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derivative.sty
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% derivative.sty
% Copyright 2019-2022 Simon Jensen
%
% This work may be distributed and/or modified under the
% conditions of the LaTeX Project Public License, either version 1.3
% of this license or (at your option) any later version.
% The latest version of this license is in
% http://www.latex-project.org/lppl.txt
% and version 1.3 or later is part of all distributions of LaTeX
% version 2005/12/01 or later.
%
% This work has the LPPL maintenance status `maintained'.
%
% The Current Maintainer of this work is Simon Jensen.
% Contributors: Romain Noel
\NeedsTeXFormat{LaTeX2e}
\RequirePackage{expl3}[2021/11/07]
\RequirePackage{xparse}[2021/11/07]
\RequirePackage{l3keys2e}
\ProvidesExplPackage{derivative}{2022/07/09}{1.2}{Nice and easy derivatives and differentials for LaTeX}
\bool_new:N \l__deriv_pkg_italic_bool
\bool_new:N \l__deriv_pkg_upright_bool
\keys_define:nn { deriv/pkg }
{
italic .choice:,
italic .usage:n = { load },
italic .default:n = { true },
italic / true .code:n =
{
\bool_set_true:N \l__deriv_pkg_italic_bool
\bool_set_false:N \l__deriv_pkg_upright_bool
},
italic / false .code:n =
{
\bool_set_false:N \l__deriv_pkg_italic_bool
\bool_set_true:N \l__deriv_pkg_upright_bool
},
italic / unknown .code:n = { \msg_error:nnx { deriv } { boolean-values-only } \l_keys_key_str },
upright .choice:,
upright .usage:n = { load },
upright .default:n = { true },
upright / true .code:n =
{
\bool_set_true:N \l__deriv_pkg_upright_bool
\bool_set_false:N \l__deriv_pkg_italic_bool
},
upright / false .code:n =
{
\bool_set_false:N \l__deriv_pkg_upright_bool
\bool_set_true:N \l__deriv_pkg_italic_bool
},
upright / unknown .code:n = { \msg_error:nnx { deriv } { boolean-values-only } \l_keys_key_str },
upright .initial:n = true,
}
\ProcessKeysPackageOptions{ deriv/pkg }
%%%%% Useful conditionals %%%%%
\prg_new_conditional:Npnn \__deriv_if_value:n #1 { T, TF }
{
\tl_if_novalue:nTF {#1}
{ \prg_return_false: }
{
\tl_if_blank:nTF {#1}
{ \prg_return_false: }
{ \prg_return_true: }
}
}
\prg_new_conditional:Npnn \__deriv_show_order:N #1 { T, TF }
{
\str_if_eq:NNTF #1 1
{ \prg_return_false: }
{ \prg_return_true: }
}
%%%%% Variables: derivatives %%%%%
\tl_new:N \l__deriv_dv_denom_tl
\seq_new:N \l__deriv_dv_var_seq
\seq_new:N \l__deriv_dv_order_seq
\seq_new:N \l__deriv_dv_variant_seq
%%%%% Variables: differential %%%%%
\seq_new:N \l__deriv_i_var_seq
\seq_new:N \l__deriv_i_order_seq
\tl_new:N \l__deriv_i_denom_tl
\seq_new:N \l__deriv_i_variant_seq
%%%%% Variables: other %%%%%
\tl_new:N \l__deriv_cs_name_tl
\tl_new:N \l__deriv_derivset_tl
\tl_new:N \l__deriv_tmpa_tl
\tl_new:N \l__deriv_tmpb_tl
\tl_new:N \l__deriv_tmpc_tl
\seq_new:N \l__deriv_tmpa_seq
\seq_new:N \l__deriv_new_var_seq
\seq_new:N \l__deriv_rubber_seq
\seq_new:N \l__deriv_add_var_bool_seq
\int_new:N \l__deriv_vmo_int
\tl_new:N \l__deriv_sym_tmpa_tl
\tl_new:N \l__deriv_num_tmpa_tl
\tl_new:N \l__deriv_sym_tmpb_tl
\tl_new:N \l__deriv_num_tmpb_tl
\tl_new:N \l__deriv_input_tl
\seq_new:N \l__deriv_input_seq
\seq_new:N \l__deriv_extract_seq
\seq_new:N \l__deriv_permutation_seq
\seq_new:N \l__deriv_sorted_seq
\seq_new:N \l__deriv_symbol_seq
\seq_new:N \l__deriv_number_seq
\int_new:N \l__deriv_var_count_int
\int_new:N \l__deriv_tmpa_int
\int_new:N \l__deriv_tmpb_int
\int_new:N \l__deriv_numerical_int
\int_new:N \l__deriv_sort_max_int
\regex_const:Nn \c__deriv_cs_numbers_regex { \A\-?\d+(?:,\d+){0,2}\Z }
\tl_const:Nn \c__deriv_digits_tl {-1234567890}
% numerator, denumerator
\DeclareDocumentCommand{\compactfrac}{ m m }
