diffcoeff (4dec18)

git-svn-id: svn://tug.org/texlive/trunk@49317 c570f23f-e606-0410-a88d-b1316a301751

2 files changed, 724 insertions, 629 deletions

diff --git a/Master/texmf-dist/tex/latex/diffcoeff/diffcoeff-doc.def b/Master/texmf-dist/tex/latex/diffcoeff/diffcoeff-doc.def
new file mode 100644
index 00000000000..34a03b2c7f2
--- /dev/null
+++ b/Master/texmf-dist/tex/latex/diffcoeff/diffcoeff-doc.def
@@ -0,0 +1,121 @@
+% file `diffcoeff.def'
+% variant forms of derivative
+% 2018-11-12
+% Andrew Parsloe ajparsloe@gmail.com
+%
+% paren, up, Up, wrapall, nabla, left, svrule
+% pvrule, padrift, psqbra, pDelta, pleft, ptxt, pscr
+%%%%%%%%%% 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      ,
+    /-op-order-sep = 0 mu
+  }
+
+\diffdef { Up } 
+  {
+    op-symbol      = \mathrm{D},
+    op-order-sep   = 0 mu      ,
+    /-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,
+    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    ,
+    /-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, scriptstyle
+\diffdef { pscr } 
+  {
+    op-symbol      = \partial,
+    op-order-sep   = 0 mu    ,
+    denom-term-sep = 0 mu    ,
+    left-delim     = \left ( ,
+    right-delim    = \right ),
+    subscr-nudge   = -3 mu
+  }
+
diff --git a/Master/texmf-dist/tex/latex/diffcoeff/diffcoeff.sty b/Master/texmf-dist/tex/latex/diffcoeff/diffcoeff.sty
index 47dd6b869a7..2a5e48a9582 100644
--- a/Master/texmf-dist/tex/latex/diffcoeff/diffcoeff.sty
+++ b/Master/texmf-dist/tex/latex/diffcoeff/diffcoeff.sty
@@ -1,705 +1,679 @@
 % This is file `diffcoeff.sty'.
 %
-% This program 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 of the License, or (at your
-% option) any later version.
+% 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}
-\ProvidesExplPackage{diffcoeff} {2018/10/25} {1.1} 
-  {Write differential coefficients easily.}
-
+\RequirePackage{xparse,l3keys2e,xtemplate}
+\ProvidesExplPackage {diffcoeff} {2018/12/02} {2} 
+  {Write differential coefficients consistently and easily.}
+%
+\keys_define:nn { diffcoeff }
+  { 
+    ISO    .bool_gset:N = \g__diffcoeff_ISO_bool,
+    def-file .tl_gset:N = \g__diffcoeff_def_tl  ,
+    def-file .initial:n = diffcoeff             ,
+    def-file .default:n = diffcoeff
+  }
+\ProcessKeysPackageOptions { diffcoeff }
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\cs_generate_variant:Nn \tl_if_eq:nnF { no }
-\cs_generate_variant:Nn \tl_if_eq:nnT { no }
-\cs_generate_variant:Nn \tl_if_in:NnTF { NV }
-\cs_generate_variant:Nn \prop_pop:NnNT { NV }
-
+\cs_generate_variant:Nn \tl_if_eq:nnTF { nV }
+
+\tl_new:N \l__diffcoeff_op_tl
+\tl_new:N \l__diffcoeff_op_alt_tl
+\tl_new:N \l__diffcoeff_ldelim_tl
+\tl_new:N \l__diffcoeff_rdelim_tl
+\tl_new:N \l__diffcoeff_oporder_tl
+\tl_new:N \l__diffcoeff_differentiand_tl
+\tl_new:N \l__diffcoeff_type_tl
+\tl_new:N \l__diffcoeff_order_spec_tl
+\tl_new:N \l__diffcoeff_denom_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_new:N \l__diffcoeff_trailing_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
+
+\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
+
+\muskip_new:N \l__diffcoeff_oporder_muskip
+\muskip_new:N \l__diffcoeff_opnudge_muskip
+\muskip_new:N \l__diffcoeff_elbowrm_muskip
+\muskip_new:N \l__diffcoeff_subnudge_muskip
+\muskip_new:N \l__diffcoeff_varsep_muskip
+\muskip_new:N \l_tmpc_muskip
+\muskip_new:N \l_tmpd_muskip
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% variables
-\tl_new:N \g_diffco_d_ldelim_tl
-\tl_new:N \g_diffco_d_rdelim_tl
-\tl_new:N \g_diffco_p_ldelim_tl
-\tl_new:N \g_diffco_p_rdelim_tl
-
-\tl_new:N \l__diffco_rentiand_tl 
-\tl_new:N \l__diffco_phantom_tl
-\tl_new:N \g_diffco_dop_tl
-\tl_new:N \l__diffco_denom_tl
-\tl_new:N \l__diffco_coeff_tl
-
-\clist_new:N \l__diffco_order_clist
-\tl_new:N \l__diffco_order_spec_tl
-
-\bool_new:N \g__diffco_erent_shape_bool
-\bool_new:N \l__diffco_no_parens_bool
-\bool_new:N \l__diffco_override_bool
-\bool_new:N \l__diffco_vars_noted_bool
+% Derivatives
+% #1 order spec(seqvar)
+% #2 order override(tlvar)
+% #3 differentiand(tlvar)
+% #4 denominator(seqvar)
+% #5 subscript(tlvar)
+\DeclareObjectType { derivative } { 5 }
+
+% defaults: ordinary deriv. values
+\DeclareTemplateInterface { derivative } { DERIV } { 5 }
+  {
+    op-symbol        : tokenlist = d       ,
+    op-symbol-alt    : tokenlist = \KeyValue { op-symbol },
+    op-order-sep     : muskip    = 1 mu    ,
+    /-op-order-sep   : muskip    = 1 mu    ,
+    *-op-left        : boolean   = false   ,
+    *-italic-nudge   : muskip    = 3 mu    ,
+    */-op-wrap       : boolean   = true    ,
+    long-var-wrap    : choice { dv, d(v), (dv) } 
+                                  = d(v)   ,
+    denom-term-sep   : muskip    = 2 mu    ,
+    /-denom-term-sep : muskip    = 1 mu    ,
+    left-delim       : tokenlist = \left . ,
+    right-delim      : tokenlist = \right |,
+    elbowroom        : muskip    = 0 mu    ,
+    subscr-nudge     : muskip    = 0 mu    ,
+    /-left-delim     : tokenlist = (       ,
+    /-right-delim    : tokenlist = )       ,
+    /-elbowroom      : muskip    = 0 mu    ,
+    /-subscr-nudge   : muskip    = 0 mu 
+  }
  
-\tl_new:N \l__diffco_orders_in_tl
-\tl_new:N \l__diffco_order_tl
-
-\tl_new:N \l__diffco_curr_tok_tl
-\tl_new:N \l__diffco_curr_term_tl
