %Y %H:%M:%S', time.localtime()))
-if len(args) == 2:
- dest = open(args[1], 'w')
-else:
- dest = sys.stdout
+ if dst is not None:
+ dest = open(dst, 'w')
+ else:
+ dest = sys.stdout
-dest.write(header)
-dest.write(desagetexed.result)
+ dest.write(header)
+ dest.write(desagetexed.result)
+
+if __name__ == "__main__":
+ run(argparser().parse_args())
% \end{macrocode}
%
% \iffalse
@@ -190,20 +206,12 @@ dest.write(desagetexed.result)
%<*extractscript>
% \fi
%
-% \subsection{extractsagecode.py}
+% \subsection{\texttt{sagetex-extract}}
%
-% Same idea as |makestatic.py|, except this does basically the opposite
+% Same idea as |sagetex-makestatic|, except this does basically the opposite
% thing.
% \begin{macrocode}
-import sys
-import time
-import getopt
-import os.path
-from sagetexparse import SageCodeExtractor
-
-def usage():
- print("""Usage: %s [-h|--help] [-o|--overwrite] inputfile [outputfile]
-
+"""
Extracts Sage code from `inputfile'.
`inputfile' can include the .tex extension or not. If you provide
@@ -212,47 +220,49 @@ otherwise the result will be printed to stdout.
Specify `-o' or `--overwrite' to overwrite the file if it exists.
-See the SageTeX documentation for more details.""" % sys.argv[0])
-
-try:
- opts, args = getopt.getopt(sys.argv[1:], 'ho', ['help', 'overwrite'])
-except getopt.GetoptError as err:
- print(str(err))
- usage()
- sys.exit(2)
-
-overwrite = False
-for o, a in opts:
- if o in ('-h', '--help'):
- usage()
- sys.exit()
- elif o in ('-o', '--overwrite'):
- overwrite = True
-
-if len(args) == 0 or len(args) > 2:
- print('Error: wrong number of arguments. Make sure to specify options first.\n')
- usage()
- sys.exit(2)
-
-if len(args) == 2 and (os.path.exists(args[1]) and not overwrite):
- print('Error: %s exists and overwrite option not specified.' % args[1])
- sys.exit(1)
-
-src, ext = os.path.splitext(args[0])
-sagecode = SageCodeExtractor(src)
-header = """\
-# This file contains Sage code extracted from %s%s.
-# Processed %s.
-
-""" % (src, ext, time.strftime('%a %d %b %Y %H:%M:%S', time.localtime()))
-
-if len(args) == 2:
- dest = open(args[1], 'w')
-else:
- dest = sys.stdout
-
-dest.write(header)
-dest.write(sagecode.result)
+See the SageTeX documentation for more details.
+"""
+import sys
+import time
+import os.path
+import argparse
+
+from sagetexparse import SageCodeExtractor
+
+def argparser():
+ p = argparse.ArgumentParser(description=__doc__.strip())
+ p.add_argument('inputfile', help="Input file name (basename or .tex)")
+ p.add_argument('outputfile', nargs='?', default=None, help="Output file name")
+ p.add_argument('-o', '--overwrite', action="store_true", default=False,
+ help="Overwrite output file if it exists")
+ p.add_argument('--no-inline', action="store_true", default=False,
+ help="Extract code only from Sage environments")
+ return p
+
+def run(args):
+ src, dst, overwrite = args.inputfile, args.outputfile, args.overwrite
+
+ if dst is not None and (os.path.exists(dst) and not overwrite):
+ print('Error: %s exists and overwrite option not specified.' % dst,
+ file=sys.stderr)
+ sys.exit(1)
+
+ src, ext = os.path.splitext(src)
+ sagecode = SageCodeExtractor(src + '.tex', inline=not args.no_inline)
+ header = ("#> This file contains Sage code extracted from %s%s.\n"
+ "#> Processed %s.\n"
+ "" % (src, ext, time.strftime('%a %d %b %Y %H:%M:%S', time.localtime())))
+
+ if dst is not None:
+ dest = open(dst, 'w')
+ else:
+ dest = sys.stdout
+
+ dest.write(header)
+ dest.write(sagecode.result)
+
+if __name__ == "__main__":
+ run(argparser().parse_args())
% \end{macrocode}
%
% \iffalse
@@ -271,6 +281,8 @@ dest.write(sagecode.result)
% over the screen.
% \begin{macrocode}
import sys
+import os
+import textwrap
from pyparsing import *
% \end{macrocode}
% First, we define this very helpful parser: it finds the matching
@@ -281,8 +293,7 @@ from pyparsing import *
% \begin{macrocode}
def skipToMatching(opener, closer):
nest = nestedExpr(opener, closer)
- nest.setParseAction(lambda l, s, t: l[s:getTokensEndLoc()])
- return nest
+ return originalTextFor(nest)
curlybrackets = skipToMatching('{', '}')
squarebrackets = skipToMatching('[', ']')
@@ -290,6 +301,7 @@ squarebrackets = skipToMatching('[', ']')
% Next, parser for |\sage|, |\sageplot|, and pause/unpause calls:
% \begin{macrocode}
sagemacroparser = r'\sage' + curlybrackets('code')
+sagestrmacroparser = r'\sagestr' + curlybrackets('code')
sageplotparser = (r'\sageplot'
+ Optional(squarebrackets)('opts')
+ Optional(squarebrackets)('format')
@@ -356,17 +368,19 @@ class SoutParser():
% that the provided |fn| is just a basename.
