% This is file `diffcoeff4.sty'.
%
% This work may be distributed and/or modified under the conditions
% of the LaTeX Project Public License, either version 1.3c
% (2008-05-04) of this license or any later version; see
% http://www.latex-project.org/lppl.txt
%
% Andrew Parsloe ajparsloe@gmail.com
%
\RequirePackage{expl3}
\RequirePackage{xparse,l3keys2e,xtemplate}
\ProvidesExplPackage {diffcoeff4} {2022/07/30} {4.2}
{Write differential coefficients easily and consistently.}
%
\keys_define:nn { diffcoeff4 }
{
ISO .bool_set:N = \l__diffcoeff_ISO_bool,
spaced .int_set:N = \l__diffcoeff_spaced_int,
spaced .default:n = 1,
spaced .initial:n = 0,
def-file .tl_gset:N = \g__diffcoeff_def_tl,
def-file .initial:n = diffcoeff,
def-file .default:n = diffcoeff
}
\ProcessKeysPackageOptions { diffcoeff4 }
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\cs_generate_variant:Nn \tl_if_eq:nnTF { nV }
\tl_new:N \l__diffcoeff_oporder_tl
\tl_new:N \l__diffcoeff_derivand_tl
\tl_new:N \l__diffcoeff_type_tl
\tl_new:N \l__diffcoeff_tot_order_tl
\tl_new:N \l__diffcoeff_curr_num_tl
\tl_new:N \l__diffcoeff_curr_var_tl
\tl_new:N \l__diffcoeff_paren_tl
\tl_const:Nn \c__diffcoeff_digits_tl { 1234567890 }
\seq_new:N \l__diffcoeff_orders_seq
\seq_new:N \l__diffcoeff_vars_seq
\seq_new:N \l__diffcoeff_denom_seq
\seq_new:N \l__diffcoeff_paren_seq
\prop_new:N \l__diffcoeff_vars_prop
\bool_new:N \l__diffcoeff_op_left_bool
\bool_new:N \l__diffcoeff_single_var_bool
\bool_new:N \l__diffcoeff_opwrap_bool
\bool_new:N \l__diffcoeff_integ_bool
\bool_new:N \l__diffcoeff_spaced_bool
\bool_new:N \l__diffcoeff_altsep_bool
\int_new:N \l__diffcoeff_vars_int
\int_new:N \l__diffcoeff_format_int
\int_new:N \l__diffcoeff_curr_tok_int
\int_new:N \l__diffcoeff_curr_state_int
\int_new:N \l__diffcoeff_nos_int
\int_new:N \l__diffcoeff_parenvar_int
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\DeclareObjectType { derivative } { 3 }
% defaults: ordinary deriv. values
\DeclareTemplateInterface { derivative } { DERIV } { 3 }
{
op-symbol : tokenlist = d ,
op-symbol-alt : tokenlist = \KeyValue { op-symbol },
op-order-sep : muskip = 1 mu ,
derivand-sep : muskip = 3 mu plus 1 mu minus 2 mu,
long-var-wrap : choice { dv, d(v), (dv) }
= d(v) ,
denom-term-sep : muskip = 2 mu ,
term-sep-adjust : muskip = -1 mu ,
left-delim : tokenlist = \left . ,
right-delim : tokenlist = \right |,
elbowroom : muskip = 0 mu ,
subscr-nudge : muskip = 0 mu ,
*-derivand-sep : muskip = \KeyValue { derivand-sep },
*-op-left : boolean = false ,
*-italic-nudge : muskip = 3 mu ,
/-derivand-sep : muskip = \KeyValue { derivand-sep },
/-denom-term-sep : muskip = 1 mu ,
/-left-delim : tokenlist = ( ,
/-right-delim : tokenlist = ) ,
/-elbowroom : muskip = 0 mu ,
/-subscr-nudge : muskip = 0 mu ,
*/-derivand-sep : muskip = \KeyValue { /-derivand-sep },
*/-op-wrap : boolean = true
}
% #1 order spec(seqvar); #2 order override(tlvar)
% #3 derivand(tlvar); #4 denominator(seqvar)