-
-\int_new:N \l__diffco_curr_tok_int
-\int_new:N \l__diffco_curr_state_int
-
-\prop_new:N \l__diffco_vars_prop
-\tl_new:N \l__diffco_vars_tl
-\clist_new:N \l__diffco_vars_clist
-
-\tl_new:N \l__diffco_curr_var_tl
-\tl_new:N \l__diffco_nos_tl
-\tl_new:N \l__diffco_nos_aux_tl
-
-\tl_new:N \l__diffco_alg_tl
-\tl_new:N  \l__diffco_alg_aux_tl
-\tl_new:N \l__diffco_alg_expr_tl
-
-\tl_const:Nn \c__diffco_digits_tl { 1234567890 }
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\keys_define:nn { diffcoeff }
+\DeclareTemplateCode { derivative } { DERIV } { 5 }
   {
-  roman .bool_gset:N  = \g_diffco_roman_bool, 
-  roman .default:n = { false }, 
-  d-delims .code:n = { 
-                      \tl_gset:Nx \g_diffco_d_ldelim_tl { \left \use_i:nn #1 }
-                      \tl_gset:Nx \g_diffco_d_rdelim_tl 
-                          { \right \use_ii:nn #1 }
-                      },
-  d-delims .default:n = { .| },
-  p-delims .code:n = { 
-                      \tl_gset:Nx \g_diffco_p_ldelim_tl { \left \use_i:nn #1 }
-                      \tl_gset:Nx \g_diffco_p_rdelim_tl 
-                          { \right \use_ii:nn #1 }
-                      },
-  p-delims .default:n = { () },
-  d-nudge .code:n = { \tl_gset:Nn \g_diffco_d_nudge_tl { \mskip #1 mu } },
-  d-nudge .default:n = { 0 },
-  p-nudge .code:n = { \tl_gset:Nn \g_diffco_p_nudge_tl { \mskip #1 mu } },
-  p-nudge .default:n = { -6 },
-  sep .code:n = { \tl_gset:Nn \g_diffco_sep_tl { \mskip #1 mu } },
-  sep .default:n = { 2 },
-  d-sep .code:n = { \tl_gset:Nn \g_diffco_d_sep_tl { \mskip #1 mu } },
-  d-sep .default:n = { 1 },
-  p-sep .code:n = { \tl_gset:Nn \g_diffco_p_sep_tl { \mskip #1 mu } },
-  p-sep .default:n = { 1 },
-  }  
-
-\DeclareDocumentCommand \diffset { o }
+    op-symbol        = \l__diffcoeff_op_tl          ,
+    op-symbol-alt    = \l__diffcoeff_op_alt_tl      ,
+    op-order-sep     = \l__diffcoeff_oporder_muskip ,
+    /-op-order-sep   = \l_tmpa_muskip               ,
+    *-op-left        = \l__diffcoeff_op_left_bool   ,
+    *-italic-nudge   = \l__diffcoeff_opnudge_muskip ,
+    */-op-wrap       = \l__diffcoeff_opwrap_bool    ,
+    long-var-wrap    = {
+                  dv = \cs_set_eq:NN \__diffcoeff_wrap_longvars:NN 
+                                \__diffcoeff_wrap_none:NN,
+                d(v) = \cs_set_eq:NN \__diffcoeff_wrap_longvars:NN 
+                                \__diffcoeff_wrap_var:NN ,
+                (dv) = \cs_set_eq:NN \__diffcoeff_wrap_longvars:NN 
+                                \__diffcoeff_wrap_dvar:NN,
+             unknown = \cs_set_eq:NN \__diffcoeff_wrap_longvars:NN 
+                                \__diffcoeff_wrap_var:NN 
+                       }                            ,
+    denom-term-sep   = \l__diffcoeff_varsep_muskip  ,
+    /-denom-term-sep = \l_tmpb_muskip               ,
+    left-delim       = \l__diffcoeff_ldelim_tl      ,
+    right-delim      = \l__diffcoeff_rdelim_tl      ,
+    elbowroom        = \l__diffcoeff_elbowrm_muskip ,
+    subscr-nudge     = \l__diffcoeff_subnudge_muskip,
+    /-left-delim     = \l_tmpa_tl                   ,
+    /-right-delim    = \l_tmpb_tl                   ,
+    /-elbowroom      = \l_tmpc_muskip               ,
+    /-subscr-nudge   = \l_tmpd_muskip
+  }
+  { 
+    \AssignTemplateKeys
+    \int_compare:nNnT { \l__diffcoeff_format_int } > { 1 }
+      { \__diffcoeff_slash_vals: }
+    \__diffcoeff_build:NNNNN #1#2#3#4#5
+  }
+%%%%%%%%%%
+\cs_new:Npn \__diffcoeff_slash_vals:
   {
-  \IfValueTF { #1 }
-    { 
-    \clist_if_empty:nTF { #1 }
-      { \keys_set:nn { diffcoeff } { roman,d-delims,p-delims,
-      d-nudge,p-nudge,sep,d-sep,p-sep } }
-      { \keys_set:nn { diffcoeff } { #1 } }
-    }
-    { 
-    \keys_set:nn { diffcoeff } { roman,d-delims,p-delims,
-    d-nudge,p-nudge,sep,d-sep,p-sep }  
-    }
+    \muskip_set:Nn \l__diffcoeff_oporder_muskip  \l_tmpa_muskip
+    \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_tmpa_tl
+    \tl_set:NV \l__diffcoeff_rdelim_tl \l_tmpb_tl
   }
-
-% now set the defaults    
-\diffset  
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-% Ordinary differential coefficient
-
-% #1 = the order
-% #2 =  differentiand
-% #3 = the variable of differentiation
-%  #4 = point of evaluation
-
-\NewDocumentCommand \diff{ s o m t/ m g } 
+\cs_new:Npn \__diffcoeff_build:NNNNN #1#2#3#4#5
+  { 
+    \bool_if:NF \l__diffcoeff_opwrap_bool 
+      { \int_set:Nn \l__diffcoeff_format_int { 4 } }
+    \exp_args:NV\tl_if_novalue:nF #5 
+      { \l__diffcoeff_ldelim_tl \mkern \l__diffcoeff_elbowrm_muskip }
+    \bool_if:NTF \l__diffcoeff_single_var_bool
+      { \__diffcoeff_single:NNN #2 #3 #4 }
+      { 
+        \seq_mapthread_function:NNN #1 #4 \__diffcoeff_map_orders:nn 
+        \__diffcoeff_mixed:NNN #2 #3 \l__diffcoeff_denom_seq 
+      }
+    \exp_args:NV\tl_if_novalue:nF #5
+      { 
+        \mkern \l__diffcoeff_elbowrm_muskip \l__diffcoeff_rdelim_tl
+        \exp_args:NV\tl_if_empty:nF #5
+          {
+            \c_math_subscript_token
+            { \mskip \l__diffcoeff_subnudge_muskip #5 }
+          }
+      }
+  }
+%%%%%%%%%%%%%%%%%%%%
+% (ptl) form denom from #1 orders, & #2 vars, seqs
+\cs_new:Npn \__diffcoeff_map_orders:nn #1#2
   {
-  \group_begin:
-  % roman or italic?