% \begin{macrocode}
class DeSageTex():
- def __init__(self, fn):
+ def __init__(self, texfn, soutfn):
self.sagen = 0
self.plotn = 0
- self.fn = fn
- self.sout = SoutParser(fn + '.sagetex.sout')
+ self.fn = os.path.basename(texfn)
+ self.sout = SoutParser(soutfn)
% \end{macrocode}
% Parse |\sage| macros. We just need to pull in the result from the
% |.sout| file and increment the counter---that's what |self.sage| does.
% \begin{macrocode}
+ strmacro = sagestrmacroparser
smacro = sagemacroparser
smacro.setParseAction(self.sage)
+ strmacro.setParseAction(self.sage)
% \end{macrocode}
% Parse the |\usepackage{sagetex}| line. Right now we don't support
% comma-separated lists of packages.
@@ -410,7 +424,7 @@ class DeSageTex():
% looks for any one of the above bits, while ignoring anything that
% should be ignored.
% \begin{macrocode}
- doit = smacro | senv | ssilent | usepackage | splot | stexindent
+ doit = smacro | senv | ssilent | usepackage | splot | stexindent |strmacro
doit.ignore('%' + restOfLine)
doit.ignore(r'\begin{verbatim}' + SkipTo(r'\end{verbatim}'))
doit.ignore(r'\begin{comment}' + SkipTo(r'\end{comment}'))
@@ -422,7 +436,7 @@ class DeSageTex():
% |transformString| on it, since that will just pick out the interesting
% bits and munge them according to the above definitions.
% \begin{macrocode}
- str = ''.join(open(fn + '.tex', 'r').readlines())
+ str = ''.join(open(texfn, 'r').readlines())
self.result = doit.transformString(str)
% \end{macrocode}
% That's the end of the class constructor, and it's all we need to do
@@ -456,7 +470,7 @@ class DeSageTex():
% Sage.
% \begin{macrocode}
class SageCodeExtractor():
- def __init__(self, fn):
+ def __init__(self, texfn, inline=True):
smacro = sagemacroparser
smacro.setParseAction(self.macroout)
@@ -483,34 +497,38 @@ class SageCodeExtractor():
sunpause = sagetexunpause
sunpause.setParseAction(self.unpause)
- doit = smacro | splot | senv | spause | sunpause
+ if inline:
+ doit = smacro | splot | senv | spause | sunpause
+ else:
+ doit = senv | spause | sunpause
+ doit.ignore('%' + restOfLine)
- str = ''.join(open(fn + '.tex', 'r').readlines())
+ str = ''.join(open(texfn, 'r').readlines())
self.result = ''
doit.transformString(str)
def macroout(self, s, l, t):
- self.result += '# \\sage{} from line %s\n' % lineno(l, s)
- self.result += t.code[1:-1] + '\n\n'
+ self.result += '#> \\sage{} from line %s\n' % lineno(l, s)
+ self.result += textwrap.dedent(t.code[1:-1]) + '\n\n'
def plotout(self, s, l, t):
- self.result += '# \\sageplot{} from line %s:\n' % lineno(l, s)
- if t.format is not '':
- self.result += '# format: %s' % t.format[0][1:-1] + '\n'
- self.result += t.code[1:-1] + '\n\n'
+ self.result += '#> \\sageplot{} from line %s:\n' % lineno(l, s)
+ if t.format != '':
+ self.result += '#> format: %s' % t.format[0][1:-1] + '\n'
+ self.result += textwrap.dedent(t.code[1:-1]) + '\n\n'
def envout(self, s, l, t):
- self.result += '# %s environment from line %s:' % (t.env,
+ self.result += '#> %s environment from line %s:' % (t.env,
lineno(l, s))
- self.result += t.code[0] + '\n'
+ self.result += textwrap.dedent(''.join(t.code)) + '\n'
def pause(self, s, l, t):
- self.result += ('# SageTeX (probably) paused on input line %s.\n\n' %
+ self.result += ('#> SageTeX (probably) paused on input line %s.\n\n' %
(lineno(l, s)))
def unpause(self, s, l, t):
- self.result += ('# SageTeX (probably) unpaused on input line %s.\n\n' %
+ self.result += ('#> SageTeX (probably) unpaused on input line %s.\n\n' %
(lineno(l, s)))
% \end{macrocode}
% \end{macro}
diff --git a/macros/latex/contrib/sagetex/setup.py b/macros/latex/contrib/sagetex/setup.py
index 28e2712065..b83a6bbac8 100644
--- a/macros/latex/contrib/sagetex/setup.py
+++ b/macros/latex/contrib/sagetex/setup.py
@@ -4,27 +4,24 @@ setup(name='sagetex',
long_description="""The SageTeX package allows you to embed code,
results of computations, and plots from the Sage mathematics
software suite (http://sagemath.org) into LaTeX documents.""",
- version='3.5',
+ version='3.6.1',
author='Dan Drake',
author_email='dr.dan.drake@gmail.com',
maintainer='SageMath developers',
maintainer_email='sage-devel@googlegroups.com',
url='https://github.com/sagemath/sagetex',
license='GPLv2+',
- py_modules=['sagetex'],
+ py_modules=['sagetex', 'sagetexparse'],
+ scripts=['sagetex-run', 'sagetex-extract', 'sagetex-makestatic', 'sagetex-remote'],
+ install_requires=['pyparsing'],
data_files = [('share/texmf/tex/latex/sagetex',
['example.tex',
'CONTRIBUTORS',
- 'extractsagecode.py',
- 'run-sagetex-if-necessary.py',
- 'makestatic.py',
'scripts.dtx',
'remote-sagetex.dtx',
- 'remote-sagetex.py',
'py-and-sty.dtx',
'sagetex.dtx',
'sagetex.ins',
- 'sagetexparse.py',
'sagetex.sty']),
('share/doc/sagetex', [
'example.tex',
diff --git a/macros/musixtex/README b/macros/musixtex/README
index eef46a1144..4047ef5726 100644
--- a/macros/musixtex/README
+++ b/macros/musixtex/README
@@ -1,4 +1,4 @@
-This is MusiXTeX, version 1.35 (2021-08-30).
