diffcoeff (27jun16)

git-svn-id: svn://tug.org/texlive/trunk@41554 c570f23f-e606-0410-a88d-b1316a301751

2 files changed, 1683 insertions, 0 deletions

diff --git a/Master/texmf-dist/tex/latex/diffcoeff/diffcoeff.sty b/Master/texmf-dist/tex/latex/diffcoeff/diffcoeff.sty
new file mode 100644
index 00000000000..bb18b85d6fa
--- /dev/null
+++ b/Master/texmf-dist/tex/latex/diffcoeff/diffcoeff.sty
@@ -0,0 +1,711 @@
+% 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.
+% 
+% Andrew Parsloe aparsloe@clear.net.nz
+%
+\RequirePackage{expl3}
+\RequirePackage{xparse}
+\ProvidesExplPackage{diffcoeff} {2016/06/27} {1.0} 
+  {Write differential coefficients easily.}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\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 }
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% 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_entiand_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
+ 
+\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 }
+  {
+  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 }
+  {
+  \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 }  
+    }
+  }
+     
+% now set the defaults    
+\diffset  
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Derivatives
+% Ordinary differential coefficient. #1 is the order; #2 the 
+% differentiand; #3 the variable of differentiation; #4 the 
+% point of evaluation. 
+\NewDocumentCommand \diff{ s o m t/ m g } 
+  {
+  \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 numerator (no star);
+% slash or fraction?
+  \IfBooleanTF { #1 }
+    { % differentiand follows diff coeff 
+    \__diffco_phantom:n { #3 }
+    \tl_set:Nn \l__diffco_coeff_tl
+      {
+      \IfBooleanTF { #4 }
+        { % slash (therefore no phantom)
+        (\g_diffco_dop_tl \l__diffco_order_tl 
+        /
+        \g_diffco_dop_tl \l__diffco_denom_tl )
+        \l__diffco_entiand_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_entiand_tl
+        }
+      }
+    }
+    { % 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 }
+        }
+      }
+    }
+  % pt of eval
+  \IfNoValueTF { #6 } 
+    { 
+    \l__diffco_coeff_tl
+    }
+    { % trailing arg: pt of eval.
+    \tl_if_empty:nTF { #6 }
+      { 
+      \l__diffco_coeff_tl
+      }
+      {
+      \g_diffco_d_ldelim_tl \l__diffco_coeff_tl \g_diffco_d_rdelim_tl 
+      \c_math_subscript_token { \g_diffco_d_nudge_tl #6 }
+      }
+    }
+  \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
+      {
+      \tl_if_head_eq_meaning_p:nN { #1 } \hfill ||
+      \tl_if_head_eq_meaning_p:nN { #1 } \hfil
+      }
+      {
+      \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_entiand_tl { #1 } 
+        }
+      }
+  }
+
+\cs_new:Npn \l__diffco_phantom_aux:nn #1#2\q_stop
+  {
+  \tl_set:Nn \l__diffco_phantom_tl { #1 }
+  \tl_set:Nn \l__diffco_entiand_tl { #2 }
+  }
+  
+\cs_new:Npn \l__diffco_phantom_aux:nnn #1#2#3\q_stop
+  {
+  \tl_set:Nn \l__diffco_phantom_tl { #1 { #2  } }
+  \tl_set:Nn \l__diffco_entiand_tl { #3 }
+  }
+%%%%%%%%%%%%%%%%%%%%
+% 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 } 
+  {
+  \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 }
+
+  % 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_entiand_tl
+          }
+          { % frac
+          \frac { \partial \__diffco_omit_order_if_i:N
+            \l__diffco_order_tl \l__diffco_phantom_tl } 
+            { \l__diffco_denom_tl } \l__diffco_entiand_tl
+          }
+        }
+    }
+    { % in numerator
+    \tl_set:Nn \l__diffco_coeff_tl
+        {
+        \IfBooleanTF { #5 }
+          {
+          \partial \__diffco_omit_order_if_i:N \l__diffco_order_tl #4 
+          / \l__diffco_denom_tl
+          }
+          {
+          \frac { \partial
+             \__diffco_omit_order_if_i:N \l__diffco_order_tl
+             #4 } { \l__diffco_denom_tl } 
+          }
+        }
+    }
+
+  \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 }
+      }
+    }
+  \group_end:  
+  } % end of \diffp 
+
+\NewDocumentCommand \jacob { m m }
+  { % need extra braces in denom for clist manipulations
