% This is file `diffcoeff.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
%
\DeclareRelease{v4}{}{diffcoeff4.sty}
\DeclareCurrentRelease{}{2023/11/14}
\RequirePackage{xtemplate,mleftright}
\ProvidesExplPackage {diffcoeff} {2023/11/14} {5.4}
{Write differential coefficients easily and consistently.}
\keys_define:nn { diffcoeff }
{
spaced .int_set:N = \l__diffcoeff_spaced_int,
spaced .default:n = 1,
spaced .initial:n = 0,
mleftright .bool_set:N = \l__diffcoeff_mLR_bool,
mleftright .default:n = true,
mleftright .initial:n = false,
def-file .tl_gset:N = \g__diffcoeff_def_tl,
DIF .clist_set:N = \l__diffcoeff_dif_clist,
ISO .bool_set:N = \l__diffcoeff_ISO_bool % v4 relic
}
\IfFormatAtLeastTF {2020-10-01} {}
{ \RequirePackage { xparse } }
\IfFormatAtLeastTF {2022-06-01}
{ \ProcessKeyOptions [ diffcoeff ] }
{
\RequirePackage { l3keys2e }
\ProcessKeysOptions { diffcoeff }
}
\bool_if:NT \l__diffcoeff_mLR_bool
{ \mleftright }
\cs_if_exist:NTF \seq_map_pairwise_function:NNN
{ \cs_set_eq:NN \__diffcoeff_braid:NNN \seq_map_pairwise_function:NNN }
{ \cs_set_eq:NN \__diffcoeff_braid:NNN \seq_mapthread_function:NNN }
%%%%%%%%%% messages %%%%%%%%%
\cs_new:Npn \__diffcoeff_msg_autocalc:n #1
{
in~the~order~spec.~[#1]~\msg_line_context:.~Calculation~of~the~
total~order~of~differentiation~fails~in~this~case.~
Use~the~override~option~(or~\tl_to_str:n { \difoverride }command)~
to~enter~the~total~order.~\msg_see_documentation_text:n {diffcoeff}
}
\cs_new:Npn \__diffcoeff_msg_style:nnn #1#2#3
{
The~style~specified~in~the~current~instance,~#1,~
\msg_line_context:,~#3~Reverting~to~default~style~#2.
}
\tl_const:Nn \c__diffcoeff_msg_vcon_tl
{ Version~5~of~diffcoeff~does~not~support~the~use~of~ }
\tl_const:Nn \c__diffcoeff_msg_revert_tl
{ Or~revert~to~version~4~by~appending~[=v4]~to~the~preamble~call;~
for~example,~\tl_to_str:n{\usepackage}{diffcoeff}[=v4] }
\msg_new:nnn { diffcoeff } { file-not-found } { File~#1.def~not~found. }
\msg_new:nnn { diffcoeff } { order-spec-general }
{ #3~followed~by~#2~\__diffcoeff_msg_autocalc:n { #1 } }
\msg_new:nnn { diffcoeff } { unknown-style }
{ \__diffcoeff_msg_style:nnn {#1} {#2} { is~unknown. } }
\msg_new:nnn { diffcoeff } { wrong-style }
{ \__diffcoeff_msg_style:nnn {#1} {#2} { conflicts~with~its~template. } }
\msg_new:nnn { diffcoeff } { version-conflict }
{
\c__diffcoeff_msg_vcon_tl #1~\msg_line_context:.~\tl_to_str:n { #2 }
\msg_see_documentation_text:n {diffcoeff}~\c__diffcoeff_msg_revert_tl
}
\msg_new:nnn { diffcoeff } { ISO }
{
Version~5~of~diffcoeff~uses~ISO~settings~by~default.~Package~option~
ISO~is~redundant.~\msg_see_documentation_text:n {diffcoeff}~
\c__diffcoeff_msg_revert_tl
}
\bool_if:NT \l__diffcoeff_ISO_bool
{ \msg_note:nn { diffcoeff } { ISO } }
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\bool_new:N \l__diffcoeff_multitok_bool
\bool_new:N \l__diffcoeff_append_bool
\bool_new:N \l__diffcoeff_op_left_bool
\bool_new:N \l__diffcoeff_exponent_bool
\tl_new:N \l__diffcoeff_override_tl
\tl_new:N \l__diffcoeff_frac_tl
\tl_new:N \l__diffcoeff_derivand_tl
\tl_new:N \l__diffcoeff_instance_tl