+This is MusiXTeX, version 1.36 (2023-01-11).
MusiXTeX is a TeX-based system for typesetting music.
The main author was Daniel Taupin, who died in a climbing
diff --git a/macros/musixtex/doc/musixdoc.pdf b/macros/musixtex/doc/musixdoc.pdf
index a3b49fe947..adbcbfc912 100644
--- a/macros/musixtex/doc/musixdoc.pdf
+++ b/macros/musixtex/doc/musixdoc.pdf
Binary files differ
diff --git a/macros/musixtex/doc/musixdoc/accidentals.tex b/macros/musixtex/doc/musixdoc/accidentals.tex
index a504837530..de374139be 100644
--- a/macros/musixtex/doc/musixdoc/accidentals.tex
+++ b/macros/musixtex/doc/musixdoc/accidentals.tex
@@ -1,5 +1,6 @@
\chapter{Accidentals}
-\vspace*{-3ex}
+\vspace*{-4ex}
+\enlargethispage*{2ex}
Accidentals can be introduced in two ways.
The first way, using explicit macros, consists for
example in coding \keyindex{fl}\pitchp~to put a \ital{flat} at the
@@ -8,6 +9,8 @@ non-spacing command and will automatically place the accidental an
appropriate distance to the left of the anticipated note head.
Naturals, sharps, double flats and double sharps are coded \keyindex{na}\pitchp,
\keyindex{sh}\pitchp, \keyindex{dfl}\pitchp~and \keyindex{dsh}\pitchp~respectively.
+Thinner accidentals are available using the definitions enabled by extension library \keyindex{musixthacc}
+described in Section~\ref{musixthacc}.
The alternate macros \keyindex{lfl}, \keyindex{lna}, \keyindex{lsh},
\keyindex{ldfl} and \keyindex{ldsh}
diff --git a/macros/musixtex/doc/musixdoc/barlines.tex b/macros/musixtex/doc/musixdoc/barlines.tex
index b3f1d545a7..6d39c30985 100644
--- a/macros/musixtex/doc/musixdoc/barlines.tex
+++ b/macros/musixtex/doc/musixdoc/barlines.tex
@@ -308,3 +308,9 @@ This is the code:
\NOTes\en\setdoubleBAR\zendextract
\end{verbatim}\end{quote}
+\section{Ledger Lines}
+
+Ledger lines are the short horizontal lines above or below the staff for high or low notes.
+As of version 1.36, these have been thickened. To restore the thickness used in
+previous versions, add \verb|\def\hlthick{0.2pt}| to the preamble after inputting
+\verb|musixtex.tex|.
diff --git a/macros/musixtex/doc/musixdoc/extensions.tex b/macros/musixtex/doc/musixdoc/extensions.tex
index 8d66b23cd7..d2bdd3d75a 100644
--- a/macros/musixtex/doc/musixdoc/extensions.tex
+++ b/macros/musixtex/doc/musixdoc/extensions.tex
@@ -1652,8 +1652,44 @@ If you need greater numbers of these elements, see Sections~\ref{musixmad_setmax
\ref{musixmad_setmaxslurs} and
\ref{musixmad_setmaxtrills}.