% #5 subscript(tlvar)
\DeclareTemplateCode { derivative } { DERIV } { 3 }
{
op-symbol = \l__diffcoeff_op_tl,
op-symbol-alt = \l__diffcoeff_op_alt_tl,
op-order-sep = \l__diffcoeff_oporder_muskip,
derivand-sep = \l__diffcoeff_derivsep_muskip,
long-var-wrap = {
dv = \cs_set_eq:NN \__diffcoeff_wrap_longvars:nn
\__diffcoeff_wrap_longvars_dv:nn,
d(v) = \cs_set_eq:NN \__diffcoeff_wrap_longvars:nn
\__diffcoeff_wrap_longvars_dvi:nn,
(dv) = \cs_set_eq:NN \__diffcoeff_wrap_longvars:nn
\__diffcoeff_wrap_longvars_dvii:nn,
unknown = \cs_set_eq:NN \__diffcoeff_wrap_longvars:nn
\__diffcoeff_wrap_longvars_dvi:nn
},
denom-term-sep = \l__diffcoeff_varsep_muskip,
term-sep-adjust = \l__diffcoeff_sep_adj_muskip,
left-delim = \l__diffcoeff_ldelim_tl,
right-delim = \l__diffcoeff_rdelim_tl,
elbowroom = \l__diffcoeff_elbowrm_muskip ,
subscr-nudge = \l__diffcoeff_subnudge_muskip,
*-derivand-sep = \l__diffcoeff_derivsepi_muskip,
*-op-left = \l__diffcoeff_op_left_bool,
*-italic-nudge = \l__diffcoeff_opnudge_muskip,
/-derivand-sep = \l__diffcoeff_derivsepii_muskip,
/-denom-term-sep = \l_tmpb_muskip,
/-left-delim = \l__diffcoeff_ldelimi_tl,
/-right-delim = \l__diffcoeff_rdelimi_tl,
/-elbowroom = \l_tmpc_muskip,
/-subscr-nudge = \l_tmpd_muskip,
*/-derivand-sep = \l__diffcoeff_derivsepiii_muskip,
*/-op-wrap = \l__diffcoeff_opwrap_bool
}
{
\AssignTemplateKeys
\bool_if:NF\l__diffcoeff_integ_bool
{
\int_compare:nNnT { \l__diffcoeff_format_int } > { 1 }
{ \__diffcoeff_slash_vals: }
\__diffcoeff_build:nnn { #1 } { #2 } { #3 }
}
}
%%%%%%%%%%
\cs_new:Npn \__diffcoeff_slash_vals:
{
\muskip_set:Nn \l__diffcoeff_varsep_muskip \l_tmpb_muskip
\muskip_set:Nn \l__diffcoeff_elbowrm_muskip \l_tmpc_muskip
\muskip_set:Nn \l__diffcoeff_subnudge_muskip \l_tmpd_muskip
\tl_set:NV \l__diffcoeff_ldelim_tl \l__diffcoeff_ldelimi_tl
\tl_set:NV \l__diffcoeff_rdelim_tl \l__diffcoeff_rdelimi_tl
}
% #1 diff'and; #2 vars clist; #3 trailing arg
\cs_new:Npn \__diffcoeff_build:nnn #1#2#3
{
\tl_set:Nn \l__diffcoeff_derivand_tl { #1 }
\seq_set_from_clist:Nn \l__diffcoeff_vars_seq { #2 }
\bool_if:nT
{
!\l__diffcoeff_opwrap_bool &&
\int_compare_p:nNn { \l__diffcoeff_format_int } > { 1 }
}
{ \int_set:Nn \l__diffcoeff_format_int { 4 } }
\__diffcoeff_spaced:n { \l__diffcoeff_spaced_int }
\bool_if:nTF
{
( \l__diffcoeff_altsep_bool && !\l__diffcoeff_spaced_bool )
|| ( !\l__diffcoeff_altsep_bool && \l__diffcoeff_spaced_bool )
}
{ \__diffcoeff_derivsep: }
{ \tl_put_left:Nn \l__diffcoeff_derivand_tl { \mskip 0 mu } }
\tl_if_novalue:nF { #3 }
{ \l__diffcoeff_ldelim_tl \mskip \l__diffcoeff_elbowrm_muskip }
\bool_if:NTF \l__diffcoeff_single_var_bool
{
\tl_set:Nx \l_tmpa_tl { \seq_use:Nn \l__diffcoeff_vars_seq { , } }
\__diffcoeff_single:NNN \l__diffcoeff_tot_order_tl \l__diffcoeff_derivand_tl \l_tmpa_tl
}
{
\int_zero:N \l_tmpa_int
\seq_mapthread_function:NNN \l__diffcoeff_orders_seq
\l__diffcoeff_vars_seq \__diffcoeff_map_orders:nn