+  \diffp{ (#1) }{ { {{(#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
+  {
+  \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_put_right:Nn \l_tmpb_tl { ^ } 
+      \tl_put_right:Nx \l_tmpb_tl { { \l_tmpa_tl } }
+      }
+
+    \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 } }
+  }
+
+% 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 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 contains current token (tl); #2 receives current state (int)
+\cs_new:Npn \__diffco_get_curr_index:NN #1#2
+  {
+  \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 }
+        }
+      ^ { 
+        \msg_error:nnxx { diffcoeff } { unknown_token }
+            { \l__diffco_order_spec_tl } { superscript } 
+        }
+      }  
+      {
+      \token_if_math_subscript:NTF #1 
+        { 
+        \msg_error:nnxx { diffcoeff } { unknown_token } 
+            { \l__diffco_order_spec_tl } { subscript } 
+        }
+        {  % var 
+        \int_set_eq:NN #2 \c_two 
+        } 
+      }
+    }
+  }
+ 
+% #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
+  {
+  \int_case:nn { #1 }
+    {
+      { \c_zero } % sgn
+        {
+        \int_case:nn { #2 }
+          {
+            { \c_zero } % tok = s
+              {
+              \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 { - } }
+              % \int_set:Nn #1 { \c_zero }
+              }
+            { \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
+              }
+          }
+        }
+      { \c_one } % num
+        {
+        \int_case:nn { #2 }
+          {
+            { \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 }
+          }
+        }      
+      { \c_two } % alg
+        {
+        \int_case:nn { #2 }
+          {
+            { \c_zero } % tok = s
+              {
+              \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
+              }
+            { \c_one } % tok = d
+              { 
+              \msg_error:nnx { diffcoeff } { variable_digit_sequence } 
+                { \l__diffco_order_spec_tl }
+              }
+            { \c_two } % tok = v
+              { \__diffco_term_var_append:NN #1 \c_two }
+          }
+        }
+    }
+  }
+
+% #1 current state; #2 current token index
+\cs_new:Npn \__diffco_term_var_append:NN #1#2
+  {
+  \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
+  }
+  
+% #1 current state; #2 current token index
+\cs_new:Npn \__diffco_term_append:NN #1#2
+  {
+  \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 
+  {
+  \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 { + } }
+  }
+
+% #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
+  { 
+  \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
+      {
+      \tl_put_left:Nn \l_tmpa_tl { , }
+      \tl_put_left:NV \l__diffco_vars_tl  \l_tmpa_tl
+      }
+    \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
+  }
+
+% #1 is num coeff; #2 is var; #3 is cumulating expr. (All tl.)
+\cs_new:Npn \__diffco_cumulate_expr:NnN #1#2#3
+  {
+  \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 }
+    }
+  }
+
+% 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
+\cs_gset:Npn \msg_error_text:n #1
+  { Unimplemented~in~#1.sty: }
+\cs_gset:Npn \msg_info_text:n #1  
+  { Use~the~order-override~option~to~specify~the~overall~order~of~
+      differentiation~(or~use~diffcoeffx.sty). }
+  
+\msg_new:nnnn { diffcoeff } { unknown_token } 
+  { \msg_error_text:n { diffcoeff }~#2~in~the~order~specification~#1~
+      \msg_line_context:. }
+  { \msg_info_text:n { diffcoeff } }
+  
+\msg_new:nnnn { diffcoeff } { variable_digit_sequence } 
+  { \msg_error_text:n { diffcoeff }~a~digit~follows~a~variable~in~the~order~
+      specification~#1~\msg_line_context:. }
+  { \msg_info_text:n { diffcoeff } }
+
+  
\ No newline at end of file
diff --git a/Master/texmf-dist/tex/latex/diffcoeff/diffcoeffx.sty b/Master/texmf-dist/tex/latex/diffcoeff/diffcoeffx.sty
new file mode 100644
index 00000000000..727175176bc
--- /dev/null
+++ b/Master/texmf-dist/tex/latex/diffcoeff/diffcoeffx.sty
@@ -0,0 +1,972 @@
+% This is file `diffcoeffx.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.