+ \section{musixmkm} \ixtt{musixmkm.tex}
+ The following special accidentals used in Turkish classical music (makam\index{makam})
+are supported:
+\smallskip
+\begin{music}
+\input musixmkm
+\normalmusicsize
+\startextract
+\Notes\shtanini i\en
+\Notes\shbuyukmucenneb i\en
+\Notes\shkucuk i\en
+\Notes\shbakiye i\en
+\Notes\shkoma i\en
+\Notes\flkoma i\en
+\Notes\flbakiye i\en
+\Notes\flkucuk i\en
+\Notes\flbuyukmucenneb i\en
+\Notes\fltanini i\en
+\endextract%
+\end{music}%
+These are generated by, respectively,
+\begin{list}{}{}
+\item{}
+\begin{tabular}{l}
+\keyindex{shtanini} $p$\\
+\keyindex{shbuyukmucenneb} $p$\\
+\keyindex{shkucuk} $p$\\
+\keyindex{shbakiye} $p$\\
+\keyindex{shkoma} $p$\\
+\keyindex{flkoma} $p$\\
+\keyindex{flbakiye} $p$\\
+\keyindex{flkucuk} $p$\\
+\keyindex{flbuyukmucenneb} $p$\\
+\keyindex{fltanini} $p$\\
+\end{tabular}
+\end{list}
-\section{musixper}\label{perc}
+ \section{musixper}\label{perc}
Provides special symbols intended for percussion parts. Included are a
\ital{drum clef}---comprising two vertical parallel lines---and notes with
@@ -1911,6 +1947,7 @@ Use as follows:
\input musixplt
...
\end{verbatim}\end{quote}
+You may need to install additional packages: \texttt{psnfss}, \texttt{palatino} and \texttt{fpl}.
The usual ``small'' type commands are supported:
\begin{quote}
@@ -1946,7 +1983,7 @@ the ``big'' ones, small-caps;
however, \keyindex{font} commands are defined
for all the usual variants at all of these sizes.
To letter-space a title, use the \verb|\so|
-command in the \verb\soul\ package.
+command in the \verb\soul\ package.
The following bold-italic fonts for dynamic marks are defined:
@@ -2127,6 +2164,25 @@ either before \keyindex{startpiece} or between \keyindex{stoppiece} and
\end{itemize}
+ \section{musixthacc}\index{musixthacc@{\tt musixthacc.tex}}\label{musixthacc}
+Provides ``thin'' accidentals
+\keyindex{thna}~$p$, \keyindex{thsh}~$p$, \keyindex{thfl}~$p$, \keyindex{thdsh}~$p$
+and \keyindex{thdfl}~$p$:
+\smallskip
+\begin{music}
+\input musixthacc
+\normalmusicsize
+\startextract
+\Notes\thna i\en
+\Notes\thsh i\en
+\Notes\thfl i\en
+\Notes\thdsh i\en
+\Notes\thdfl i\en
+\endextract%
+\end{music}%
+Any necessary adjustment of horizontal position and spacing is up to
+the user and \keyindex{relativeaccid} adjustment is not effective.
+
\section{musixtmr}\index{musixtmr@{\tt musixtmr.tex}}\label{times}
Replaces the default Computer Modern text fonts by Times fonts;
see Section~\ref{UserFonts}.
@@ -2216,7 +2272,7 @@ An auxiliary program \verb|msxlint| distributed in the \verb\musixtnt\ package c
\keyindex{TransformNotes} may be used anywhere between \keyindex{startpiece}
and the command that ends the piece.
-\subsection{Extracting single-instrument parts from multi-instrument scores}
+\subsection{Extracting single-instrument parts from multi-instrument scores}\index{extracting parts}
To extract
a single-instrument part from a (copy of a) multi-instrument \musixtex\ score:
diff --git a/macros/musixtex/doc/musixdoc/frontmatter.tex b/macros/musixtex/doc/musixdoc/frontmatter.tex
index e2f919ce7e..6079e9b04d 100644
--- a/macros/musixtex/doc/musixdoc/frontmatter.tex
+++ b/macros/musixtex/doc/musixdoc/frontmatter.tex
@@ -1,6 +1,6 @@
\title{\Huge\bfseries\musixtex\\[\bigskipamount]
\LARGE\bfseries Using \TeX{} to write polyphonic\\or
-instrumental music\\\Large\itshape Version 1.35}
+instrumental music\\\Large\itshape Version 1.36}
\author{}
@@ -68,7 +68,7 @@ Since then, the only significant update to \musixtex\ has been in version 1.15 (
takes advantage of the greater capacity of the e\TeX\ version of \TeX.
This manual
is the definitive reference to all features of
-\musixtex\ version~1.33a.
+\musixtex\ version~1.36.
Novice users need not start here.
Most
diff --git a/macros/musixtex/doc/musixdoc/miscellaneous.tex b/macros/musixtex/doc/musixdoc/miscellaneous.tex
index 83b62bed6d..7b568bda91 100644
--- a/macros/musixtex/doc/musixdoc/miscellaneous.tex
+++ b/macros/musixtex/doc/musixdoc/miscellaneous.tex
@@ -349,7 +349,7 @@ the place it is entered, while adding no space:
\end{music}
- \subsection{Arpeggios}
+ \subsection{Arpeggios}\index{arpeggios}
\ital{Arpeggios} (i.e.~~~\arpeggio{-2}3) can be coded with the macro
\keyindex{arpeggio}\pitchp\itbrace{m}
where $p$ is the pitch of
@@ -361,7 +361,7 @@ Its variant \keyindex{larpeggio} sets the arpeggio symbol roughly
one note head width to the left of the default position, and is intended to
avoid collision with single accidentals on chord notes.
- \subsection{Arbitrary length trills}
+ \subsection{Arbitrary length trills}\index{arbitrary length trills}
There are two styles of arbitrary length trills\index{trills}, each with two
variants.