\__diffcoeff_mixed:NNN \l__diffcoeff_tot_order_tl
\l__diffcoeff_derivand_tl \l__diffcoeff_denom_seq
}
\tl_if_novalue:nF { #3 }
{
\mskip \l__diffcoeff_elbowrm_muskip \l__diffcoeff_rdelim_tl
\tl_if_empty:nF { #3 }
{
\c_math_subscript_token
{ \mskip \l__diffcoeff_subnudge_muskip { #3 } }
}
}
}
%%%%%%%%%%%%%%%%%%%%
\cs_new_protected:Npn \__diffcoeff_spaced:n #1
{
\int_case:nn { \int_sign:n { #1 } }
{
{ 1 } { \bool_set_true:N \l__diffcoeff_spaced_bool }
{ 0 } { \bool_set_false:N \l__diffcoeff_spaced_bool }
{ -1 }
{
\int_compare:nNnTF { 1 } <
{ \tl_count:N \l__diffcoeff_derivand_tl }
{ \bool_set_true:N \l__diffcoeff_spaced_bool }
{ \bool_set_false:N \l__diffcoeff_spaced_bool }
}
}
}
\cs_new_protected:Npn \__diffcoeff_derivsep:
{
\tl_put_left:Nx \l__diffcoeff_derivand_tl
{
\int_case:nn { \l__diffcoeff_format_int }
{
{ 0 } { \mskip \l__diffcoeff_derivsep_muskip }
{ 1 } { \mskip \l__diffcoeff_derivsepi_muskip }
{ 2 } { \mskip \l__diffcoeff_derivsepii_muskip }
{ 3 } { \mskip \l__diffcoeff_derivsepiii_muskip }
{ 4 } { \mskip \l__diffcoeff_derivsepiii_muskip }
}
}
}
\cs_new:Npn \__diffcoeff_wrap_longvars_dv:nn #1#2
{ \l__diffcoeff_op_alt_tl { {}#2 }^{ #1 } }
\cs_new:Npn \__diffcoeff_wrap_longvars_dvi:nn #1#2
{ \l__diffcoeff_op_alt_tl { {}(#2) }^{ #1 } }
\cs_new:Npn \__diffcoeff_wrap_longvars_dvii:nn #1#2
{ (\l__diffcoeff_op_alt_tl { {}#2) }^{ #1 } }
% (ptl) form denom #1 from orders seq & #2 from vars seq
\cs_new_protected:Npn \__diffcoeff_map_orders:nn #1#2
{
\tl_if_eq:nnTF { #1 } { 1 }
{ \seq_put_right:Nn \l__diffcoeff_denom_seq { \l__diffcoeff_op_alt_tl { #2 } } }
{
\int_compare:nNnTF { \tl_count:n { #2 } } = { 1 }
{
\seq_put_right:Nn \l__diffcoeff_denom_seq
{ \l__diffcoeff_op_alt_tl { #2 }^{ #1 } }
}
{
\seq_put_right:Nn \l__diffcoeff_denom_seq
{ \__diffcoeff_wrap_longvars:nn { #1\vphantom{)} } { #2 } }
}
}
}
% #1 order(tlvar) ; #2 diff'iand(tlvar); #3 denom(tlvar)
\cs_new:Npn \__diffcoeff_single:NNN #1#2#3
{
\__diffcoeff_numer:N { #1 }
\__diffcoeff_form_deriv:NNn
\l__diffcoeff_oporder_tl
\l__diffcoeff_derivand_tl
{ \__diffcoeff_denom_single:NN #1 #3 }
}
% #1 total order; #2 derivand; #3 denom seq
\cs_new_protected:Npn \__diffcoeff_mixed:NNN #1#2#3
{
\__diffcoeff_numer:N #1
\__diffcoeff_form_deriv:NNn
\l__diffcoeff_oporder_tl
\l__diffcoeff_derivand_tl
{ \__diffcoeff_denom_sep:N #3 }
}
\cs_new:Npn \__diffcoeff_denom_sep:N #1
{
\int_zero:N \l_tmpa_int
\seq_map_inline:Nn #1
{
\int_incr:N \l_tmpa_int ##1
\int_compare:nNnT { \l_tmpa_int } < { \l__diffcoeff_vars_int }
{
\seq_pop:NN \l__diffcoeff_orders_seq \l_tmpa_tl
\str_if_eq:VnTF \l_tmpa_tl { 1 }
{ \mskip \l__diffcoeff_varsep_muskip }
{
\mskip \muskip_eval:n { \l__diffcoeff_varsep_muskip +
\l__diffcoeff_sep_adj_muskip }
}
}
}
}
% #1(tl) total order
\cs_new_protected:Npn \__diffcoeff_numer:N #1
{
\bool_if:NTF \l__diffcoeff_op_left_bool
{
\tl_set:Nn \l__diffcoeff_oporder_tl
{ \mskip \l__diffcoeff_opnudge_muskip }
}
{ \tl_clear:N \l__diffcoeff_oporder_tl }