-  \bool_if:NF \g__diffco_erent_shape_bool
-    { \__diffco_shape:N d }
-  
-  \IfValueTF { #2 } 
-    { 
-    \tl_set:Nn \l__diffco_order_tl { ^{ \g_diffco_d_sep_tl #2 } }
-    \int_compare:nNnTF { \tl_count:n { #5 } } > { \c_one }
-      { \tl_set:Nn \l__diffco_denom_tl { (#5)^{ #2 } } }
-      { \tl_set:Nn \l__diffco_denom_tl { #5^{ #2 } } }
-    }
-    { 
-    \tl_set:Nn \l__diffco_order_tl { }
-    \tl_if_in:nnTF { #5 } { ^ }
-      { \tl_set:Nn \l__diffco_denom_tl { (#5) } }
-      { \tl_set:Nn \l__diffco_denom_tl { #5 } } 
-    }
-  
-  % position of differentiand: appended (star) or in numerator (no star);
-  % slash or fraction?
-  \IfBooleanTF { #1 }
-    { % differentiand follows diff coeff 
-    \__diffco_phantom:n { #3 }
-    \tl_set:Nn \l__diffco_coeff_tl
+    \tl_if_eq:nnTF { #1 } { 1 }
+      { \seq_put_right:Nn \l__diffcoeff_denom_seq { \l__diffcoeff_op_alt_tl #2 } }
       {
-      \IfBooleanTF { #4 }
-        { % slash (therefore no phantom)
-        (\g_diffco_dop_tl \l__diffco_order_tl 
-        /
-        \g_diffco_dop_tl \l__diffco_denom_tl )
-        \l__diffco_rentiand_tl
-        }
-        { % frac
-        \frac { \g_diffco_dop_tl \l__diffco_order_tl \l__diffco_phantom_tl }
-            { \g_diffco_dop_tl \l__diffco_denom_tl } \l__diffco_rentiand_tl
-        }
+        \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:Nx \l__diffcoeff_denom_seq 
+                { \__diffcoeff_wrap_longvars:NN { #1 } { #2 } } 
+          }
       }
-    }
-    { % differentiand in numerator
-    \tl_set:Nn \l__diffco_coeff_tl
-      {
-      \IfBooleanTF { #4 }
-        { % slash
-        \g_diffco_dop_tl \l__diffco_order_tl #3
-        /
-        \g_diffco_dop_tl \l__diffco_denom_tl 
-        }
-        { % frac
-        \frac { \g_diffco_dop_tl \l__diffco_order_tl #3  }
-          { \g_diffco_dop_tl \l__diffco_denom_tl }
-        }
+  }
+% #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_differentiand_tl
+        { \__diffcoeff_denom_single:NN #1 #3 }
+  }
+% #1 total order
+% #2 differentiand
+% #3 denominator seq
+\cs_new:Npn \__diffcoeff_mixed:NNN #1#2#3
+  {
+    \__diffcoeff_numer:N #1
+    \__diffcoeff_form_deriv:NNn 
+        \l__diffcoeff_oporder_tl
+        \l__diffcoeff_differentiand_tl
+        { \seq_use:Nn #3 { \mskip \l__diffcoeff_varsep_muskip } }
+  }
+% #1(tl) total order
+\cs_new: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 } 
       }
-    }
-  % pt of eval
-  \IfNoValueTF { #6 } 
-    { 
-    \l__diffco_coeff_tl
-    }
-    { % trailing arg: pt of eval.