+% 
+% Andrew Parsloe aparsloe@clear.net.nz
+%
+\RequirePackage{expl3}
+\RequirePackage{xparse}
+\ProvidesExplPackage{diffcoeffx} {2015/06/27} {1.0} 
+  {Write differential coefficients easily.}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\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 }
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% 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_entiand_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
+\tl_new:N \l__diffco_nudge_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_ordinary_bool
+\bool_new:N \l__diffco_fp_bool
+\bool_new:N \l__diffco_vars_noted_bool
+
+\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
+\int_new:N \l__diffco_prev_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_curr_qvar_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 { diffcoeffx }
+  {
+  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 }
+  {
+  \IfValueTF { #1 }
+    { 
+    \clist_if_empty:nTF { #1 }
+      { 
+      \keys_set:nn { diffcoeffx } { roman,d-delims,p-delims,
+      d-nudge,p-nudge,sep,d-sep,p-sep }
+      }
+      { 
+      \keys_set:nn { diffcoeffx } { #1 } 
+      }
+    }
+    { 
+    \keys_set:nn { diffcoeffx } { roman,d-delims,p-delims,
+    d-nudge,p-nudge,sep,d-sep,p-sep }
+    }
+  }
+   
+% now set the defaults    
+\diffset  
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Derivatives
+% Ordinary differential coefficient. #1 (star) is the append boolean;
+% #2 is the order; #3 the differentiand; #4 slash / boolean;
+% #5 the variable of differentiation; #6 the point of evaluation. 
+ 
+\NewDocumentCommand \diff{ s o m t/ m g } 
+  {
+  \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 } } 
+    }
+  
+  % differentiand appended (star) or numerator (no star);
+  % slash or fraction?
+  \IfBooleanTF { #1 }
+    { % differentiand follows diff coeff 
+    \__diffco_phantom:n { #3 }
+    \tl_set:Nn \l__diffco_coeff_tl
+      {
+      \IfBooleanTF { #4 }
+        { % slash (therefore no phantom)
+        (\g_diffco_dop_tl \l__diffco_order_tl 
+        /
+        \g_diffco_dop_tl \l__diffco_denom_tl )
+        \l__diffco_entiand_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_entiand_tl
+        }
+      }
+    }
+    { % 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 }
+        }
+      }
+    }
+    
+  % point of eval?
+  \IfNoValueTF { #6 }
+    { % no
+    \l__diffco_coeff_tl 
+    }
+    { % yes
+    \bool_set_true:N \l__diffco_ordinary_bool
+    \__diffco_delims:nnnnN #6;;;;\q_stop \l__diffco_ordinary_bool
+    }
+  \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 \diffdelta { 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 \Diffdelta { 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_phantom:n #1
+  {
+  \bool_if:nTF
+      {
+      \tl_if_head_eq_meaning_p:nN { #1 } \hfill ||
+      \tl_if_head_eq_meaning_p:nN { #1 } \hfil
+      }
+      {
+      \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_entiand_tl { #1 } 
+        }
+      }
+  }
+
+\cs_new:Npn \l__diffco_phantom_aux:nn #1#2\q_stop
+  {
+  \tl_set:Nn \l__diffco_phantom_tl { #1 }
+  \tl_set:Nn \l__diffco_entiand_tl { #2 }
+  }
+  