\tl_put_right:No \l__diffcoeff_oporder_tl \l__diffcoeff_op_tl
\exp_args:NnV \tl_if_eq:nnF { 1 } #1
{
\tl_put_right:Nn \l__diffcoeff_oporder_tl
{ \mskip \l__diffcoeff_oporder_muskip ^ { #1 } }
}
\bool_if:NT \l__diffcoeff_op_left_bool
{ \tl_put_right:Nn \l__diffcoeff_oporder_tl { \hfill } }
}
% #1 order; #2 var
\cs_new_protected:Npn \__diffcoeff_denom_single:NN #1#2
{
\tl_if_eq:nVTF { 1 } #1
{ \l__diffcoeff_op_alt_tl {}#2 }
{
\int_compare:nNnTF { \tl_count:N #2 } = { 1 }
{ \l__diffcoeff_op_alt_tl {}#2^{ #1 } }
{ \__diffcoeff_wrap_longvars:nn { #1\vphantom) } { #2 } }
}
}
% #1 op+order; #2 diff'iand; #3 denom
% 0 frac; 1 frac append; 2 slash ; 3 ( slash ) append; 4 slash append
\cs_new:Npn \__diffcoeff_form_deriv:NNn #1#2#3
{
\int_case:nn { \l__diffcoeff_format_int }
{
{ 0 } { \frac { #1 #2 } { #3 } }
{ 1 } { \frac { #1 } { #3 } #2 }
{ 2 } { #1 #2 / #3 }
{ 3 } { ( #1 / #3 ) #2 }
{ 4 } { #1 / #3 #2 }
}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% differential
% #1 variant; #2 = space in mu before d (0--9)
% note \group_end placement for \vec{x} etc
\NewDocumentCommand \dl { d.. t- m }
{
\group_begin:
\bool_set_true:N \l__diffcoeff_integ_bool
\bool_set_true:N \l__diffcoeff_single_var_bool
\seq_set_from_clist:Nn \l__diffcoeff_orders_seq { 1 }
\tl_set:Nn \l__diffcoeff_tot_order_tl { 1 }
\IfValueTF { #1 }
{ \tl_set:Nn \l__diffcoeff_type_tl { .#1 } }
{ \tl_set:Nn \l__diffcoeff_type_tl { } }
\UseInstance { derivative } { ord\l__diffcoeff_type_tl }
\c_empty_tl \c_empty_seq \c_empty_tl
\tl_if_in:NnTF \c__diffcoeff_digits_tl { #3 }
{ \mskip \IfBooleanT #2 { - }#3 mu \l__diffcoeff_op_tl \group_end: }
{ \l__diffcoeff_op_tl \group_end: {} #3 }
}
\NewDocumentCommand \negmu {} { \mskip -1 mu }
\NewDocumentCommand \nilmu {} { \mskip 0 mu }
\NewDocumentCommand \onemu {} { \mskip 1 mu }
\NewDocumentCommand \twomu {} { \mskip 2 mu }
% derivative
% #1(tl) = name of variant; #2(*)= append diff'iand boolean
% #3(clist) = orders of diff. in each var.; #4(tl) = order override
% #5(bool) spacing switch; #6(tl) = diff'iand; #7( / ) = slash boolean
% #8(clist) = vars of diff.; #9(tl) = pt of eval./vars held const
\NewDocumentCommand \diff { d.. s O{1} o t! >{\TrimSpaces} m t/ m !o }
{
\group_begin:
\IfBooleanTF #5
{ \bool_set_true:N \l__diffcoeff_altsep_bool }
{ \bool_set_false:N \l__diffcoeff_altsep_bool }
\seq_set_from_clist:Nn \l__diffcoeff_orders_seq { #3 }
\int_set:Nn \l_tmpb_int { \seq_count:N \l__diffcoeff_orders_seq }
\int_set:Nn \l__diffcoeff_vars_int { \clist_count:n { #8 } }
\int_compare:nNnTF { \l__diffcoeff_vars_int } = { 1 }
{ \bool_set_true:N \l__diffcoeff_single_var_bool }
{
\int_compare:nNnTF { \l__diffcoeff_vars_int } < { \l_tmpb_int }
{
\msg_error:nnxxxx { diffcoeff } { numbers-conflict }
{ \int_use:N \l__diffcoeff_vars_int } { \int_use:N \l_tmpb_int }
{ \seq_use:Nn \l__diffcoeff_orders_seq { , } }
{ \clist_use:nn { #8 } { , } }
}
{ % pad orders seq if nec.