-    \tl_if_empty:nTF { #6 }
+      { \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
       { 
-      \l__diffco_coeff_tl
+        \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:Npn \__diffcoeff_denom_single:NN #1#2
+  { 
+    \tl_if_eq:nVTF { 1 } #1 
+      { \l__diffcoeff_op_alt_tl #2 }
       {
-      \g_diffco_d_ldelim_tl \l__diffco_coeff_tl \g_diffco_d_rdelim_tl 
-      \c_math_subscript_token { \g_diffco_d_nudge_tl #6 }
+        \int_compare:nNnTF { \tl_count:N #2 } = { 1 }
+          { \l__diffcoeff_op_alt_tl #2^{ #1 } }
+          { \__diffcoeff_wrap_longvars:NN #1 #2 }
       }
-    }
-  \group_end:  
-  }  
-
-\NewDocumentCommand \Diff { o m m g }
-  {
-  \group_begin:
-  \__diffco_shape:N D 
-  \bool_gset_true:N \g__diffco_erent_shape_bool
-  \diff[#1]{#2}{#3}{#4}
-  \bool_gset_false:N \g__diffco_erent_shape_bool
-  \group_end:
-  }
-  
-\NewDocumentCommand \diffd { o m m g } 
-  {
-  \group_begin:
-  \__diffco_shape:N \delta
-  \bool_gset_true:N \g__diffco_erent_shape_bool
-  \diff[#1]{#2}{#3}{#4}
-  \bool_gset_false:N \g__diffco_erent_shape_bool
-  \group_end:
-  }
-  
-\NewDocumentCommand \Diffd { o m m g }
-  {
-  \group_begin:
-  \__diffco_shape:N \Delta
-  \bool_gset_true:N \g__diffco_erent_shape_bool
-  \diff[#1]{#2}{#3}{#4}
-  \bool_gset_false:N \g__diffco_erent_shape_bool
-  \group_end:
   }
-    
-\cs_new_nopar:Npn \__diffco_shape:N #1    
-  {
-  \bool_if:NTF \g_diffco_roman_bool
-    { \tl_gset:Nn \g_diffco_dop_tl { \mathrm{ #1} } }
-    { \tl_gset:Nn \g_diffco_dop_tl { #1 } }
-  } 
-%%%%%
-\cs_new:Npn \__diffco_append:nn #1#2
-  {
-  \g_diffco_d_ldelim_tl \l__diffco_coeff_tl \g_diffco_d_rdelim_tl 
-    \c_math_subscript_token { \mskip #1 mu #2 }
-  }
-  
-\cs_new:Npn \__diffco_phantom:n #1
-  {
-  \bool_if:nTF
+\cs_new:Npn \__diffcoeff_wrap_none:NN #1#2
+  { \l__diffcoeff_op_alt_tl #2^{#1} }
+\cs_new:Npn \__diffcoeff_wrap_var:NN #1#2
+  { \l__diffcoeff_op_alt_tl (#2)^{#1} }
+\cs_new:Npn \__diffcoeff_wrap_dvar:NN #1#2
+  { (\l__diffcoeff_op_alt_tl #2)^{#1} }
+
+% #1 op+order; #2 diff'iand; #3 denom
+% 0 frac; 1 frac append; 2 slash ; 3 slash append
+\cs_new:Npn \__diffcoeff_form_deriv:NNn #1#2#3
+  { 
+    \int_case:nn { \l__diffcoeff_format_int }
       {
-        \tl_if_head_eq_meaning_p:nN { #1 } \hfill ||
-        \tl_if_head_eq_meaning_p:nN { #1 } \hfil
+        { 0 } { \frac { #1 #2 } { #3 } }
+        { 1 } { \frac { #1 } { #3 } { #2 } }
+        { 2 } { #1 #2 / #3 }
+        { 3 } { ( #1 / #3 ) { #2 } }
+        { 4 } { #1 / #3 { #2 } }
+      }
+  }
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% 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 }
       }
-      { \l__diffco_phantom_aux:nn #1\q_stop }
       {
-        \bool_if:nTF
-            {
-            \tl_if_head_eq_meaning_p:nN { #1 } \hspace ||
-            \tl_if_head_eq_meaning_p:nN { #1 } \hphantom
-            }
-          { \l__diffco_phantom_aux:nnn #1\q_stop }
-          { \tl_set:Nn \l__diffco_rentiand_tl { #1 } }
+        \IfInstanceExistTF { derivative } { ord.#1 }
+          { \EditInstance { derivative } { ord.#1 } { #2 } } 
+          { 
+            \DeclareInstance { derivative } { ord.#1 } 
+                { DERIV } { #2 } 
+          }
       }
   }
+% superseded relic from version 1
+\NewDocumentCommand \diffset { o } 
+  { \msg_warning:nn { diffcoeff } { obsolete } }
 
-\cs_new:Npn \l__diffco_phantom_aux:nn #1#2\q_stop
+% ordinary
+\DeclareInstance { derivative } { ord } { DERIV } { }
+\bool_if:NTF \g__diffcoeff_ISO_bool
   {
-  \tl_set:Nn \l__diffco_phantom_tl { #1 }
-  \tl_set:Nn \l__diffco_rentiand_tl { #2 }
+    \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} }
   }
-  
-\cs_new:Npn \l__diffco_phantom_aux:nnn #1#2#3\q_stop
+  { \diffdef { D } { op-symbol = D } }
+
+% partial
+\diffdef { p }
   {
-  \tl_set:Nn \l__diffco_phantom_tl { #1 { #2  } }
-  \tl_set:Nn \l__diffco_rentiand_tl { #3 }
+    op-symbol    = \partial ,
+    left-delim   = \left (  ,
+    right-delim  = \right ) ,
+    subscr-nudge = -6 mu
   }
-  
-%%%%%%%%%%%%%%%%%%%%
-% Partial differential coefficient. 
-% #1 (star) = append differentiand boolean
-% #2 = comma list of the orders of diff. in each var.;
-% #3 = order override for the numerator; #4 = differentiand; 
-% #5 slash / boolean; #6 = comma list of vars of diff.; 
-% #7 = list of vars held const.
-\NewDocumentCommand \diffp{ s o o m t/ m g } 
+\NewDocumentCommand \diffp { } { \diff.p. }
+
+\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 variants
+\file_if_exist:nT { \g__diffcoeff_def_tl.def }
+  { \file_input:n { \g__diffcoeff_def_tl.def } }
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% derivative
+% #1(tl)    = name of variant
+% #2(*)     = append differentiand boolean
+% #3(clist) = orders of diff. in each var.