\tl_new:N \l__diffcoeff_ord_tl
\tl_new:N \l__diffcoeff_var_tl
\tl_new:N \l__diffcoeff_tot_ord_tl
\tl_new:N \l__diffcoeff_vph_tl
\tl_new:N \l__diffcoeff_exponent_tl
\tl_new:N \l__diffcoeff_curr_num_tl
\tl_new:N \l__diffcoeff_curr_var_tl
\tl_new:N \l__diffcoeff_paren_tl
\seq_new:N \l__diffcoeff_ords_seq
\seq_new:N \l__diffcoeff_vars_seq
\seq_new:N \l__diffcoeff_paren_seq
\int_new:N \l__diffcoeff_group_int
\int_new:N \l__diffcoeff_style_int
\int_new:N \l__diffcoeff_curr_tok_int
\int_new:N \l__diffcoeff_curr_state_int
\int_new:N \l__diffcoeff_nos_int
\int_new:N \l__diffcoeff_parenvar_int
\prop_new:N \l__diffcoeff_vars_prop
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\DeclareObjectType { diffcoeff } { 5 }
% #1 append boolean; #2 order spec(clist); #3 derivand(tl);
% #4 diff variables(clist); #5 pt of eval(tl)
\DeclareTemplateInterface { diffcoeff } { DIF } { 5 }
{
style-group : choice { f, s, c, j, l } = f,
style : choice { frac, tfrac, dfrac,
/, auto, big, Big, bigg, Bigg,
_, dl,d^
} = frac ,
slash-tok : tokenlist = / ,
slash-sep : tokenlist = 0 mu,
derivand-sep : tokenlist = 3 mu plus 1 mu minus 2 mu,
op-symbol : tokenlist = \mathrm{d},
op-symbol-alt : tokenlist = \KeyValue { op-symbol },
op-order-nudge : tokenlist = 0 mu ,
var-sup-nudge : tokenlist = 1 mu ,
multi-term-sep : tokenlist = 2 mu plus 1 mu minus 1 mu,
term-sep-adjust : tokenlist = -1 mu,
long-var-wrap : choice { dv, d(v), (dv) }
= d(v) ,
lvwrap-Ldelim : tokenlist = \mleft (,
lvwrap-Rdelim : tokenlist = \mright ),
lvwrap-sup-nudge : tokenlist = -2 mu,
outer-Ldelim : tokenlist = \left ( ,
outer-Rdelim : tokenlist = \right ),
elbowroom : tokenlist = 0 mu ,
sub-nudge : tokenlist = -5 mu,
op-sub-nudge : tokenlist = 0 mu ,
*derivand-sep : tokenlist = \KeyValue { derivand-sep },
*op-set-left : boolean = false,
*italic-nudge : tokenlist = 0 mu ,
*inner-wrap : boolean = false,
*inner-Ldelim : tokenlist = (,
*inner-Rdelim : tokenlist = ),
*outer-Ldelim : tokenlist = \bigl [,
*outer-Rdelim : tokenlist = \bigr ],
*sub-nudge : tokenlist = 0 mu
}
\DeclareTemplateCode { diffcoeff } { DIF } { 5 }
{
style-group = {
f = \int_set:Nn \l__diffcoeff_group_int { 0 },
s = \int_set:Nn \l__diffcoeff_group_int { 1 },
c = \int_set:Nn \l__diffcoeff_group_int { 2 },
j = \int_set:Nn \l__diffcoeff_group_int { 3 },
l = \int_set:Nn \l__diffcoeff_group_int { 4 }
},
style = {
frac = \__diffcoeff_style:nn { 0 } {},
tfrac = \__diffcoeff_style:nn { 1 } {},
dfrac = \__diffcoeff_style:nn { 2 } {},
/ = \__diffcoeff_style:nn { 3 } {},
auto = \__diffcoeff_style:nn { 4 } {},
big = \__diffcoeff_style:nn { 5 } { big },
Big = \__diffcoeff_style:nn { 5 } { Big },
bigg = \__diffcoeff_style:nn { 5 } { bigg },
Bigg = \__diffcoeff_style:nn { 5 } { Bigg },
_ = \__diffcoeff_style:nn { 6 } {},
d^ = \__diffcoeff_style:nn { 6 } {},
dl = \__diffcoeff_style:nn { 7 } {},
unknown = \__diffcoeff_style:nn { 9 } {}
},
slash-tok = \l__diffcoeff_slashtok_tl,
slash-sep = \l__diffcoeff_slashsep_tl,
derivand-sep = \l__diffcoeff_derivsep_tl,
op-symbol = \l__diffcoeff_opi_tl,
op-symbol-alt = \l__diffcoeff_opii_tl,
op-order-nudge = \l__diffcoeff_opordsep_tl,