\int_step_inline:nnnn
{ 1 + \l_tmpb_int } { 1 } { \l__diffcoeff_vars_int }
{ \seq_put_right:Nn \l__diffcoeff_orders_seq { 1 } }
}
}
% override/calc total order
\IfValueTF { #4 }
{ \tl_set:Nn \l__diffcoeff_tot_order_tl { #4 } }
{
\bool_if:NTF \l__diffcoeff_single_var_bool
{ \tl_set:Nn \l__diffcoeff_tot_order_tl { #3 } }
{
\__diffcoeff_calc_tot_order:NN \l__diffcoeff_orders_seq
\l__diffcoeff_tot_order_tl
}
}
\IfValueTF { #1 }
{ \tl_set:Nn \l__diffcoeff_type_tl { .#1 } }
{ \tl_set:Nn \l__diffcoeff_type_tl { } }
% append? slash?
\int_zero:N \l__diffcoeff_format_int
\IfBooleanT #2 { \int_incr:N \l__diffcoeff_format_int }
\IfBooleanT #7 { \int_add:Nn \l__diffcoeff_format_int { 2 } }
\UseInstance { derivative } { ord\l__diffcoeff_type_tl } {#6}{#8}{#9}
\group_end:
} % end of \diff
%%%%%%%%%%%%%%%%%%%
% #2(seq) expr in; #1(tlv) expr out
\cs_new:Npn \__diffcoeff_calc_tot_order:NN #1 #2
{
\tl_clear:N \l__diffcoeff_nos_tl
\exp_args:Nx\__diffcoeff_digest_expr:n { \seq_use:Nn #1 { + } }
\prop_if_empty:NTF \l__diffcoeff_vars_prop
{ \tl_set:NV #2 \l__diffcoeff_nos_tl }
{ \__diffcoeff_evaluate:NN \l__diffcoeff_vars_prop #2 }
}
\cs_new:Npn \__diffcoeff_digest_expr:n #1
{
\tl_set:Nn \l__diffcoeff_curr_num_tl { + }
\tl_set:Nn \l__diffcoeff_paren_tl { +1 }
\tl_set:Nn \l__diffcoeff_nos_tl { 0 }
\int_zero:N \l__diffcoeff_curr_state_int
\int_zero:N \l__diffcoeff_curr_tok_int
\tl_map_inline:nn { #1+ }
{
\__diffcoeff_get_curr_ndx:nN { ##1 } \l__diffcoeff_curr_tok_int
\__diffcoeff_transitions:nNN { ##1 }
\l__diffcoeff_curr_state_int \l__diffcoeff_curr_tok_int
}
\int_set:Nn \l__diffcoeff_nos_int { \l__diffcoeff_nos_tl }
\tl_set:Nx \l__diffcoeff_nos_tl { \int_use:N \l__diffcoeff_nos_int }
\int_compare:nNnT { \l__diffcoeff_nos_int } = { 0 }
{ \tl_clear:N \l__diffcoeff_nos_tl }
}
% #1 curr tok (tl); #2 <== curr tok ndx (int)
\cs_new_protected:Npn \__diffcoeff_get_curr_ndx:nN #1#2
{
\tl_if_in:NnTF \c__diffcoeff_digits_tl { #1 }
{ \int_set:Nn #2 { 1 } } % digit
{
\str_case:nnF { #1 }
{
{ + } { \int_set:Nn #2 { 0 } }
{ - } { \int_set:Nn #2 { 0 } }
{ ( } { \int_set:Nn #2 { 3 } }
{ ) } { \int_set:Nn #2 { 4 } }
}
{ \int_set:Nn #2 { 2 } } % var
}
}
% #1(tl) curr tok; #2(int) curr state; #3(int) curr tok ndx
\cs_new:Npn \__diffcoeff_transitions:nNN #1#2#3
{
\int_case:nn { #2 }
{
{ 0 } % sgn + -
{ \__diffcoeff_sgn_transitions:nNN { #1 }#2#3 }
{ 1 } % num
{ \__diffcoeff_num_transitions:nNN { #1 }#2#3 }
{ 2 } % alg
{ \__diffcoeff_alg_transitions:nNN { #1 }#2#3 }
{ 4 } % )