+% #4(tl)    = order override
+% #5(tl)    = differentiand
+% #6 ( / )  = slash boolean
+% #7(clist) = vars of diff. in order
+% #8(tl)    = pt of eval./vars held constant
+% #9(tl)    = #8 for backwards compatibility
+\NewDocumentCommand \diff{ d.. s O{1} o m t/ m !O{#9} g } 
   {
-  \group_begin:
-  
-  % diff. order list 
-  \tl_clear:N \l__diffco_order_clist
-  \IfValueT { #2 }
-    { 
-    \clist_set:Nn \l__diffco_order_clist { #2 }
-    \tl_set:Nx \l__diffco_order_spec_tl 
-        { [\clist_use:Nn \l__diffco_order_clist { , }]}
-    }
-  
-  % order list override  
-  \IfValueT { #3 }
-    { 
-    \bool_set_true:N \l__diffco_override_bool
-    \tl_set:Nn \l__diffco_order_tl { #3 } 
-    }
-    
-  \__diffco_orders:Nn \l__diffco_order_clist { #6 }
+    \group_begin:
+    \tl_set:Nn \l__diffcoeff_differentiand_tl { #5 }
+    \tl_set:Nn \l__diffcoeff_trailing_tl { #8 }
 
-  % position of differentiand
-  \IfBooleanTF { #1 }
-    { % appended
-    \__diffco_phantom:n { #4 }
-    \tl_set:Nn \l__diffco_coeff_tl
-        {
-        \IfBooleanTF { #5 }
-          { % slash (therefore no phantom)
-            ( \partial \__diffco_omit_order_if_i:N
-            \l__diffco_order_tl
-            /
-            \l__diffco_denom_tl ) \l__diffco_rentiand_tl
-          }
-          { % frac
-            \frac { \partial \__diffco_omit_order_if_i:N
-              \l__diffco_order_tl \l__diffco_phantom_tl } 
-              { \l__diffco_denom_tl } \l__diffco_rentiand_tl
-          }
-        }
-    }
-    { % in numerator
-    \tl_set:Nn \l__diffco_coeff_tl
-        {
-        \IfBooleanTF { #5 }
+    \tl_set:Nn \l__diffcoeff_denom_tl { #7 }
+    \seq_set_split:Nnn \l__diffcoeff_vars_seq { , } { #7 }
+
+    \seq_set_from_clist:Nn \l__diffcoeff_orders_seq { #3 }
+    \tl_set:Nn \l__diffcoeff_order_spec_tl { [#3] }
+    
+    \int_set:Nn \l_tmpa_int { \seq_count:N \l__diffcoeff_vars_seq }
+    \int_set:Nn \l_tmpb_int { \seq_count:N \l__diffcoeff_orders_seq }
+    \int_compare:nNnTF { \l_tmpa_int } = { 1 }
+      { \bool_set_true:N \l__diffcoeff_single_var_bool }
+      {
+        \int_compare:nNnTF { \l_tmpa_int } < { \l_tmpb_int }
           {
-          \partial \__diffco_omit_order_if_i:N \l__diffco_order_tl #4 
-          / \l__diffco_denom_tl
+            \msg_error:nnxx { diffcoeff } { numbers-conflict } 
+           { \int_use:N \l_tmpa_int } { \int_use:N \l_tmpb_int }
           }
-          {
-            \frac { \partial
-                \__diffco_omit_order_if_i:N \l__diffco_order_tl
-                #4 } { \l__diffco_denom_tl } 
+          { % pad orders seq if nec.
+            \int_step_inline:nnnn 
+                { 1 + \l_tmpb_int } { 1 } { \l_tmpa_int }
+                { \seq_put_right:Nn \l__diffcoeff_orders_seq { 1 } }
+            \tl_set:NV \l__diffcoeff_denom_tl \l__diffcoeff_vars_seq
           }
-        }
-    }
-
-  \IfNoValueTF { #7 }
-    { \l__diffco_coeff_tl }
-    {
-    \tl_if_empty:nTF { #7 }
-      { 
-      \l__diffco_coeff_tl
       }
-      {
-      \g_diffco_p_ldelim_tl \l__diffco_coeff_tl \g_diffco_p_rdelim_tl
-      \c_math_subscript_token { \g_diffco_p_nudge_tl #7 }
+    % 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 
+          }
       }
-    }
-  \group_end:  
-  } % end of \diffp 
-
-\NewDocumentCommand \jacob { m m }
-  { % need extra braces in denom for clist manipulations
-  \diffp{ (#1) }{ { {{(#2)}} } }
+    \IfValueT { #1 } { \tl_set:Nn \l__diffcoeff_type_tl { .#1 } }
+    \int_zero:N \l__diffcoeff_format_int
+    % append? slash?
+    \IfBooleanT #2 { \int_incr:N \l__diffcoeff_format_int }
+    \IfBooleanT #6 { \int_add:Nn \l__diffcoeff_format_int { 2 } }
+
+    \UseInstance { derivative } { ord\l__diffcoeff_type_tl } 
+        \l__diffcoeff_orders_seq
+        \l__diffcoeff_tot_order_tl
+        \l__diffcoeff_differentiand_tl
+        \l__diffcoeff_denom_tl
+        \l__diffcoeff_trailing_tl
+    \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 }
   }
- 
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
-
-% #1 is the clist of diff. orders
-% #2 is the tl of variables (if commas present treat as clist)
-\cs_new:Npn \__diffco_orders:Nn #1#2
+\cs_new:Npn \__diffcoeff_digest_expr:n #1
   {
-  \int_zero:N \l_tmpa_int
-  \tl_clear:N \l_tmpb_tl
-  \clist_clear:N \l_tmpa_clist
-  \clist_clear:N \l_tmpb_clist
-  \clist_clear:N \l__diffco_vars_clist
-    
-  \clist_set:Nn \l__diffco_vars_clist { #2 }
-  \clist_map_inline:Nn \l__diffco_vars_clist
-    {
-    \bool_set_false:N \l__diffco_no_parens_bool
-    
-    % get order of each variable
-    \clist_pop:NNF #1 \l_tmpa_tl 
-      { \tl_set:Nn \l_tmpa_tl { 1 } }
-
-    \tl_if_eq:noT { 1 } \l_tmpa_tl
-      { \bool_set_true:N \l__diffco_no_parens_bool }
-
-    \clist_put_right:NV \l_tmpa_clist \l_tmpa_tl 
-   
-    % create the denominator
-    \tl_clear:N \l_tmpb_tl
-    \bool_if:nTF
-        {
-        \int_compare_p:nNn { \tl_count:n { ##1 } } = { \c_one } 
-        ||
-        \l__diffco_no_parens_bool
-        }
-      { \tl_put_right:Nn \l_tmpb_tl { \partial ##1 } }
-      { \tl_put_right:Nn \l_tmpb_tl { \partial (##1) } }