var-sup-nudge = \l__diffcoeff_varsupnudge_tl,
multi-term-sep = \l__diffcoeff_termsep_tl,
term-sep-adjust = \l__diffcoeff_sep_adj_tl,
long-var-wrap = {
dv = \cs_set_eq:NN \__diffcoeff_wrap_longvars:nn
\__diffcoeff_wrap_longvars_dv:nn,
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
},
lvwrap-Ldelim = \l__diffcoeff_lvw_ldelim_tl,
lvwrap-Rdelim = \l__diffcoeff_lvw_rdelim_tl,
lvwrap-sup-nudge = \l__diffcoeff_lvsupnudge_tl,
outer-Ldelim = \l__diffcoeff_ldelim_tl,
outer-Rdelim = \l__diffcoeff_rdelim_tl,
elbowroom = \l__diffcoeff_elbowrm_tl ,
sub-nudge = \l__diffcoeff_subnudge_tl,
op-sub-nudge = \l__diffcoeff_opsubnudge_tl,
*derivand-sep = \l__diffcoeff_derivsepi_tl,
*op-set-left = \l__diffcoeff_op_left_bool,
*italic-nudge = \l__diffcoeff_opleftnudge_tl,
*inner-wrap = \l__diffcoeff_innerwrap_bool,
*inner-Ldelim = \l__diffcoeff_lopwrap_tl,
*inner-Rdelim = \l__diffcoeff_ropwrap_tl,
*outer-Ldelim = \l__diffcoeff_ldelimapp_tl,
*outer-Rdelim = \l__diffcoeff_rdelimapp_tl,
*sub-nudge = \l__diffcoeff_subnudgeapp_tl
}
{
\AssignTemplateKeys
\__diffcoeff_check_style:nn
{ \l__diffcoeff_group_int } { \l__diffcoeff_style_int }
\__diffcoeff_append:n { #1 }
\__diffcoeff_orders_vars:nn { #2 } { #4 }
\__diffcoeff_derivand:n { #3 }
\__diffcoeff_build:nn { #4 } { #5 }
}
%%%%%%%%%%
\cs_new_protected:Npn \__diffcoeff_style:nn #1#2
{
\int_set:Nn \l__diffcoeff_style_int { #1 }
\tl_set:Nn \l__diffcoeff_frac_tl { \prg_do_nothing: }
\int_case:nn { #1 }
{
{ 0 } { \tl_set:Nn \l__diffcoeff_frac_tl { \frac } }
{ 1 } { \tl_set:Nn \l__diffcoeff_frac_tl { \tfrac } }
{ 2 } { \tl_set:Nn \l__diffcoeff_frac_tl { \dfrac } }
{ 3 } { \tl_set:Nn \l__diffcoeff_frac_tl { \difstfrac } }
{ 4 } { \tl_set:Nn \l__diffcoeff_frac_tl { \difsafrac } }
{ 5 } { \tl_set:Nn \l__diffcoeff_frac_tl { \difsbfrac[#2] } }
{ 6 } { \tl_set:Nn \l__diffcoeff_frac_tl {} }
{ 7 } { \tl_set:Nn \l__diffcoeff_frac_tl {} }
{ 9 }
{
\msg_error:nnxx { diffcoeff } { unknown-style }
{ \l__diffcoeff_instance_tl }
{ \__diffcoeff_style_group_base:n { \l__diffcoeff_group_int } }
}
}
}
% #1 group int; #2 style int
\cs_new_protected:Npn \__diffcoeff_check_style:nn #1#2
{
\bool_if:nF
{
( \int_compare_p:nNn { \int_div_truncate:nn {#2} {3} } = { #1 }
&& \int_compare_p:nNn { #1 } < { 3 } ) % f,s,c
|| ( \int_compare_p:nNn { \int_div_truncate:nn {#2} {2} } < { #1 }
&& \int_compare_p:nNn { #1 } = { 3 } ) % j
|| \int_compare_p:nNn { #1 + #2 } > { 9 } % l
}
{
\msg_warning:nnxx { diffcoeff } { wrong-style }
{ \l__diffcoeff_instance_tl }
{ \__diffcoeff_style_group_base:n { #1 } }
\int_compare:nNnTF { #1 } = { 3 }
{ \__diffcoeff_style:nn { 0 } {} }
{
\int_compare:nNnTF { #1 } = { 4 }
{ \__diffcoeff_style:nn { 7 } {} }
{ \__diffcoeff_style:nn { 3*#1 } {} }
}
}
\bool_if:nT
{ \int_compare_p:nNn { #1 } > { 0 } && \int_if_even_p:n { #1 } }
{ \tl_set_eq:NN \l__diffcoeff_opii_tl \l__diffcoeff_opi_tl }
\int_compare:nNnF { #1 } = { 1 }
{ \bool_set_false:N \l__diffcoeff_innerwrap_bool }
}
\cs_new:Npn \__diffcoeff_style_group_base:n #1
{ \clist_item:nn { frac, /, _, frac, dl } { #1 + 1 } }
%%%%%%%%% append? (& wrap slash diff operator?)