+\cs_new:Npn \l__diffco_phantom_aux:nnn #1#2#3\q_stop
+  {
+  \tl_set:Nn \l__diffco_phantom_tl { #1 { #2  } }
+  \tl_set:Nn \l__diffco_entiand_tl { #3 }
+  }
+%%%%%%%%%%%%%%%%%%%%
+% Partial differential coefficient. #1 (star) = append differentiand 
+% to diff. coeff.(displace from numerator); #2 = comma list of the
+%  orders of diff. in each var.; #3 = order override for the 
+% numerator; #4 = differentiand; #5 = clist of vars of diff. in
+% order; #6 = list of vars held constant
+\NewDocumentCommand \diffp{ s o o t/ m m 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 }
+
+  % position of differentiand
+  \IfBooleanTF { #1 }
+    { % appended
+    \__diffco_phantom:n { #5 }
+    \tl_set:Nn \l__diffco_coeff_tl
+        {
+        \frac { \partial
+          \__diffco_omit_order_if_i:N \l__diffco_order_tl
+          \l__diffco_phantom_tl } { \l__diffco_denom_tl }
+        \l__diffco_entiand_tl
+        }
+    }
+    { % in numerator
+    \tl_set:Nn \l__diffco_coeff_tl
+        {
+        \frac { \partial
+           \__diffco_omit_order_if_i:N \l__diffco_order_tl
+           #5 } { \l__diffco_denom_tl }  
+        }
+    }
+  
+  \IfNoValueTF { #7 }
+    { 
+    \l__diffco_coeff_tl 
+    }
+    { % hold some vars const./ pt of eval.
+    \bool_set_false:N \l__diffco_ordinary_bool
+    \__diffco_delims:nnnnN #7;;;;\q_stop \l__diffco_ordinary_bool
+    }
+  
+  \group_end:  
+  } % end of \diffp 
+  
+
+\NewDocumentCommand \jacob { m m }
+  { % need extra braces in denom for clist manipulations
+  \diffp{ (#1) }{ { {{(#2)}} } }
+  }
+ 
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
+% #1 subscript; #2 superscript; #3 delims; #4 nudge override
+% #5 detritus; #6 boolean (true = ordinary deriv.; false = partial deriv.)
+\cs_new:Npn \__diffco_delims:nnnnN #1;#2;#3;#4;#5\q_stop#6
+  {
+  \tl_set:Nn \l__diffco_sub_tl { #1 }
+  \tl_set:Nn \l__diffco_super_tl { #2 }
+  \tl_if_empty:nTF { #3 }
+    { % default delims 
+    \bool_if:NTF #6
+      { % ordinary
+      \tl_set_eq:NN \l__diffco_ldelim_tl \g_diffco_d_ldelim_tl
+      \tl_set_eq:NN \l__diffco_rdelim_tl \g_diffco_d_rdelim_tl
+      \tl_if_empty:nTF { #4 }
+        { \tl_set_eq:NN \l__diffco_nudge_tl \g_diffco_d_nudge_tl }
+        { \tl_set:Nn \l__diffco_nudge_tl { \mskip #4 mu } }
+      }
+      { % partial
+      \tl_set_eq:NN \l__diffco_ldelim_tl \g_diffco_p_ldelim_tl
+      \tl_set_eq:NN \l__diffco_rdelim_tl \g_diffco_p_rdelim_tl
+      \tl_if_empty:nTF { #4 }
+        { \tl_set_eq:NN \l__diffco_nudge_tl \g_diffco_p_nudge_tl }
+        { \tl_set:Nn \l__diffco_nudge_tl { \mskip #4 mu } }
+      }
+    }
+    { % delims specified
+    \tl_set:Nn \l__diffco_ldelim_tl { \left \use_i:nn #3 }
+    \tl_set:Nn \l__diffco_rdelim_tl { \right \use_ii:nn #3 }
+    \tl_if_empty:nTF { #4 }
+      { 
+      \tl_set:NV \l_tmpa_tl { \use_ii:nn #3 } 
+      \__diffco_get_nudge:N \l_tmpa_tl
+      }
+      { 
+      \tl_set:Nx \l__diffco_nudge_tl { \mskip #4 mu } 
+      }
+    }
+  \l__diffco_ldelim_tl \l__diffco_coeff_tl \l__diffco_rdelim_tl
+  \tl_if_empty:NF \l__diffco_sub_tl
+    { \c_math_subscript_token { \l__diffco_nudge_tl \l__diffco_sub_tl } }
+  \tl_if_empty:NF \l__diffco_super_tl