{ \__diffcoeff_rpar_transitions:nNN { #1 }#2#3 }
}
}
% transitions from the signed state
% #1(tl) curr tok; #2(int) 0, curr state; #3 curr tok ndx
\cs_new_protected:Npn \__diffcoeff_sgn_transitions:nNN #1#2#3
{
\int_case:nnT { #3 }
{
{ 0 } % tok = s
{
\tl_if_eq:nVTF { #1 } \l__diffcoeff_curr_num_tl
{ \tl_set:Nn \l__diffcoeff_curr_num_tl { + } }
{ \tl_set:Nn \l__diffcoeff_curr_num_tl { - } }
}
{ 1 } % tok = d
{ \tl_put_right:Nn \l__diffcoeff_curr_num_tl { #1 } }
{ 2 } % tok = v
{
\tl_put_right:Nn \l__diffcoeff_curr_num_tl { 1 }
\tl_set:Nn \l__diffcoeff_curr_var_tl { #1 }
}
{ 3 } % tok = (
{
\seq_push:NV \l__diffcoeff_paren_seq \l__diffcoeff_paren_tl
\tl_put_left:NV \l__diffcoeff_paren_tl \l__diffcoeff_curr_num_tl
\tl_set:Nn \l__diffcoeff_curr_num_tl { + }
\int_set:Nn #3 { 0 }
}
}
{ \int_set_eq:NN #2 #3 }
}
% transitions from the numeric state
% #1 = curr. tok.; #2 = 0, curr. state; #3 curr. tok. index
\cs_new_protected:Npn \__diffcoeff_num_transitions:nNN #1#2#3
{
\int_case:nnT { #3 }
{
{ 0 } % tok = s
{
\tl_put_right:NV\l__diffcoeff_nos_tl
{ \l__diffcoeff_paren_tl * \l__diffcoeff_curr_num_tl }
\tl_set:Nn \l__diffcoeff_curr_num_tl { #1 }
}
{ 1 } % tok = d
{ \tl_put_right:Nn \l__diffcoeff_curr_num_tl { #1 } }
{ 2 } % tok = v
{
\tl_if_in:nnTF { ^ \times * / \div } { #1 }
{
\msg_error:nnxxx { diffcoeff } { order-specification }
{ \seq_use:Nn \l__diffcoeff_orders_seq { , } }
{ #1 } { number }
}
{ \tl_set:Nn \l__diffcoeff_curr_var_tl { #1 } }
}
{ 3 } % tok = (
{
\seq_push:NV \l__diffcoeff_paren_seq \l__diffcoeff_paren_tl
\tl_put_left:Nn \l__diffcoeff_paren_tl { * }
\tl_put_left:NV \l__diffcoeff_paren_tl \l__diffcoeff_curr_num_tl
\tl_set:Nn \l__diffcoeff_curr_num_tl { + }
\int_set:Nn #3 { 0 }
}
{ 4 } % tok = )
{
\tl_put_right:NV \l__diffcoeff_nos_tl
{ \l__diffcoeff_paren_tl * \l__diffcoeff_curr_num_tl }
}
}
{
\int_set_eq:NN #2 #3 }
}
% transitions from the algebraic state
% #1 = curr. tok.; #2 = 2, curr. state; #3 curr. tok. index
\cs_new:Npn \__diffcoeff_alg_transitions:nNN #1#2#3
{
\int_case:nnT { #3 }
{
{ 0 } % tok = s
{
\int_compare:nNnTF { \l__diffcoeff_parenvar_int } = { 0 }
{
\__diffcoeff_store_var:NNN \l__diffcoeff_curr_var_tl
\l__diffcoeff_paren_tl \l__diffcoeff_curr_num_tl
\tl_clear:N \l__diffcoeff_curr_var_tl
\tl_set:Nn \l__diffcoeff_curr_num_tl { #1 }
}
{
\tl_put_right:Nn \l__diffcoeff_curr_var_tl { #1 }
\int_set:Nn #3 { 2 }
}
}
{ 1 } % tok = d
{
\tl_put_right:Nn \l__diffcoeff_curr_var_tl { #1 }
\int_set:Nn #3 { 2 }
}
{ 2 } % tok = v