\cs_new_protected:Npn \__diffcoeff_append:n #1
{
\bool_if:nTF
{ #1 || \int_compare_p:nNn { \l__diffcoeff_group_int } = {2} }
{
\bool_set_true:N \l__diffcoeff_append_bool
\bool_if:NT \l__diffcoeff_innerwrap_bool
{ \tl_put_right:Nn \l__diffcoeff_frac_tl { * } }
}
{ \bool_set_false:N \l__diffcoeff_append_bool }
}
%%%%%%%%% #1 orders, #2 vars
\cs_new_protected:Npn \__diffcoeff_orders_vars:nn #1#2
{
\str_if_eq:nnT { #2 } { / }
{ % v4 notation
\msg_error:nnnn { diffcoeff } { version-conflict } { / }
{ Use~\difs or~\difsp instead.~ }
}
\clist_if_empty:nTF { #2 }
{
\seq_set_from_clist:Nn \l__diffcoeff_vars_seq { \prg_do_nothing: }
\__diffcoeff_orders:nn { 1 } { #1 }
}
{
\exp_args:NnV
\str_if_in:nnTF { #2 } \c_colon_str
{
\str_set:Nn \l_tmpa_str { #2 }
\clist_map_inline:Nn \l_tmpa_str
{
\exp_args:NNV
\seq_set_split:Nnn \l_tmpa_seq \c_colon_str { ##1 }
\seq_pop:NN \l_tmpa_seq \l_tmpa_tl
\seq_put_right:NV \l__diffcoeff_vars_seq \l_tmpa_tl
\seq_if_empty:NTF \l_tmpa_seq
{ \seq_put_right:Nn \l__diffcoeff_ords_seq { 1 } }
{
\seq_pop:NN \l_tmpa_seq \l_tmpa_tl
\tl_set_rescan:Nno
\l_tmpa_tl \ExplSyntaxOn \l_tmpa_tl
\seq_put_right:NV \l__diffcoeff_ords_seq \l_tmpa_tl
}
}
}
{
\seq_set_from_clist:Nn \l__diffcoeff_vars_seq { #2 }
\exp_args:Nx \__diffcoeff_orders:nn
{ \int_max:nn { 1 } { \clist_count:n {#2} } } { #1 }
}
}
\__diffcoeff_override:N \l__diffcoeff_override_tl
}
% #1(int) no. of vars; #2(clist) orders spec
\cs_new_protected:Npn \__diffcoeff_orders:nn #1#2
{
\bool_if:NTF \l__diffcoeff_exponent_bool
{
\exp_args:NNx
\seq_set_from_clist:Nn \l__diffcoeff_ords_seq
{ \prg_replicate:nn { #1 } { \l__diffcoeff_exponent_tl, } }
}
{
\seq_set_from_clist:Nn \l__diffcoeff_ords_seq { #2 }
\exp_args:Nnx\__diffcoeff_adj_ords_seq:nn { #1 }
{ \seq_count:N \l__diffcoeff_ords_seq }
}
\tl_set:Nx \l__diffcoeff_vph_tl { \seq_use:Nn\l__diffcoeff_ords_seq {} }
}
\cs_new_protected:Npn \__diffcoeff_adj_ords_seq:nn #1#2
{
\int_compare:nNnTF { #1 } < { #2 }
{ % truncate
\int_step_inline:nn { #2 - #1 }
{ \seq_pop_right:NN \l__diffcoeff_ords_seq \l_tmpa_tl }
}
{ % pad
\int_step_inline:nnnn { 1 + #2 } { 1 } { #1 }
{ \seq_put_right:Nn \l__diffcoeff_ords_seq { 1 } }
}
}
\cs_new_protected:Npn \__diffcoeff_override:N #1
{
\tl_if_empty:NTF #1
{
\__diffcoeff_calc_tot_order:NN \l__diffcoeff_ords_seq
\l__diffcoeff_tot_ord_tl
}
{ \tl_set_eq:NN \l__diffcoeff_tot_ord_tl #1 }
\seq_pop_right:NN \l__diffcoeff_ords_seq \l__diffcoeff_ord_tl
}
%%%%%%%%%% calc. total order %%%%%%%%%%
% #1(seq) expr in; #2(tl) expr out
\cs_new_protected:Npn \__diffcoeff_calc_tot_order:NN #1 #2
{
\tl_clear:N \l__diffcoeff_nos_tl
\exp_args:Nx \__diffcoeff_digest_expr:n { \seq_use:Nn #1 { + } }
\prop_if_empty:NTF \l__diffcoeff_vars_prop
{ \tl_set:NV #2 \l__diffcoeff_nos_tl }
{
\int_compare:nNnT { \l__diffcoeff_nos_int } = { 0 }
{ \tl_clear:N \l__diffcoeff_nos_tl }
\__diffcoeff_evaluate:NN \l__diffcoeff_vars_prop #2
}
}
\cs_new_protected:Npn \__diffcoeff_digest_expr:n #1
{
\tl_set:Nn \l__diffcoeff_curr_num_tl { + }
\tl_set:Nn \l__diffcoeff_paren_tl { +1 }
\tl_set:Nn \l__diffcoeff_nos_tl { 0 }
\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 }
}
% #1 curr tok (tl); #2 <== curr tok ndx (int)
\cs_new_protected:Npn \__diffcoeff_get_curr_ndx:nN #1#2
{
\tl_if_in:nnTF { 1234567890 } { #1 }