+    { \c_math_superscript_token { \l__diffco_nudge_tl \l__diffco_super_tl } }
+  }
+
+\cs_new:Npn \__diffco_get_nudge:N #1
+  { 
+  \exp_args:NV\tl_case:NnF #1
+    {
+    ) { \tl_set:Nn \l__diffco_nudge_tl { \mskip -6mu } }
+    > { \tl_set:Nn \l__diffco_nudge_tl { \mskip -6mu } }
+    \} { \tl_set:Nn \l__diffco_nudge_tl { \mskip -4mu } }
+    \rangle { \tl_set:Nn \l__diffco_nudge_tl { \mskip -6mu } }
+    }
+    { \tl_set:Nn \l__diffco_nudge_tl { \mskip 0mu } }
+  }
+
+% #1 is the clist of diff. orders
+% #2 is the clist of variables
+\cs_new:Npn \__diffco_orders:Nn #1#2
+  {
+  \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_put_right:Nn \l_tmpb_tl { ^ } 
+      \tl_put_right:Nx \l_tmpb_tl { { \l_tmpa_tl } }
+      }
+
+    \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 } }
+  }
+
+% 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 #1 \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 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_prev_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 contains current token (tl); #2 receives current token index (int)
+\cs_new:Npn \__diffco_get_curr_index:NN #1#2
+  {
+  \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 }
+      ^ { \int_set_eq:NN #2 \c_three }
+      * { \int_set_eq:NN #2 \c_five }
+      \times 
+        { 
+        \int_set_eq:NN #2 \c_five
+        \tl_set:Nn \l__diffco_curr_tok_tl { * }
+        }
+      ( { \int_set_eq:NN #2 \c_six }
+      ) { \int_set_eq:NN #2 \c_seven }
+      }  
+      {
+      \token_if_math_subscript:NTF #1 
+        { \int_set_eq:NN #2 { \c_four } }
+        { 
+        \int_set_eq:NN #2 \c_two }  % var
+      }
+    }
+  }
+ 
+% #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
+  { 
+  \int_case:nn { #1 }
+    { 
+      { \c_zero } % sgn
+        { \__diffco_sgn_transitions:NNNN #1#2#3#4 }
+      { \c_one } % num
+        { \__diffco_num_transitions:NNNN #1#2#3#4 }
+      { \c_two } % alg
+        { \__diffco_alg_transitions:NNNNN #1#2#3#4#5 }
+      { \c_three } % exp
+        { \__diffco_exp_transitions:NN #1#2 }
+      { \c_four } % sub (_)
+        { \__diffco_sub_transitions:NN #1#2 }
+      { \c_five } % mul (*,X)
+        { \__diffco_mul_transitions:NNNN #1#2#3#4 }
+    }
+  }
+  
+% transitions from the signed state
+% #1 = 0, current state; #2 current token index
+% #3 store num. part; #4 store alg. part
+\cs_new:Npn \__diffco_sgn_transitions:NNNN #1#2#3#4
+  {
+  \int_case:nnF { #2 }
+    {
+      { \c_zero } % tok = s
+        {
+        \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 { - } }
+        \int_set_eq:NN \l__diffco_prev_state_int #1
+        % \int_set:Nn #1 { \c_zero }
+        }
+      { \c_one } % tok = d
+        { \__diffco_term_qvar_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
+        }
+      { \c_six } % tok = (
+        {
+        \tl_put_right:Nn \l__diffco_curr_term_tl { 1*( }
+        \tl_put_right:NV #3 \l__diffco_curr_term_tl
+        \tl_put_right:NV #4 \l__diffco_curr_term_tl
+        \tl_set:Nn \l__diffco_curr_term_tl { + }
+        \int_set_eq:NN \l__diffco_prev_state_int #1
+        \int_set:Nn #1 { \c_zero }
+        }
+      { \c_seven } % tok = )
+        {