-
-    \tl_if_eq:noF { 1 } \l_tmpa_tl
+    \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+ }
       { 
-      \tl_put_right:Nn \l_tmpb_tl { ^ } 
-      \tl_put_right:Nx \l_tmpb_tl { { \l_tmpa_tl } }
+        \__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 
       }
-
-    \clist_put_right:No \l_tmpb_clist \l_tmpb_tl
-    } % end of inline map
-
-  % numerator order 
-  \bool_if:NF \l__diffco_override_bool
-    {
-    \tl_set:Nx \l__diffco_orders_in_tl { \clist_use:Nn \l_tmpa_clist {+} }
-    \diff_simplify_orders:NN \l__diffco_orders_in_tl \l__diffco_order_tl
-    }
-
-  % denominator
-  \tl_set:Nx \l__diffco_denom_tl { \clist_use:Nn
-        \l_tmpb_clist { \g_diffco_sep_tl } }
+    \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 }
   }
-
-% don't display order 1 superscript
-\cs_new:Npn \__diffco_omit_order_if_i:N #1
-    {
-    \tl_if_eq:noF { 1 } #1
-      { ^{ \g_diffco_p_sep_tl \l__diffco_order_tl } }
-    }
-%%%%%%%%%%%%%%%%%%%%%%
-% #1 is expr. in; #2 is expr. out
-\cs_new:Npn \diff_simplify_orders:NN #1 #2
-  {
-  \tl_clear:N \l__diffco_nos_tl
- 
-  \__diffco_digest_expr:NNNN \l__diffco_orders_in_tl \l__diffco_nos_tl 
-      \l__diffco_alg_tl \l__diffco_vars_prop
-
-  \__diffco_eval_nos:N \l__diffco_nos_tl
-  
-  \tl_if_empty:NF \l__diffco_alg_tl
-    { \__diffco_eval_vars:NN \l__diffco_alg_tl \l__diffco_vars_prop }
-  
-  \__diffco_manicure_result:NNN \l__diffco_nos_tl \l__diffco_alg_tl #2
+% #1 curr tok (tl); #2 <== curr tok ndx (int)
+\cs_new: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 is the expression; #2 (tl) receives the numerical part;
-% #3 (tl) receives the algebraic part; #4 (prop) receives the vars
-\cs_new:Npn \__diffco_digest_expr:NNNN #1#2#3#4
-  {
-  \tl_put_right:Nn #1 { + }
-  \tl_set:Nn \l__diffco_curr_term_tl { + }
-  \int_set:Nn \l__diffco_curr_state_int { \c_zero }
-  \int_set:Nn \l__diffco_curr_tok_int { \c_zero }
-  \tl_clear:N #3
-  \prop_clear:N #4
-    
-  \tl_map_inline:Nn #1
-    { 
-    \tl_set:Nn \l__diffco_curr_tok_tl { ##1 }
-    \__diffco_get_curr_index:NN ##1 \l__diffco_curr_tok_int
-    \__diffco_compare_states:NNNNN \l__diffco_curr_state_int 
-        \l__diffco_curr_tok_int #2#3#4
-    }
-  \tl_if_empty:NT #2 { \tl_set:Nn #2 { 0 } }
+% #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 }
+      }
   }
-
-% #1 contains current token (tl); #2 receives current state (int)
-\cs_new:Npn \__diffco_get_curr_index:NN #1#2
+% transitions from the signed state
+% #1(tl) curr tok; #2(int) 0, curr state; #3 curr tok ndx
+\cs_new:Npn \__diffcoeff_sgn_transitions:nNN #1#2#3
   {
-  \tl_if_in:NnTF \c__diffco_digits_tl { #1 }
-    { % digit
-    \int_set:Nn #2 { \c_one }
-    }
-    {
-      \tl_case:NnF #1
-        {
-        + { \int_set_eq:NN #2 \c_zero }
-        - { \int_set_eq:NN #2 \c_zero }
-        ( {
-            \msg_error:nnxx { diffcoeff } { unknown_token } 
-                { \l__diffco_order_spec_tl } { parentheses }
+    \int_case:nnTF { #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 }
           }
-        ^ { 
-            \msg_error:nnxx { diffcoeff } { unknown_token }
-                { \l__diffco_order_spec_tl } { superscript } 
+        { 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 }
           }
-        }  
-        {
-          \token_if_math_subscript:NTF #1 
-            { 
-              \msg_error:nnxx { diffcoeff } { unknown_token } 
-                  { \l__diffco_order_spec_tl } { subscript } 
-            }
-            { \int_set_eq:NN #2 \c_two } % var
-        }
-    }
+      }
+      { \int_set_eq:NN #2 #3 }
+      {
+        \msg_error:nnxxx { diffcoeff } { order-specification } 
+          { \l__diffcoeff_order_spec_tl } { #1 } { sign }
+      }
   }
- 
-% #1 (int) is curr. state; #2 (int) is curr token index; 
-% #3 (tl) receives the numerical part; 
-% #4 (tl) receives the algebraic part; 
-% #5 (prop) receives the vars
-\cs_new:Npn \__diffco_compare_states:NNNNN #1#2#3#4#5
+% transitions from the numeric state
+% #1 = curr. tok.; #2 = 0, curr. state; #3 curr. tok. index
+\cs_new:Npn \__diffcoeff_num_transitions:nNN #1#2#3
   {
-  \int_case:nn { #1 }
-    {
-      { \c_zero } % sgn
-        {
-        \int_case:nn { #2 }
+    \int_case:nnTF { #3 }
+      {
+        { 0 } % tok = s
           {
-            { \c_zero } % tok = s
+            \__diffcoeff_store_num:NNN \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_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 = )
+          {
+            \__diffcoeff_store_num:NNN \l__diffcoeff_nos_tl 
+                \l__diffcoeff_paren_tl \l__diffcoeff_curr_num_tl
+          }
+      }
+      { 
+        \int_set_eq:NN #2 #3 }
+      {
+        \msg_error:nnxxx { diffcoeff } { order-specification } 
+          { \l__diffcoeff_order_spec_tl } { #1 } { number }
+      }
+  }
+% 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:nnTF { #3 }
+      {
+        { 0 } % tok = s
+          { 
+            \int_compare:nNnTF { \l__diffcoeff_parenvar_int } = { 0 }
               {