{ \int_set:Nn #2 { 1 } } % digit
{
\tl_if_in:nnTF { +- } { #1 }
{ \int_set:Nn #2 { 0 } }
{
\tl_if_eq:nnTF { ( } { #1 }
{ \int_set:Nn #2 { 3 } }
{
\tl_if_eq:nnTF { ) } { #1 }
{ \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
{
\str_if_eq:nVTF { #1 } \l__diffcoeff_curr_num_tl
{ \tl_set:Nn \l__diffcoeff_curr_num_tl { + } }
{ \tl_set:Nn \l__diffcoeff_curr_num_tl { - } }
}
{ 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 * / } { #1 }
{
\msg_error:nnxxx { diffcoeff } { order-spec-general }
{ \seq_use:Nn \l__diffcoeff_ords_seq { , } }
{ #1 } { number }
}
{ \tl_set:Nn \l__diffcoeff_curr_var_tl { #1 } }
}
{ 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-spec-general }
{ \seq_use:Nn \l__diffcoeff_ords_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
{
\seq_clear:N \l_tmpa_seq
\seq_clear:N \l_tmpb_seq
\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_set:Nx \l_tmpa_tl
{
\__diffcoeff_braid: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 } { +#1 } { +#2#1 } }
{
\int_compare:nNnT { #2 } < { 0 }
{ \int_compare:nNnTF { #2 } = { -1 } { -#1 } { #2#1 } }
}
}
%%%%%%%%% derivand
\cs_new_protected:Npn \__diffcoeff_derivand:n #1
{
\tl_set:Nn \l__diffcoeff_derivand_tl { #1 }
\int_compare:nNnTF { \tl_count:N \l__diffcoeff_derivand_tl } > { 1 }
{ \bool_set_true:N \l__diffcoeff_multitok_bool }
{
\str_if_eq:VnT \l__diffcoeff_derivand_tl { ! }
{ \msg_error:nnnn { diffcoeff } { version-conflict } { #1 } {} }
}
}
%%%%%%%%% build #1 vars clist; #2 trailing arg
\cs_new_protected:Npn \__diffcoeff_build:nn #1#2
{
\seq_pop_right:NN \l__diffcoeff_vars_seq \l__diffcoeff_var_tl
\int_compare:nNnF { \l__diffcoeff_group_int } = { 4 }
{
\tl_put_left:Nx \l__diffcoeff_derivand_tl
{ \__diffcoeff_spaced:n { \l__diffcoeff_spaced_int } }
}
\__diffcoeff_wrap_and_form:nn { #2 }
{
\__diffcoeff_form_deriv:xNN
{ \__diffcoeff_build_numer:Vn \l__diffcoeff_tot_ord_tl
{ \l__diffcoeff_style_int } }
\__diffcoeff_build_denom:
\l__diffcoeff_derivand_tl
}
}
% extra braces for \[ \alert{\dl x} \] in beamer
\cs_new:Npn \__diffcoeff_wrap_and_form:nn #1#2
{
\tl_if_novalue:nTF {#1}
{{ #2 }}
{{
\__diffcoeff_delim:N l \mskip \l__diffcoeff_elbowrm_tl
#2
\__diffcoeff_trailing_arg:n { #1 }
}}
}
\cs_new:Npn \__diffcoeff_delim:N #1
{
\bool_if:nTF { \l__diffcoeff_innerwrap_bool && \l__diffcoeff_append_bool }
{ \use:c { l__diffcoeff_#1 delimapp_tl } }
{ \use:c { l__diffcoeff_#1 delim_tl } }
}
\cs_new:Npn \__diffcoeff_subnudge:
{
\bool_if:nTF { \l__diffcoeff_innerwrap_bool && \l__diffcoeff_append_bool }
{ \l__diffcoeff_subnudgeapp_tl } { \l__diffcoeff_subnudge_tl }
}
\cs_new:Npn \__diffcoeff_trailing_arg:n #1
{
\mskip \l__diffcoeff_elbowrm_tl \__diffcoeff_delim:N r
\tl_if_empty:nF { #1 }
{ \c_math_subscript_token { \mskip \__diffcoeff_subnudge: #1 } }
}
\cs_new:Npn \__diffcoeff_spaced:n #1
{
\int_case:nn { \int_sign:n { #1 } }
{
{ 1 } { \__diffcoeff_derivsep: }
{ 0 } { \mskip 0 mu }
{-1 }
{
\bool_lazy_or:nnT { \l__diffcoeff_multitok_bool }
{ \int_compare_p:nNn { \l__diffcoeff_group_int } = { 2 } }
{ \__diffcoeff_derivsep: }
}
}
}
\cs_new:Npn \__diffcoeff_derivsep:
{
\bool_if:NTF \l__diffcoeff_append_bool
{ \mskip \l__diffcoeff_derivsepi_tl }
{ \mskip \l__diffcoeff_derivsep_tl }
}
%%%%%%%%% numerator #1 total order tl #2 style int