+        \tl_put_right:Nn #3 { ) }
+        \tl_put_right:Nn #4 { ) }
+        \tl_set:Nn \l__diffco_curr_term_tl { + }
+        \int_set_eq:NN \l__diffco_prev_state_int #1
+        \int_set:Nn #1 { \c_zero }
+        }
+    }
+    {
+    \msg_error:nnxxx { diffcoeffx } { order_spec_construct } 
+      { \l__diffco_order_spec_tl } { \l__diffco_curr_tok_tl } { sign }
+    }
+  }
+  
+% transitions from the numeric state
+% #1 = 1, current state; #2 current token index
+% #3 store num. part; #4 store alg. part
+\cs_new:Npn \__diffco_num_transitions:NNNN #1#2#3#4
+  {
+  \int_case:nnF { #2 }
+    {
+      { \c_zero } % tok = s
+        {
+        \tl_put_right:NV #3 \l__diffco_curr_term_tl 
+        \tl_clear:N \l__diffco_curr_qvar_tl
+        \tl_clear:N \l__diffco_curr_term_tl
+        \__diffco_term_append:NN #1#2
+        }
+      { \c_one } % tok = d
+        { \__diffco_term_qvar_append:NN #1 #2 }
+      { \c_two } % tok = v
+        { 
+        \tl_clear:N \l__diffco_curr_qvar_tl
+        \__diffco_term_var_append:NN #1#2 
+        }
+      { \c_three } % tok = ^
+        { \__diffco_term_qvar_append:NN #1#2 }  
+      { \c_five } % tok = *
+        { 
+        \tl_clear:N \l__diffco_curr_qvar_tl
+        \__diffco_term_append:NN #1#2
+        }
+      { \c_six } % tok = (
+        {
+        \tl_put_right:Nn \l__diffco_curr_term_tl { *( }
+        \tl_put_right:NV #3 \l__diffco_curr_term_tl
+        \tl_put_right:NV #4 \l__diffco_curr_term_tl
+        \tl_set:Nn \l__diffco_curr_term_tl { + }
+        \int_set_eq:NN \l__diffco_prev_state_int #1
+        \int_set:Nn #1 { \c_zero }
+        } 
+      { \c_seven } % tok = )
+        {
+        \tl_put_right:Nn \l__diffco_curr_term_tl { ) }
+        \tl_put_right:NV #3 \l__diffco_curr_term_tl
+        \tl_put_right:Nn #4 { +0) }
+        \tl_set:Nn \l__diffco_curr_term_tl { + }
+        \int_set_eq:NN \l__diffco_prev_state_int #1
+        \int_set:Nn #1 { \c_zero }
+        }
+    }
+    {
+    \msg_error:nnxxx { diffcoeffx } { order_spec_construct } 
+      { \l__diffco_order_spec_tl } { \l__diffco_curr_tok_tl } { number }
+    }
+  }
+
+% transitions from the algebraic state
+% #1 = 2, current state; #2 current token index
+% #3 store num. part; #4 store alg. part; #5 var store
+\cs_new:Npn \__diffco_alg_transitions:NNNNN #1#2#3#4#5
+  { 
+  \int_case:nnF { #2 }
+    {
+      { \c_zero } % tok = s
+        { 
+        \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
+        \tl_put_right:NV #4 \l__diffco_curr_term_tl
+        \tl_clear:N \l__diffco_curr_term_tl
+        \__diffco_term_append:NN #1 #2
+        }
+      { \c_one } % tok = d
+        {
+        \int_compare:nNnTF { \l__diffco_prev_state_int } = { \c_three }
+          { \__diffco_term_var_append:NN #1 \c_two }
+          { 
+          \msg_error:nnxxx { diffcoeffx } { order_spec_construct } 
+            { \l__diffco_order_spec_tl } { \l__diffco_curr_tok_tl } 
+            { variable }
+          }
+        }
+      { \c_two } % tok = v
+        { \__diffco_term_var_append:NN #1 #2 }
+
+      { \c_three } % tok = ^
+        { \__diffco_term_var_append:NN #1#2 }  
+      { \c_four } % tok = _
+        { \__diffco_term_var_append:NN #1#2 }