For a trill with preassigned length, use \keyindex{trille}\pitchp\itbrace{l}
@@ -423,7 +423,7 @@ whose coding is
\end{verbatim}\end{quote}
- \subsection{Tremolos}\label{tremolos}
+ \subsection{Tremolos}\label{tremolos}\index{tremolos}
The command \keyindex{trml}\verb|{|$p$\verb|}|~is used to indicate that the immediately
following
diff --git a/macros/musixtex/doc/musixdoc/settingup.tex b/macros/musixtex/doc/musixdoc/settingup.tex
index 5de88fc3e6..17b8697848 100644
--- a/macros/musixtex/doc/musixdoc/settingup.tex
+++ b/macros/musixtex/doc/musixdoc/settingup.tex
@@ -68,7 +68,7 @@ or \verb|\relax|.
\section{Usual setup commands}\label{whatspecify}
-\subsection{Music size}
+\subsection{Music size}\index{music size}
The first decision is what size type to use. \musixtex\ offers four sizes:
``small'' \mbox{(\texttt{16pt}-high staves),} ``normal'' (\texttt{20pt}),\index{sizes} ``large''
@@ -79,7 +79,7 @@ enter \keyindex{smallmusicsize}, \keyindex{largemusicsize}, or
desired staff size but many other related sizes such as note heads, ornaments,
stem lengths, etc.
-\subsection{Number of instruments}
+\subsection{Number of instruments}\index{number of instruments}
The command \keyindex{instrumentnumber}\onen~defines the
number of instruments to be $n$. If not entered, the default is $1$. This number is used in loops
@@ -88,7 +88,7 @@ set key signatures, set meters, etc., so if it differs from $1$ it must be expli
defined before any further commands. The default maximum number of instruments is $6$
but this can be increased by using \keyindex{setmaxinstruments}\onen.
-\subsection{Number of staves per instrument}
+\subsection{Number of staves per instrument}\index{number of staves per instrument}
An instrument may have one or more staves (e.g.,~a piano would normally have 2 staves).
The differences between one
@@ -111,7 +111,7 @@ number of the instrument. In \musixtex, instruments are numbered
So for example \verb|setstaffs32|
assigns two staves to the third instrument from the bottom.
-\subsection{Clefs for each staff}
+\subsection{Clefs for each staff}\index{clefs for each staff}
The default clef for every staff is the \ital{treble} clef. To assign
any other clef, the command is
@@ -141,7 +141,7 @@ could be specified by
Treble and bass clefs with the digit $8$ above or below are also possible; see
Section~\ref{treblelowoct}.
-\subsection{Key signatures}
+\subsection{Key signatures}\index{key signatures}
To set a common key signature for all instruments, use
\keyindex{generalsignature}\verb|{|$s$\verb|}|,
@@ -153,7 +153,7 @@ the common key signature for instrument $n$, use
\keyindex{setsign}\verb|{|$n$\verb|}{|$s$\verb|}|. Note that differing
key signatures cannot be assigned to different staves of the same instrument.
-\subsection{Meters}
+\subsection{Meters}\index{meters}
A common \itxem{meter} for all staves can be specified by
\keyindex{generalmeter}\verb|{|$m$\verb|}|,\label{generalmeter}
@@ -219,7 +219,7 @@ sets the meter to 12/8 for the first staff of the third instrument, and
\ital{alla breve} for the second staff.
-\subsection{Instrument names}
+\subsection{Instrument names}\index{instrument names}
To set an \itxem{instrument name}, use
\keyindex{setname}\verb|{|$n$\verb|}{|\ital{name of the instrument}\verb|}|.
diff --git a/macros/musixtex/dvips/psslurs.pro b/macros/musixtex/dvips/psslurs.pro
index b1ba95253d..b18ba9bd3a 100644
--- a/macros/musixtex/dvips/psslurs.pro
+++ b/macros/musixtex/dvips/psslurs.pro
@@ -219,8 +219,8 @@ slur@Dict begin
/y1 ED
/x1 ED
gsave
- 1 psxAR ceiling setlinewidth % line thickness: this results
- 1 setlinecap % to exactly 2 pixels in 300 dpi
+ 2.5 psxAR ceiling setlinewidth % line thickness: this results
+ 1 setlinecap % to exactly 2.5 pixels in 300 dpi
1 setlinejoin
x2 y2 10 psxAR add moveto % the 10's specify wideness of the
x1 y1 lineto % open end of the crescendo,
@@ -236,7 +236,7 @@ slur@Dict begin
/y1 ED
/x1 ED
gsave
- 1 psxAR ceiling setlinewidth
+ 2.5 psxAR ceiling setlinewidth
1 setlinecap
1 setlinejoin
x2 y2 11 psxAR add moveto
diff --git a/macros/musixtex/tex/musixmkm.tex b/macros/musixtex/tex/musixmkm.tex
new file mode 100644
index 0000000000..1aca900845
--- /dev/null
+++ b/macros/musixtex/tex/musixmkm.tex
@@ -0,0 +1,54 @@
+%
+% This file is part of MusiXTeX
+%
+% MusiXTeX is free software; you can redistribute it and/or modify
+% it under the terms of the GNU General Public License as published by
+% the Free Software Foundation; either version 2, or (at your option)
+% any later version.