\cs_new:Npn \__diffcoeff_build_numer:nn #1#2
{
\int_compare:nNnF { #2 } > { 5 }
{
\bool_if:NT \l__diffcoeff_op_left_bool
{ \mskip \l__diffcoeff_opleftnudge_tl }
\exp_not:o \l__diffcoeff_opi_tl
\str_if_eq:nnF {#1} {1}
{ ^ { \mskip \l__diffcoeff_opordsep_tl \exp_not:o {#1} } }
\bool_if:NT \l__diffcoeff_op_left_bool
{ \exp_not:o { \hfill } }
}
}
\cs_generate_variant:Nn \__diffcoeff_build_numer:nn { V }
%%%%%%%%%% denominator %%%%%%%%%
\cs_new:Npn \__diffcoeff_build_denom:
{
\__diffcoeff_braid:NNN \l__diffcoeff_ords_seq
\l__diffcoeff_vars_seq \__diffcoeff_build_denom_items:nn
\__diffcoeff_build_denom_item:VV \l__diffcoeff_ord_tl \l__diffcoeff_var_tl
\str_if_eq:VnF \l__diffcoeff_ord_tl { 1 }
{
\int_compare:nNnT { \l__diffcoeff_group_int } < { 2 }
{ \mskip -\l__diffcoeff_sep_adj_tl}
}
}
\cs_new:Npn \__diffcoeff_build_denom_items:nn#1#2
{
\__diffcoeff_build_denom_item:nn {#1} {#2}
\mskip \l__diffcoeff_termsep_tl
}
% #1 order #2 var
\cs_new:Npn \__diffcoeff_build_denom_item:nn #1#2
{
\int_compare:nNnTF { \l__diffcoeff_style_int } = { 6 }
{ \__diffcoeff_build_denom_difc:onn \l__diffcoeff_vph_tl {#1}{#2} }
{ \__diffcoeff_build_denom_dif:nn {#1} {#2} }
}
\cs_generate_variant:Nn \__diffcoeff_build_denom_item:nn { VV }
% #1 vphantom orders #2 order #3 var
\cs_new:Npn \__diffcoeff_build_denom_difc:nnn #1#2#3
{
\exp_not:o \l__diffcoeff_opii_tl
\int_compare:nNnTF { \l__diffcoeff_group_int } = { 4 }
{
\str_if_eq:nnF { #2 } { 1 }
{ ^{ \mskip \l__diffcoeff_opordsep_tl \exp_not:o {#2} } }
#3
}
{
\c_math_subscript_token { \mskip \l__diffcoeff_opsubnudge_tl {}#3 }
^
{
\mskip \l__diffcoeff_opordsep_tl \exp_not:o { \vphantom{#1} }
\str_if_eq:nnF { #2 } { 1 }
{ \exp_not:o {#2} \mskip \l__diffcoeff_sep_adj_tl }
}
}
}
\cs_generate_variant:Nn \__diffcoeff_build_denom_difc:nnn { o }
% #1 order #2 var
\cs_new:Npn \__diffcoeff_build_denom_dif:nn #1#2
{
\str_if_eq:nnTF { #1 } { 1 }
{ \exp_not:o { \l__diffcoeff_opii_tl #2 } }
{
\int_compare:nNnTF { \tl_count:n { #2 } } = { 1 }
{ \exp_not:o { \l__diffcoeff_opii_tl {}#2^
{ \mskip \l__diffcoeff_varsupnudge_tl #1 } } }
{ \__diffcoeff_wrap_longvars:nn { #1 } { #2 } }
\mskip \l__diffcoeff_sep_adj_tl
}
}
\cs_new:Npn \__diffcoeff_wrap_longvars_dv:nn #1#2
{ \exp_not:o { \l__diffcoeff_opii_tl {{}#2 }^
{ \mskip \l__diffcoeff_varsupnudge_tl #1 } } }
\cs_new:Npn \__diffcoeff_wrap_longvars_dvi:nn #1#2
{
\exp_not:o { \l__diffcoeff_opii_tl \l__diffcoeff_lvw_ldelim_tl #2
\l__diffcoeff_lvw_rdelim_tl^{ \mskip \l__diffcoeff_lvsupnudge_tl #1 } }
}
\cs_new:Npn \__diffcoeff_wrap_longvars_dvii:nn #1#2
{
\exp_not:o { \l__diffcoeff_lvw_ldelim_tl \l__diffcoeff_opii_tl {}#2
\l__diffcoeff_lvw_rdelim_tl^{ \mskip \l__diffcoeff_lvsupnudge_tl #1 } }
}
%%%%%%%%%%
% #1 op+order; #2 denom; #3 diff'iand
\cs_new:Npn \__diffcoeff_form_deriv:nNN #1#2#3
{
\bool_if:NTF \l__diffcoeff_append_bool
{ \l__diffcoeff_frac_tl { #1 } { #2 } #3 }
{ \l__diffcoeff_frac_tl { #1 #3 } { #2 } }
}
\cs_generate_variant:Nn \__diffcoeff_form_deriv:nNN { x }
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\file_get:nnNT { diffcoeff.DIF } {} \l_tmpa_tl
{ \exp_args:Nnno \EditTemplateDefaults { diffcoeff } { DIF } \l_tmpa_tl }
\exp_args:Nnno \EditTemplateDefaults { diffcoeff } { DIF }
\l__diffcoeff_dif_clist
% Child template with some restricted, some new defaults.