+      { \c_seven } % tok = )
+        {
+        \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 
+        \tl_put_right:Nn \l__diffco_curr_term_tl { ) }
+        \tl_put_right:Nn #3 { +0) }
+        \tl_put_right:NV #4 \l__diffco_curr_term_tl
+        \tl_set:Nn \l__diffco_curr_term_tl { + }
+        \int_set_eq:NN \l__diffco_prev_state_int #1
+        \int_set:Nn #1 { \c_zero }
+        }              
+    }
+    {
+    \msg_error:nnxxx { diffcoeffx } { order_spec_construct } 
+      { \l__diffco_order_spec_tl } { \l__diffco_curr_tok_tl } { variable }
+    }
+  }
+
+% transitions from the exponent state
+% #1 = 3, current state; #2 current token index
+\cs_new:Npn \__diffco_exp_transitions:NN #1#2
+  {
+  \int_case:nn { \l__diffco_prev_state_int }
+    { 
+      { \c_one } % prev = num
+        { 
+        \int_case:nnF { #2 }
+          {
+            { \c_one } % tok = d
+              {
+              \tl_clear:N \l__diffco_curr_qvar_tl
+              \tl_put_right:Nn \l__diffco_curr_tok_tl { * }
+              \__diffco_term_append:NN #1 \c_five
+              \bool_set_true:N \l__diffco_fp_bool
+              }
+            { \c_two } % tok = v
+              {
+              \__diffco_term_qvar_append:NN #1 \c_two
+              \tl_set_eq:NN \l__diffco_curr_var_tl \l__diffco_curr_qvar_tl
+              \tl_clear:N \l__diffco_curr_qvar_tl
+              }
+          }
+          {
+          \msg_error:nnxxx { diffcoeffx } { order_spec_construct } 
+            { \l__diffco_order_spec_tl } { \l__diffco_curr_tok_tl } { ^ }
+          }
+        }
+      { \c_two } % prev = alg
+        {
+        \int_compare:nNnTF { #2 } < { \c_three }
+          { \__diffco_term_var_append:NN #1 \c_two }
+          {
+          \msg_error:nnxxx { diffcoeffx } { order_spec_construct } 
+            { \l__diffco_order_spec_tl } { \l__diffco_curr_tok_tl } { ^ }
+          }
+        }
+    }
+  }
+
+% transitions from the subscript state
+% #1 = 4, current state; #2 current token index
+\cs_new:Npn \__diffco_sub_transitions:NN #1#2  
+  {
+  \bool_if:nTF 
+      {(
+      \int_compare_p:nNn { \l__diffco_prev_state_int } = { \c_two } &&
+      \int_compare_p:nNn { #2 } < { \c_three }
+      )}
+    { 
+    \__diffco_term_var_append:NN #1 \c_two 
+    }
+    {
+    \msg_error:nnxxx { diffcoeffx } { order_spec_construct } 
+      { \l__diffco_order_spec_tl } { \l__diffco_curr_tok_tl } { _ }
+    }
+  }
+  
+% transitions from the multiplicative state
+% #1 = 5, current state; #2 current token index
+% #3 store num. part; #4 store alg. part
+\cs_new:Npn \__diffco_mul_transitions:NNNN #1#2#3#4
+  { 
+  \int_case:nnF { #2 }
+    {
+      { \c_zero } % tok = s
+        {
+        \int_compare:nNnTF {\l__diffco_prev_state_int } = { \c_three }
+          {
+          \tl_put_right:Nn \l__diffco_curr_term_tl { 1 }
+          \tl_put_right:NV #3 \l__diffco_curr_term_tl
+          \tl_clear:N \l__diffco_curr_term_tl
+          \__diffco_term_append:NN #1 #2 
+          }
+          {
+          \msg_error:nnxxx { diffcoeffx } { order_spec_construct } 
+            { \l__diffco_order_spec_tl } { \l__diffco_curr_tok_tl } 
+            { multiplicative~token }