{ \tl_put_right:Nn \l__diffcoeff_curr_var_tl { #1 } }
{ 3 } % tok = (
{
\tl_put_right:Nn \l__diffcoeff_curr_var_tl { #1 }
\int_set:Nn #3 { 2 }
\int_incr:N \l__diffcoeff_parenvar_int
}
{ 4 } % tok = )
{
\int_compare:nNnTF { \l__diffcoeff_parenvar_int } = { 0 }
{
\__diffcoeff_store_var:NNN \l__diffcoeff_curr_var_tl
\l__diffcoeff_paren_tl \l__diffcoeff_curr_num_tl
\tl_clear:N \l__diffcoeff_curr_var_tl
}
{
\tl_put_right:Nn \l__diffcoeff_curr_var_tl { #1 }
\int_set:Nn #3 { 2 }
\int_decr:N \l__diffcoeff_parenvar_int
}
}
}
{ \int_set_eq:NN #2 #3 }
}
% transitions from the ) state
% #1 = curr. tok.; #2 = 4, curr. state; #3 curr. tok. index
\cs_new:Npn \__diffcoeff_rpar_transitions:nNN #1#2#3
{
\int_compare:nNnTF { \int_mod:nn { #3 } { 4} } = { 0 }
{
\tl_set:Nn \l__diffcoeff_curr_num_tl { #1 }
\seq_pop:NN \l__diffcoeff_paren_seq \l__diffcoeff_paren_tl
\int_set_eq:NN #2 #3
}
{
\msg_error:nnxxx { diffcoeff } { order-specification }
{ \seq_use:Nn \l__diffcoeff_orders_seq { , } } { #1 } { ) }
}
}
% #1 is var. (tlvar); #2 is num. (tlvar); #3 num. coeff. (tlvar)
\cs_new:Npn \__diffcoeff_store_var:NNN #1#2#3
{
\prop_get:NVNF \l__diffcoeff_vars_prop #1 \l_tmpa_tl
{ \tl_clear:N \l_tmpa_tl }
\tl_put_right:NV \l_tmpa_tl { #2 * #3 }
\prop_put:NVV \l__diffcoeff_vars_prop #1 \l_tmpa_tl
}
% #1 (propv) key=var, val=coeff; #2 <= total order
\cs_new_protected:Npn \__diffcoeff_evaluate:NN #1#2
{
\prop_map_inline:Nn #1 { \seq_put_left:Nn \l_tmpa_seq { ##1 } }
\seq_sort:Nn \l_tmpa_seq
{
\int_compare:nNnTF { \tl_count:n { ##1 } } < { \tl_count:n { ##2 } }
{ \sort_return_same: } { \sort_return_swapped: }
}
\seq_map_inline:Nn \l_tmpa_seq
{
\prop_pop:NnN #1 { ##1 } \l_tmpb_tl
\seq_put_right:Nx \l_tmpb_seq { \int_eval:n \l_tmpb_tl }
}
\tl_clear:N \l_tmpa_tl
\seq_mapthread_function:NNN \l_tmpa_seq \l_tmpb_seq
\__diffcoeff_tot_order:nn
\exp_args:NV \tl_if_head_eq_charcode:nNTF \l_tmpa_tl +
{
\tl_set:Nx \l_tmpb_tl { \tl_tail:N \l_tmpa_tl }
\int_compare:nNnT { \l__diffcoeff_nos_int } > { 0 }
{ \tl_put_left:Nn \l__diffcoeff_nos_tl { + } }
\tl_concat:NNN #2 \l_tmpb_tl \l__diffcoeff_nos_tl
}
{
\int_compare:nNnTF { \l__diffcoeff_nos_int } > { 0 }
{ \tl_concat:NNN #2 \l__diffcoeff_nos_tl \l_tmpa_tl }
{ \tl_concat:NNN #2 \l_tmpa_tl \l__diffcoeff_nos_tl }
}
\tl_set_rescan:Nno #2 { } #2
}
\cs_new:Npn \__diffcoeff_tot_order:nn #1#2
{
\int_compare:nNnTF { #2 } > { 0 }
{
\int_compare:nNnTF { #2 } = { 1 }
{ \tl_put_left:Nn \l_tmpa_tl { +#1 } }
{ \tl_put_left:Nn \l_tmpa_tl { +#2#1 } }
}
{
\int_compare:nNnT { #2 } < { 0 }