% #1 object type #2 parent template #3 child template
% #4 restricted defaults (key=value) #5 new defaults (key=value)
\NewDocumentCommand \DeclareChildTemplate { m m m m m }
{
\DeclareRestrictedTemplate {#1} {#2} {#3} {}
\EditTemplateDefaults {#1} {#3} {#5}
\DeclareRestrictedTemplate {#1} {#3} {#3} {#4}
}
% create new, edit existing templates/instances;
% #1 edit defaults with (no *) or without (*) inheritance;
% #2 id: f,s,c,fp, sp, cp, j,l; #3 name; #4 key-value list
\NewDocumentCommand \difdef { >{ \TrimSpaces } m >{ \TrimSpaces } m m }
{
\clist_map_inline:nn { #1 }
{
\tl_if_empty:nTF { #2 }
{
\DeclareChildTemplate { diffcoeff }
{ DIF\str_uppercase:n {##1} } { DIF\str_uppercase:n {##1} }
{ style-group = \use_i:nn ##1 \c_empty_tl } { #3 }
\DeclareInstance { diffcoeff } { dif##1 }
{ DIF\str_uppercase:n {##1} } {}
}
{
\IfInstanceExistTF { diffcoeff } { dif##1.#2 }
{ \EditInstance { diffcoeff } { dif##1.#2 } { #3 } }
{ \exp_args:Nnnx
\DeclareInstance { diffcoeff } { dif##1.#2 }
{ DIF\str_uppercase:n {##1} } { #3 }
}
}
}
}
\DeclareDocumentCommand \diffdef { m m }
{
\msg_error:nnnn { diffcoeff } { version-conflict } { \diffdef~(two~
arguments) } { Use~\difdef~(three~arguments)~instead.~ }
}
\DeclareChildTemplate { diffcoeff } { DIF } { DIFF }
{ style-group = f } {}
\DeclareChildTemplate { diffcoeff } { DIFF } { DIFFP }
{ style-group = f }
{
op-symbol = \partial,
op-order-nudge = 1 mu,
*italic-nudge = 3 mu
}
\DeclareChildTemplate { diffcoeff } { DIF } { DIFS }
{ style-group = s }
{
style = /,
derivand-sep = 2 mu plus 1 mu minus 2 mu,
outer-Ldelim = (,
outer-Rdelim = ),
sub-nudge = 0 mu,
*inner-wrap = true
}
\DeclareChildTemplate { diffcoeff } { DIFS } { DIFSP }
{ style-group = s }
{
op-symbol = \partial,
op-order-nudge = 1 mu
}
\DeclareChildTemplate { diffcoeff } { DIF } { DIFC }
{ style-group = c }
{
style = _ ,
derivand-sep = 1 mu plus 1 mu minus 1 mu ,
multi-term-sep = 1 mu ,
term-sep-adjust = 0 mu ,
outer-Ldelim = \bigl (,
outer-Rdelim = \bigr ),
sub-nudge = -2 mu
}
\DeclareChildTemplate { diffcoeff } { DIFC } { DIFCP }
{ style-group = c }
{
op-symbol = \partial,
op-order-nudge = 1 mu
}
\DeclareInstance { diffcoeff } { diff } { DIFF } {}
\DeclareInstance { diffcoeff } { diffp } { DIFFP } {}
\DeclareInstance { diffcoeff } { difs } { DIFS } {}
\DeclareInstance { diffcoeff } { difsp } { DIFSP } {}
\DeclareInstance { diffcoeff } { difc } { DIFC } {}
\DeclareInstance { diffcoeff } { difcp } { DIFCP } {}
% jacobian
\DeclareChildTemplate { diffcoeff } { DIF } { DIFJ }
{ style-group = j }
{
op-symbol = \partial,
outer-Ldelim = ,
outer-Rdelim =
}
\DeclareInstance { diffcoeff } { difj } { DIFJ } {}
% differential
\DeclareChildTemplate { diffcoeff } { DIF } { DIFL }
{ style-group = l }
{
style = dl ,
derivand-sep = 0 mu,
long-var-wrap = dv ,
outer-Ldelim = {\,},
outer-Rdelim =
}
\DeclareInstance { diffcoeff } { difl } { DIFL } {}
\file_if_exist:nTF { \g__diffcoeff_def_tl.def }