+%
+% MusiXTeX is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+% GNU General Public License for more details.
+%
+% You should have received a copy of the GNU General Public License
+% along with MusiXTeX; see the file COPYING. If not, write to
+% the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
+% Boston, MA 02111-1307, USA.
+%
+\immediate\write16{MusiXMaKaM v.001\space<2022-12-25>}%
+
+\edef\catcodeat{\the\catcode`\@}\catcode`\@=11
+\catcodesmusic
+
+
+\font\fetaeleven=feta20 scaled \magstephalf
+\font\fetathirteen=feta20 scaled \magstep1
+\font\fetasixteen=feta20 scaled \magstep2
+\font\fetatwenty=feta20 scaled \magstep3
+\font\fetatwentyfour=feta20 scaled \magstep4
+\font\fetatwentynine=feta20 scaled \magstep5
+
+\let\fetanorfont\fetatwenty
+\def\fetachar{\fetafont\char}
+
+
+\def\writ@ka{\pl@base\raise\y@i\llap{\fetachar\n@v\kern\accshift}}
+\def\set@ka{\let\@Ti=\writ@ka}
+
+\def\shtanini#1{\set@ka \n@v30 \check@staff \inhgetn@i#1\relax\expandafter\@Ti\fi}
+\def\shbuyukmucenneb#1{\set@ka \n@v26 \check@staff \inhgetn@i#1\relax\expandafter\@Ti\fi}
+\def\shkucuk#1{\set@ka \n@v27 \check@staff \inhgetn@i#1\relax\expandafter\@Ti\fi}
+\def\shbakiye#1{\set@ka \n@v20 \check@staff \inhgetn@i#1\relax\expandafter\@Ti\fi}
+\def\shkoma#1{\set@ka \n@v25 \check@staff \inhgetn@i#1\relax\expandafter\@Ti\fi}
+\def\flkoma#1{\set@ka \n@v45 \check@staff \inhgetn@i#1\relax\expandafter\@Ti\fi}
+\def\flbakiye#1{\set@ka \n@v42 \check@staff \inhgetn@i#1\relax\expandafter\@Ti\fi}
+\def\flkucuk#1{\set@ka \n@v37 \check@staff \inhgetn@i#1\relax\expandafter\@Ti\fi}
+\def\flbuyukmucenneb#1{\set@ka \n@v43 \check@staff \inhgetn@i#1\relax\expandafter\@Ti\fi}
+\def\fltanini#1{\set@ka \n@v47 \check@staff \inhgetn@i#1\relax\expandafter\@Ti\fi}
+
+\let\fetafont\fetanorfont
+
+\endcatcodesmusic
+\catcode`\@=\catcodeat
+\endinput
diff --git a/macros/musixtex/tex/musixps.tex b/macros/musixtex/tex/musixps.tex
index 9ab8b0ce3f..7bff890330 100644
--- a/macros/musixtex/tex/musixps.tex
+++ b/macros/musixtex/tex/musixps.tex
@@ -2,6 +2,7 @@
% Coded by Stanislav Kneifl
% RDT added \psRslurskip \iRslur \tRslur \psRtieskip \tRtie \psLtieskip \tLtie 2019/06/17
% RDT added \iRtieu \iRtied 2020/09/07
+% RDT modified /DC to produce thicker hairpins 2022/12/29
\ifx\undefined\startpiece\errmessage{Input musixtex.tex before musixps.tex}\fi
\ifx\undefined\liftcresc\else\endinput\fi
diff --git a/macros/musixtex/tex/musixtex.tex b/macros/musixtex/tex/musixtex.tex
index 7dda85bd90..06333281b9 100644
--- a/macros/musixtex/tex/musixtex.tex
+++ b/macros/musixtex/tex/musixtex.tex
@@ -25,15 +25,27 @@
\def\mufl@x{0.83}%
\def\mxmajorvernumber{1}
-\def\mxminorvernumber{34}
+\def\mxminorvernumber{36}
\def\mxvernumber{\mxmajorvernumber\mxminorvernumber}% make it possible to compare with \ifnum
\def\mxversuffix{}%
\edef\mxversion{\mxmajorvernumber.\mxminorvernumber\mxversuffix}
-\def\mxdate{2021-07-24}
+\def\mxdate{2023-01-11}
\immediate\write16{MusiXTeX(c) \mxversion\space<\mxdate>}%
\everyjob{\immediate\write16{MusiXTeX(c) \mxversion\space<\mxdate>}}%
+% version 1.36
+%
+% Support for Turkish classical music accidentalsi; see musixmkm.tex.
+% Re-define \hlthick to produce thicker ledger lines.
+% Provide thinner accidentals; see musixthacc.tex.
+% Thicker Postscript hairpins.
+
+% version 1.35
+%
+% This release includes a handwriting font from MuseScore and an extension
+% library musixjt.tex to support it.