{
\int_compare:nNnTF { #2 } = { -1 }
{ \tl_put_right:Nn \l_tmpa_tl { -#1 } }
{ \tl_put_right:Nn \l_tmpa_tl { #2#1 } }
}
}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% create new instances or edit existing ones
% #1 = name; #2 = key-value list
\NewDocumentCommand \diffdef { > { \TrimSpaces } m m }
{
\tl_if_empty:nTF { #1 }
{
\EditTemplateDefaults { derivative }
{ DERIV } { #2 }
\EditInstance { derivative } { ord } { #2 }
}
{
\IfInstanceExistTF { derivative } { ord.#1 }
{ \EditInstance { derivative } { ord.#1 } { #2 } }
{
\DeclareInstance { derivative } { ord.#1 }
{ DERIV } { #2 }
}
}
}
% relic from version 1
\NewDocumentCommand \diffset { o }
{ \msg_warning:nn { diffcoeff } { obsolete } }
% ordinary & D
\DeclareInstance { derivative } { ord } { DERIV } { }
\bool_if:NTF \l__diffcoeff_ISO_bool
{
\diffdef { }
{
op-symbol = \mathrm{d},
op-order-sep = 0 mu ,
left-delim = \left ( ,
right-delim = \right ) ,
subscr-nudge = -6 mu
}
\diffdef { D } { op-symbol = \mathrm{D} }
}
{ \diffdef { D } { op-symbol = D } }
% partial
\diffdef { p }
{
op-symbol = \partial ,
left-delim = \left ( ,
right-delim = \right ) ,
subscr-nudge = -6 mu
}
\NewDocumentCommand \diffp {} { \diff.p. }
\NewDocumentCommand \dlp {} { \dl.p. }
% delta
\diffdef { delta }
{
op-symbol = \delta ,
op-order-sep = 0 mu
}
\diffdef { Delta }
{
op-symbol = \Delta ,
op-order-sep = 0 mu
}
% for compatibility with version 1
\NewDocumentCommand \Diff { } { \diff.D. }
\NewDocumentCommand \diffd { } { \diff.delta. }
\NewDocumentCommand \Diffd { } { \diff.Delta. }
% user-defined
\file_if_exist:nT { \g__diffcoeff_def_tl.def }
{ \file_input:n { \g__diffcoeff_def_tl.def } }
%%%%%%%%%%%%%%%%%%%%
% Jacobian
\NewDocumentCommand \jacob { m t/ m }
{
\group_begin:
\IfBooleanTF #2
{ \partial(#1) / \partial(#3) }
{ \frac{ \partial(#1) } { \partial(#3) } }
\group_end:
}
%%%%%%%%%%%%%%%%%%%%
% messages
\msg_new:nnn { diffcoeff } { order-specification }
{
#3~followed~by~#2~in~the~order~specification~[#1]~\msg_line_context:.~
Diffcoeff~cannot~calculate~the~overall~order~of~differentiation~in~
this~case.~Use~the~order-override~option~to~enter~the~overall~order.
}
\msg_new:nnn { diffcoeff } { obsolete }
{
Obsolete~command:~\diffset is~superseded~by~the~\diffdef\
command.~\msg_see_documentation_text:n { diffcoeff }
}
\msg_new:nnn { diffcoeff } { numbers-conflict }
{
#2~orders~of~differentiation~specified~for~#1~variables;~
orders~[#3]\ (\msg_line_context:)~for~variables~#4.
}
% end of file diffcoeff4.sty