-                \tl_if_eq:NNTF \l__diffco_curr_term_tl \l__diffco_curr_tok_tl
-                  { \tl_set:Nn \l__diffco_curr_term_tl { + } }
-                  { \tl_set:Nn \l__diffco_curr_term_tl { - } }
+                \__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 }
               }
-            { \c_one } % tok = d
-              { \__diffco_term_append:NN #1#2 }
-            { \c_two } % tok = v
               {
-              \tl_put_right:Nn \l__diffco_curr_term_tl { 1 }
-              \__diffco_term_var_append:NN #1#2
+                \tl_put_right:Nn \l__diffcoeff_curr_var_tl { #1 }
+                \int_set:Nn #3 { 2 }
               }
           }
-        }
-      { \c_one } % num
-        {
-        \int_case:nn { #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 = (
           {
-            { \c_zero } % tok = s
-              {
-              \tl_put_right:NV #3 \l__diffco_curr_term_tl 
-              \tl_clear:N \l__diffco_curr_term_tl
-              \__diffco_term_append:NN #1#2
-              }
-            { \c_one } % tok = d
-              { \__diffco_term_append:NN #1 \c_one }
-            { \c_two } % tok = v
-              { \__diffco_term_var_append:NN #1#2 }
+            \tl_put_right:Nn \l__diffcoeff_curr_var_tl { #1 }
+            \int_set:Nn #3 { 2 }
+            \int_incr:N \l__diffcoeff_parenvar_int
           }
-        }      
-      { \c_two } % alg
-        {
-        \int_case:nn { #2 }
+        { 4 } % tok = )
           {
-            { \c_zero } % tok = s
+            \int_compare:nNnTF { \l__diffcoeff_parenvar_int } = { 0 }
               {
-              \tl_put_right:NV #4 \l__diffco_curr_term_tl
-              \tl_clear:N \l__diffco_curr_term_tl
-              \bool_if:NF \l__diffco_vars_noted_bool
-                { \__diffco_store_var:NN #5 \l__diffco_curr_var_tl }
-              \tl_clear:N \l__diffco_curr_var_tl 
-              \__diffco_term_append:NN #1#2
+                \__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
               }
-            { \c_one } % tok = d
-              { 
-              \__diffco_term_var_append:NN #1 \c_two
-              \msg_error:nnx { diffcoeff } { variable_digit_sequence } 
-                { \l__diffco_order_spec_tl }
+              {
+                \tl_put_right:Nn \l__diffcoeff_curr_var_tl { #1 }
+                \int_set:Nn #3 { 2 }
+                \int_decr:N \l__diffcoeff_parenvar_int
               }
-            { \c_two } % tok = v
-              { \__diffco_term_var_append:NN #1 \c_two }
           }
-        }
-    }
+      }
+      { \int_set_eq:NN #2 #3 }
+      {
+        \msg_error:nnxxx { diffcoeff } { order-specification } 
+          { \l__diffcoeff_order_spec_tl } { #1 } 
+            { variable }
+      }
   }
-
-% #1 current state; #2 current token index
-\cs_new:Npn \__diffco_term_var_append:NN #1#2
+% 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
   {
-  \tl_put_right:NV \l__diffco_curr_term_tl \l__diffco_curr_tok_tl
-  \tl_put_right:NV \l__diffco_curr_var_tl \l__diffco_curr_tok_tl
-  \int_set_eq:NN #1 #2
+    \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 } 
+            { \l__diffcoeff_order_spec_tl } { #1 } { ) }
+      }
   }
-  
-% #1 current state; #2 current token index
-\cs_new:Npn \__diffco_term_append:NN #1#2
+% #1=store (tlvar); #2=num. coeff. (tlvar); #3=num.(tlvar)
+\cs_new:Npn \__diffcoeff_store_num:NNN #1#2#3
   {
-  \tl_put_right:NV \l__diffco_curr_term_tl \l__diffco_curr_tok_tl
-  \int_set_eq:NN #1 #2
-  }    
- 
-% #1 is prop list; #2 is tl containing var
-\cs_new:Npn  \__diffco_store_var:NN #1 #2
-  {
-  \int_set:Nn \l_tmpa_int { \exp_args:NV \tl_count_tokens:n #2 }
-  \prop_get:NVNTF #1 \l_tmpa_int \l_tmpa_tl
-    {
-    \tl_put_right:Nn \l_tmpa_tl { , }
-    \tl_put_right:NV \l_tmpa_tl #2
-    \prop_put:NVV #1 \l_tmpa_int \l_tmpa_tl
-    }
-    {
-    \prop_put:NVV #1 \l_tmpa_int #2
-    }
-  }
-  
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% evals numerical expr. in #1, which receives the
-% evaluated expr.
-\cs_new:Npn \__diffco_eval_nos:N #1 
+    \tl_put_right:NV #1 #2
+    \tl_put_right:Nn #1 { * }
+    \tl_put_right:NV #1 #3
+  }
+% #1 is var. (tlvar); #2 is num. (tlvar); #3 num. coeff. (tlvar)
+\cs_new:Npn \__diffcoeff_store_var:NNN #1#2#3
   {
-  \int_set:Nn \l_tmpa_int { #1 }
-  \tl_set:Nx  #1 { \int_use:N \l_tmpa_int }
-  \int_compare:nNnT { \l_tmpa_int } > { \c_zero }
-    { \tl_put_left:Nn #1 { + } }
+    \prop_get:NVNF \l__diffcoeff_vars_prop #1 \l_tmpa_tl
+      { \tl_clear:N \l_tmpa_tl }
+    \__diffcoeff_store_num:NNN \l_tmpa_tl #2 #3
+    \prop_put:NVV \l__diffcoeff_vars_prop #1 \l_tmpa_tl
   }
-
-% #1 (tl) has algebraic part & receives eval. expression
-% #2 (prop) contains the variables
-% The idea is to remove each var but leave coeffs, split into
-% num & alg parts, eval. the num part for the net coeff of var
-\cs_new:Npn \__diffco_eval_vars:NN #1#2
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% #1 (prop) vars (keys) & coeffs (vals); #2 total order
+\cs_new:Npn \__diffcoeff_evaluate:NN #1#2
   { 
-  \bool_set_true:N \l__diffco_vars_noted_bool