+
% version 1.34
%
% redefine \tabfnt... commands to allow re-definition in musixftab.tex
@@ -1643,6 +1655,7 @@
\newdimen\b@amthick % half beamthickness
\newdimen\Interligne% de la base d'une ligne a l'autre
\newdimen\Internote % la moitie de \Interligne
+
\let\internote\Internote
\def\musixchar{\musixfont\char}
\def\keychar{\musickeyfont\char}
@@ -1651,22 +1664,27 @@
\def\set@Largenotesize{\let\musixfont\musicLargefont
\let\xgregfont\xgregLargefont
+ \let\fetafont\fetaLargefont % RDT 1.36
\b@amthick.3456\Interligne \interbeam1.08\Interligne }
\def\set@largenotesize{\let\musixfont\musiclargefont
\let\xgregfont\xgreglargefont
+ \let\fetafont\fetalargefont % RDT 1.36
\b@amthick.288\Interligne \interbeam.9\Interligne }
\def\set@normalnotesize{\let\musixfont\musicnorfont
\let\xgregfont\xgregnorfont
+ \let\fetafont\fetanorfont % RDT 1.36
\b@amthick.24\Interligne \interbeam\p@seven5\Interligne }
\def\set@smallnotesize{\let\musixfont\musicsmallfont
\let\xgregfont\xgregsmallfont
+ \let\fetafont\fetasmallfont % RDT 1.36
\b@amthick\p@ne92\Interligne \interbeam.6\Interligne }
\def\set@tinynotesize{\let\musixfont\musictinyfont
\let\xgregfont\xgregtinyfont
+ \let\fetafont\fetatinyfont % RDT 1.36
\b@amthick\p@ne536\Interligne \interbeam.48\Interligne }
\def\normalnotesize{\set@normalnotesize\comput@specifics
@@ -1742,7 +1760,8 @@
\newskip\big@spc
\newdimen\lthick \lthick=.4pt
-\def\hlthick{\h@lf\lthick}
+% \def\hlthick{\h@lf\lthick}
+\def\hlthick{0.4pt} % 1.36 RDT
%%%
@@ -1767,6 +1786,11 @@
\let\xgregnorfont\xgregsixteen
\let\xgregsmallfont\xgregthirteen
\let\xgregtinyfont\xgregeleven
+ \let\fetaLargefont\fetatwentyfour % 1.36 RDT
+ \let\fetalargefont\fetatwenty
+ \let\fetanorfont\fetasixteen
+ \let\fetasmallfont\fetathirteen
+ \let\fetatinyfont\fetaeleven
\let\slurd\slurdsixteen \let\sluru\slurusixteen
\let\hslurd\hslurdsixteen \let\hsluru\hslurusixteen
\let\meternorfont\tenbf \let\metersmallfont\eightbf % version 1.16 RDT
@@ -1780,7 +1804,7 @@
\else\ifdim\internote<1.19\Internote \smalltype\it
\else\ifdim\internote<1.43\Internote \Smalltype\it
\else\normtype\it\fi\fi\fi}%
- \let\tabnorfnt\tabfntsixteen \let\tablargefnt\tabfnttwenty % 1.34 RDT
+ \let\tabnorfnt\tabfntsixteen \let\tablargefnt\tabfnttwenty % 1.34 RDT
\let\tabLargefnt\tabfnttwentyfour \let\tabsmallfnt\tabfntthirteen
\let\tabnorcleffnt\eightdc \let\tablargecleffnt\tendc
\let\tabLargecleffnt\twelvedc \let\tabsmallcleffnt\sixdc
@@ -1799,6 +1823,11 @@
\let\xgregnorfont\xgregtwentyfour
\let\xgregsmallfont\xgregtwenty
\let\xgregtinyfont\xgregsixteen
+ \let\fetaLargefont\fetatwentynine % 1.36 RDT
+ \let\fetalargefont\fetatwentynine
+ \let\fetanorfont\fetatwentyfour
+ \let\fetasmallfont\fetatwenty
+ \let\fetatinyfont\fetasixteen
\let\sluru\slurutwenty \let\slurd\slurdtwenty
\let\hsluru\hslurutwenty \let\hslurd\hslurdtwenty
\let\meternorfont\frtbf \let\metersmallfont\twelvebf % version 1.18 RDT
@@ -1831,6 +1860,11 @@
\let\xgregnorfont\xgregtwentynine
\let\xgregsmallfont\xgregtwentyfour
\let\xgregtinyfont\xgregtwenty
+ \let\fetaLargefont\fetatwentynine % 1.36 RDT
+ \let\fetalargefont\fetatwentynine
+ \let\fetanorfont\fetatwentynine
+ \let\fetasmallfont\fetatwentyfour
+ \let\fetatinyfont\fetatwenty
\let\sluru\slurutwenty \let\slurd\slurdtwenty
\let\hsluru\hslurutwenty \let\hslurd\hslurdtwenty
\let\slurud\slurutwentyd \let\slurdd\slurdtwentyd % +ickd
@@ -1871,6 +1905,11 @@
\let\xgregnorfont\xgregtwenty
\let\xgregsmallfont\xgregsixteen
\let\xgregtinyfont\xgregthirteen
+ \let\fetalargefont\fetatwentyfour % 1.36 RDT
+ \let\fetaLargefont\fetatwentynine
+ \let\fetanorfont\fetatwenty
+ \let\fetasmallfont\fetasixteen
+ \let\fetatinyfont\fetathirteen
\let\sluru\slurutwenty \let\slurd\slurdtwenty
\let\hsluru\hslurutwenty \let\hslurd\hslurdtwenty
\let\meternorfont\twelvebf \let\metersmallfont\tenbf % version 1.18 RDT
diff --git a/macros/musixtex/tex/musixthacc.tex b/macros/musixtex/tex/musixthacc.tex
new file mode 100644
index 0000000000..b20ed567cb
--- /dev/null
+++ b/macros/musixtex/tex/musixthacc.tex
@@ -0,0 +1,49 @@
+%
+% This file is part of MusiXTeX
+%
+% MusiXTeX is free software; you can redistribute it and/or modify
+% it under the terms of the GNU General Public License as published by
+% the Free Software Foundation; either version 2, or (at your option)
+% any later version.