+          }
+        }
+      { \c_one } % tok = d
+        { \__diffco_term_qvar_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
+        }
+      { \c_five } % tok = *
+        { \prg_do_nothing: }  
+      { \c_six } % tok = (
+        {
+        \tl_put_right:Nn \l__diffco_curr_term_tl { ( }
+        \tl_put_right:NV #3 \l__diffco_curr_term_tl
+        \tl_put_right:NV #4 \l__diffco_curr_term_tl
+        \tl_set:Nn \l__diffco_curr_term_tl { + }
+        \int_set_eq:NN \l__diffco_prev_state_int #1
+        \int_set:Nn #1 { \c_zero }
+        }
+    }
+    {
+    \msg_error:nnxxx { diffcoeffx } { order_spec_construct } 
+      { \l__diffco_order_spec_tl } { \l__diffco_curr_tok_tl } 
+      { multiplicative~token }
+    }
+  }
+
+%%%%%%%%%%%%%%%%%%%
+% term/var/qvar appending routines  
+% #1 current state; #2 current token index
+\cs_new:Npn \__diffco_term_var_append:NN #1#2
+  {
+  \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 \l__diffco_prev_state_int #1
+  \int_set_eq:NN #1 #2
+  }
+  
+% #1 current state; #2 current token index
+\cs_new:Npn \__diffco_term_qvar_append:NN #1#2
+  {
+  \tl_put_right:NV \l__diffco_curr_term_tl \l__diffco_curr_tok_tl
+  \tl_put_right:NV \l__diffco_curr_qvar_tl \l__diffco_curr_tok_tl
+  \int_set_eq:NN \l__diffco_prev_state_int #1
+  \int_set_eq:NN #1 #2
+  }  
+
+% #1 current state; #2 current token index
+\cs_new:Npn \__diffco_term_append:NN #1#2
+  {
+  \tl_put_right:NV \l__diffco_curr_term_tl \l__diffco_curr_tok_tl
+  \int_set_eq:NN \l__diffco_prev_state_int #1
+  \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 
+  {
+  \bool_if:NTF \l__diffco_fp_bool
+    { % exponent; use l3fp
+    \fp_set:Nn \l_tmpa_fp { #1 }
+    \int_set:Nn \l_tmpa_int { \fp_use:N \l_tmpa_fp }
+    \bool_set_false:N \l__diffco_fp_bool
+    }
+    { % normal mode; use l3int
+    \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 { + } }
+  }
+
+% #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
+  { 
+  \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
+      {
+      \tl_put_left:Nn \l_tmpa_tl { , }
+      \tl_put_left:NV \l__diffco_vars_tl  \l_tmpa_tl
+      }
+    \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
+  \bool_if:NF \l__diffco_override_bool
+    {
+    \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
+  }
+
+% #1 is num coeff; #2 is var; #3 is cumulating expr. (All tl.)
+\cs_new:Npn \__diffco_cumulate_expr:NnN #1#2#3
+  { 
+  \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 } 
+    \exp_args:NNx \tl_if_in:NnT \c__diffco_digits_tl { \tl_head:n { #2 } }
+      { \tl_put_right:Nn #3 { \times} }
+    \tl_put_right:Nn #3 { #2 }
+    }
+  }
+
+% 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
+\cs_gset:Npn \msg_error_text:n #1
+  { #1.sty.~Is~this~construction~intended }
+\cs_gset:Npn \msg_info_text:n #1  
+  { If~intended~then~use~the~order-override~option~to~specify~the~overall~
+      order~of~differentiation. }
+  
+\msg_new:nnnn { diffcoeffx } { order_spec_construct } 
+  { \msg_error_text:n { diffcoeffx }:~#3~followed~by~#2~in~the~order~
+      specification~#1~\msg_line_context:? } 
+  { \msg_info_text:n { diffcoeffx } }
\ No newline at end of file