-  \prop_set_eq:NN \l_tmpa_prop #2
-  \int_set_eq:NN \l_tmpa_int \c_one
-  \bool_until_do:nn { \prop_if_empty_p:N #2 }
-    {
-    \prop_pop:NVNT #2 \l_tmpa_int \l_tmpa_tl
+    \prop_map_inline:Nn #1
+      { 
+        \int_compare:nNnF { \int_eval:n { ##2 } } = { 0 }
+          {
+            \seq_put_right:Nx \l_tmpa_seq 
+                { { +\int_eval:n { ##2 } } { ##1 } }
+          }
+      }
+    \seq_sort:Nn \l_tmpa_seq
       {
-      \tl_put_left:Nn \l_tmpa_tl { , }
-      \tl_put_left:NV \l__diffco_vars_tl  \l_tmpa_tl
+        \int_compare:nNnTF 
+            { \tl_count:V { \use_ii:nn ##1 } } < 
+                { \tl_count:V { \use_ii:nn ##2 } }
+          { \sort_return_swapped: }
+          { \sort_return_same: }
       }
-    \int_incr:N \l_tmpa_int
-    }
-    
-  \clist_set:NV \l__diffco_vars_clist \l__diffco_vars_tl
-  \clist_remove_duplicates:N \l__diffco_vars_clist
-  
-  \clist_map_inline:Nn \l__diffco_vars_clist
-    {
-    \tl_replace_all:Nnn #1 { ##1 } { }
-    \__diffco_digest_expr:NNNN #1 \l__diffco_nos_aux_tl \l__diffco_alg_aux_tl 
-        \l_tmpa_prop
-
-    \__diffco_eval_nos:N \l__diffco_nos_aux_tl
-      
-    \__diffco_cumulate_expr:NnN \l__diffco_nos_aux_tl { ##1 }
-        \l__diffco_alg_expr_tl
-     
-    \tl_set_eq:NN #1 \l__diffco_alg_aux_tl
-    \tl_clear:N \l__diffco_nos_aux_tl
-    \tl_clear:N \l__diffco_alg_aux_tl
-    }
-
-  \tl_set_eq:NN #1 \l__diffco_alg_expr_tl
+    \tl_set:Nx \l_tmpa_tl { \seq_use:Nn \l_tmpa_seq { } }
+    \seq_set_split:NnV \l_tmpa_seq {} \l_tmpa_tl
+    \tl_clear:N \l_tmpa_tl
+    \seq_map_inline:Nn \l_tmpa_seq
+      { 
+        \tl_if_eq:nnTF { +-1 } { ##1 }
+          { \tl_put_right:Nn \l_tmpa_tl { - } }
+          {
+            \tl_if_eq:nnTF { +1 } { ##1 }
+              { \tl_put_right:Nn \l_tmpa_tl { + } }
+              { \tl_put_right:Nn \l_tmpa_tl { ##1 } }
+          }
+      }
+    \tl_replace_all:Nnn \l_tmpa_tl { +- } { - }
+    \exp_args:NV \tl_if_head_eq_charcode:nNTF \l_tmpa_tl +
+      { 
+        \int_compare:nNnT { \l__diffcoeff_nos_int } > { 0 }
+          { \tl_put_left:Nn \l__diffcoeff_nos_tl { + } }
+        \tl_set:Nx \l_tmpb_tl { \tl_tail:N \l_tmpa_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
   }
-
-% #1 is num coeff; #2 is var; #3 is cumulating expr. (All tl.)
-\cs_new:Npn \__diffco_cumulate_expr:NnN #1#2#3
+%%%%%%%%%%%%%%%%%%%%
+% Jacobian
+\NewDocumentCommand \jacob { m t/ m }
   {
-  \int_case:nnF { #1 }
-    {
-      { 0 } { \prg_do_nothing: }
-      { +1 } { \tl_put_right:Nn #3 { + #2 } }
-      { -1 } { \tl_put_right:Nn #3 { - #2 } }
-    }
-    {
-    \tl_put_right:NV #3 { #1 } 
-    \tl_put_right:Nn #3 { #2 }
-    }
+    \group_begin:
+    \IfBooleanTF #2
+      { \partial(#1) / \partial(#3) }
+      { \frac{ \partial(#1) } { \partial(#3) } }
+    \group_end:
   }
-
-% alg. part precedes num. part unless alg. starts 
-% with - and nums > 0. #1 nums, #2 alg, #3 output 
-\cs_new:Npn \__diffco_manicure_result:NNN #1#2#3
-  { % alg < 0 ?
-  \exp_args:NV \tl_if_head_eq_charcode:nNTF #2 -
-    {
-    \int_compare:nNnTF { #1 } > { \c_zero }
-      {  % nums > 0
-      \tl_concat:NNN #3 #1 #2
-      }
-      {  % nums =< 0
-      \seq_set_split:NnV \l_tmpa_seq { + } #2    
-      \seq_pop:NN \l_tmpa_seq \l_tmpa_tl
-      \tl_set:Nx \l_tmpb_tl { \seq_use:Nn \l_tmpa_seq { + } }
-      \int_compare:nNnF { #1 } = { \c_zero }
-        { \tl_concat:NNN \l_tmpa_tl \l_tmpa_tl #1 }
-      \tl_concat:NNN #3 \l_tmpb_tl \l_tmpa_tl
-      }
-    }
-    { % alg >= 0
-    \int_compare:nNnTF { #1 } = { \c_zero }
-      { \tl_set_eq:NN #3 #2 }
-      { \tl_concat:NNN #3 #2 #1 }
-    }
-  
-  % if everything cancels, output 0
-  \tl_if_empty:NTF #3 { \tl_set:Nn #3 { 0 } }
-    {
-    % trim initial + sign
-    \exp_args:NV \tl_if_head_eq_charcode:nNT #3 +
-      { \tl_set:Nx #3 { \tl_tail:N #3 } }
-    }
-  }
-%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%
 % messages
-\tl_gset:Nn \g__diffcoeff_info_text: 
-  { Use~the~order-override~option~to~specify~the~overall~order~of~
-      differentiation. }
-  
-\msg_new:nnnn { diffcoeff } { unknown_token } 
-  { Unimplemented~in~diffcoeff.sty:~#2~in~the~order~specification~#1~
-      \msg_line_context:. }
-  { \g__diffcoeff_info_text: }
-  
-\msg_new:nnnn { diffcoeff } { variable_digit_sequence } 
-  { Unimplemented~in~diffcoeff.sty:~a~digit~follows~a~variable~in~the~order~
-      specification~#1~\msg_line_context:. }
-  { \g__diffcoeff_info_text: }
-
-%% version history
-% 1.1 Fix message handling mess; avoids conflict with mhchem.sty
\ No newline at end of file
+\msg_new:nnn { diffcoeff } { order-specification } 
+  {
+    Is~this~intended:~#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 has~been~superseded~by~the~\diffdef\ 
+    command.~\msg_see_documentation_text:n { diffcoeff }
+  }
+\msg_new:nnn { diffcoeff } { numbers-conflict } 
+  { 
+    #2~orders~specified~for~#1~variables;~\l__diffcoeff_order_spec_tl
+    \ (\msg_line_context:)~for~variables~\l__diffcoeff_denom_tl.
+  }
+% end of file diffcoeff.sty
\ No newline at end of file