+%
+% MusiXTeX is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+% GNU General Public License for more details.
+%
+% You should have received a copy of the GNU General Public License
+% along with MusiXTeX; see the file COPYING. If not, write to
+% the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
+% Boston, MA 02111-1307, USA.
+%
+\immediate\write16{MusiXTHinACCidentals v.001\space<2022-12-29>}%
+
+\edef\catcodeat{\the\catcode`\@}\catcode`\@=11
+\catcodesmusic
+
+
+\font\fetaeleven=feta20 scaled \magstephalf
+\font\fetathirteen=feta20 scaled \magstep1
+\font\fetasixteen=feta20 scaled \magstep2
+\font\fetatwenty=feta20 scaled \magstep3
+\font\fetatwentyfour=feta20 scaled \magstep4
+\font\fetatwentynine=feta20 scaled \magstep5
+
+\let\fetanorfont\fetatwenty
+\def\fetachar{\fetafont\char}
+
+
+\def\writ@ka{\pl@base\raise\y@i\llap{\fetachar\n@v\kern\accshift}}
+\def\set@ka{\let\@Ti=\writ@ka}
+
+\def\thdsh#1{\set@ka \n@v30 \check@staff \inhgetn@i#1\relax\expandafter\@Ti\fi}
+\def\thsh#1{\set@ka \n@v20 \check@staff \inhgetn@i#1\relax\expandafter\@Ti\fi}
+\def\thna#1{\set@ka \n@v32 \check@staff \inhgetn@i#1\relax\expandafter\@Ti\fi}
+\def\thfl#1{\set@ka \n@v37 \check@staff \inhgetn@i#1\relax\expandafter\@Ti\fi}
+\def\thdfl#1{\set@ka \n@v47 \check@staff \inhgetn@i#1\relax\expandafter\@Ti\fi}
+
+\let\fetafont\fetanorfont
+
+\endcatcodesmusic
+\catcode`\@=\catcodeat
+\endinput
diff --git a/macros/xetex/plain/unimath-plain-xetex/doc/unimath-plain-xetex-doc.pdf b/macros/xetex/plain/unimath-plain-xetex/doc/unimath-plain-xetex-doc.pdf
index 725f5e6fb1..98e89d1aaf 100644
--- a/macros/xetex/plain/unimath-plain-xetex/doc/unimath-plain-xetex-doc.pdf
+++ b/macros/xetex/plain/unimath-plain-xetex/doc/unimath-plain-xetex-doc.pdf
Binary files differ
diff --git a/macros/xetex/plain/unimath-plain-xetex/doc/unimath-plain-xetex-doc.tex b/macros/xetex/plain/unimath-plain-xetex/doc/unimath-plain-xetex-doc.tex
index e14f943981..d89096a6e1 100644
--- a/macros/xetex/plain/unimath-plain-xetex/doc/unimath-plain-xetex-doc.tex
+++ b/macros/xetex/plain/unimath-plain-xetex/doc/unimath-plain-xetex-doc.tex
@@ -112,7 +112,7 @@
\centerline{Zhang Tingxuan}
\medskip
-\centerline{2023/01/03\quad Version 0.2}
+\centerline{2023/01/11\quad Version 0.2a}
\biggskip
\begingroup\parskip0pt
diff --git a/macros/xetex/plain/unimath-plain-xetex/tex/unimath-plain-xetex.tex b/macros/xetex/plain/unimath-plain-xetex/tex/unimath-plain-xetex.tex
index 47da54ce41..c5732c0e58 100644
--- a/macros/xetex/plain/unimath-plain-xetex/tex/unimath-plain-xetex.tex
+++ b/macros/xetex/plain/unimath-plain-xetex/tex/unimath-plain-xetex.tex
@@ -473,6 +473,14 @@
\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi
}
\input unicode-math-table
+
+% patch the delimiters
+\Udelcode `\< = \delimiterfam "27E8
+\Udelcode `\> = \delimiterfam "27E9
+% According to xetexref, the math class of a delimiter should be 4 or 5,
+% but here we use 0 instead.
+\def\|{\Udelimiter 0 \delimiterfam "2016 }
+
% deal with `!'
\Umathcode `\! = 5 \ordfam "0021
\Umathchardef \mathexclam = 4 \ordfam "0021