{ \file_input:n { \g__diffcoeff_def_tl.def } }
{
\tl_if_empty:NF \g__diffcoeff_def_tl
{ \msg_note:nnx { diffcoeff } { file-not-found }
{ \g__diffcoeff_def_tl } }
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\NewDocumentCommand \negmu {} { \mskip -1 mu }
\NewDocumentCommand \nilmu {} { \mskip 0 mu }
\NewDocumentCommand \onemu {} { \mskip 1 mu }
\NewDocumentCommand \twomu {} { \mskip 2 mu }
\NewDocumentCommand \difstfrac { s m m }
{ \__diffcoeff_slashfracs:Nnnn #1 { #2 } { #3 } {} }
\NewDocumentCommand \difsbfrac { o s m m }
{ \__diffcoeff_slashfracs:Nnnn #2 { #3 } { #4 } { \use:c{#1} } }
\NewDocumentCommand \difsafrac { s m m }
{ \__diffcoeff_slashfracs:Nnnn #1 { \left. #2\vphantom{#3} }
{ #3\right.} { \middle } }
\cs_new:Npn \__diffcoeff_slashfracs:Nnnn #1#2#3#4
{
\bool_if:NT #1 { \l__diffcoeff_lopwrap_tl }
#2 \mskip \l__diffcoeff_slashsep_tl
#4 \l__diffcoeff_slashtok_tl
\mskip \l__diffcoeff_slashsep_tl #3
\bool_if:NT #1 { \l__diffcoeff_ropwrap_tl }
}
\NewDocumentCommand \difoverride { >{\TrimSpaces} m }
{ \tl_set:Nn \l__diffcoeff_override_tl { #1 } }
% derivatives
% #1(tl) variant name; #2(*) append boolean; #3(*) switch #5#6 order;
% #4(clist) diff. orders; #5(tl) = derivand; #6(clist) = diff. vars;
% #7(tl) = pt of eval./vars held const
\clist_map_inline:nn { f,s,c, fp, sp, cp }
{
\exp_args:Nc \NewDocumentCommand {dif#1}
{ >{\TrimSpaces} D..{} s s O{1} D<>{} >{\TrimSpaces} m m !o }
{
\IfBooleanTF ##3
{ \__diffcoeff_inputs:nnnnnnnn {#1}
{##1} {##2} {##4} {##7} {##6} {##8} {##5} }
{ \__diffcoeff_inputs:nnnnnnnn {#1}
{##1} {##2} {##4} {##6} {##7} {##8} {##5} }
}
}
\cs_new_protected:Npn \__diffcoeff_inputs:nnnnnnnn #1#2#3#4#5#6#7#8
{
\group_begin:
\tl_if_empty:nF { #8 }
{ \tl_set:Nn \l__diffcoeff_override_tl { #8 } }
\tl_set:Nx \l__diffcoeff_instance_tl
{ dif#1 \tl_if_empty:nF { #2 } { .#2 } }
\UseInstance { diffcoeff } { \l__diffcoeff_instance_tl }
{#3} {#4} {#5} {#6} {#7}
\group_end:
}
% Jacobian
\NewDocumentCommand \jacob { >{\TrimSpaces} D..{} m m }
{
\group_begin:
\int_zero:N \l__diffcoeff_spaced_int
\tl_set:Nx \l__diffcoeff_instance_tl
{ difj \tl_if_empty:nF { #1 } { .#1 } }
\UseInstance { diffcoeff } { \l__diffcoeff_instance_tl }
{ \c_false_bool } {}
{ \l__diffcoeff_lvw_ldelim_tl #2 \l__diffcoeff_lvw_rdelim_tl }
{ {\l__diffcoeff_lvw_ldelim_tl #3\l__diffcoeff_lvw_rdelim_tl } } {}
\group_end:
}
\NewDocumentCommand \difj {} { \jacob }
% differential; #1 variant ; #2 ord(s); #3 vars; #4 exponent
\NewDocumentCommand \dl { >{ \TrimSpaces } D..{} O{1} m e{^} }
{
\group_begin:
\tl_set:Nx \l__diffcoeff_instance_tl
{ difl \tl_if_empty:nF { #1 } { .#1 } }
\difoverride {}
\tl_set:Nn \l__diffcoeff_exponent_tl { #4 }
\tl_if_novalue:nTF {#4}
{ \bool_set_false:N \l__diffcoeff_exponent_bool }
{ \bool_set_true:N \l__diffcoeff_exponent_bool }
\UseInstance { diffcoeff } { \l__diffcoeff_instance_tl }
{\c_false_bool} {#2} {} {#3} {}
\group_end:
}
\NewDocumentCommand \difl {} { \dl }
% end of file diffcoeff.sty