{ #1 #2 }
%%%%% default values %%%%%
\prop_const_from_keyval:Nn \c__deriv_dv_pkg_keys_prop
{
style-inf = d,
style-frac = \frac,
style-frac-/ = \slashfrac,
style-frac-/! = \slashfrac,
style-frac-! = \compactfrac,
style-var = {single-right},
style-var-* = {multiple-right},
style-var-/ = {single-mixed},
style-var-! = {multiple-mixed},
style-var-/! = {single-single},
style-var-*/! = {multiple-left},
style-var-*/ = {single-right},
style-var-*! = {multiple-right},
scale-eval = auto,
scale-eval-/ = auto,
scale-fun = auto,
scale-var = auto,
scale-frac = auto,
scale-frac-/ = auto,
delims-eval = .\rvert,
delims-eval-/ = .\rvert,
delims-fun = (),
delims-var = (),
delims-frac = (),
delims-frac-/ = (),
sep-inf-ord = 0,
sep-inf-fun = 0,
sep-ord-fun = 0,
sep-frac-fun = 0,
sep-inf-var = 0,
sep-var-ord = 0,
sep-var-inf = \mathop{}\!,
sep-ord-inf = \mathop{}\!,
sep-ord-ord = {,},
sep-ord-var = 0,
sep-var-var = {,},
sep-eval-sb = 0,
sep-eval-sp = 0,
switch-* = false,
switch-/ = false,
switch-! = false,
switch-sort = true,
sort-method = {sign, symbol, abs},
sort-numerical = auto,
sort-abs-reverse = false,
sort-number-reverse = false,
sort-sign-reverse = false,
sort-symbol-reverse = false,
sort-lexical-reverse = false,
fun = false,
frac = false,
var = none,
order = 1,
mixed-order = 1
}
\prop_const_from_keyval:Nn \c__deriv_i_pkg_keys_prop
{
style-inf = d,
style-var = {multiple-left},
style-var-* = {single-mixed},
scale-var = auto,
scale-var-* = auto,
delims-var = (),
delims-var-* = (),
sep-begin = \mathop{}\!,
sep-inf-ord = 0,
sep-inf-var = 0,
sep-ord-var = 0,
sep-var-ord = 0,
sep-ord-inf = \mathop{}\!,
sep-var-inf = \mathop{}\!,
sep-var-var = {,},
sep-ord-ord = {,},
sep-end = 0,
switch-* = false,
var = none,
order = 1
}
%%%%%% Key-val for all %%%%%%
\prop_new:N \l__deriv_all_all_user_keys_prop
\prop_const_from_keyval:Nn \c__deriv_all_pkg_keys_prop
{ scale-auto = leftright }
\keys_define:nn { deriv/all/all }
{
scale-auto .choice:,
scale-auto / leftright .code:n =
{
\cs_set_eq:NN \__deriv_auto_left:n \left
\cs_set_eq:NN \__deriv_auto_right:n \right
},
scale-auto / mleftmright .code:n =
{
\cs_set_nopar:Npn \__deriv_auto_left:n { \mleft }
\cs_set_nopar:Npn \__deriv_auto_right:n { \mright }
}
}
%%%%%% Key-val: derivatives %%%%%%
\cs_new:Npn \__deriv_dv_define_keys:n #1
{
\keys_define:nn { deriv/dv/#1 }
{
style-inf .tl_set:c = { l__deriv_dv_#1_style_inf_tl },
style-var .code:n = { \__deriv_set_style_var:nnn {dv_#1} {##1} {} },
style-var-* .code:n = { \__deriv_set_style_var:nnn {dv_#1} {##1} {_star} },
style-var-/ .code:n = { \__deriv_set_style_var:nnn {dv_#1} {##1} {_slash} },
style-var-! .code:n = { \__deriv_set_style_var:nnn {dv_#1} {##1} {_compact} },
style-var-*/ .code:n = { \__deriv_set_style_var:nnn {dv_#1} {##1} {_star_slash} },
style-var-*! .code:n = { \__deriv_set_style_var:nnn {dv_#1} {##1} {_star_compact} },
style-var-/! .code:n = { \__deriv_set_style_var:nnn {dv_#1} {##1} {_slash_compact} },
style-var-*/! .code:n = { \__deriv_set_style_var:nnn {dv_#1} {##1} {_star_slash_compact} },
style-frac .cs_set:cp = { __deriv_dv_#1_style_frac:nn } {##1},
style-frac-/ .cs_set:cp = { __deriv_dv_#1_style_frac_slash:nn } {##1},
style-frac-! .cs_set:cp = { __deriv_dv_#1_style_frac_compact:nn } {##1},
style-frac-/! .cs_set:cp = { __deriv_dv_#1_style_frac_slash_compact:nn } {##1},
scale-eval .choices:nn = { auto, none, big, Big, bigg, Bigg } { \__deriv_set_scale:nnn {dv_#1} {##1} { eval } },
scale-eval-/ .choices:nn = { auto, none, big, Big, bigg, Bigg } { \__deriv_set_scale:nnn {dv_#1} {##1} { eval_slash } },
scale-fun .choices:nn = { auto, none, big, Big, bigg, Bigg } { \__deriv_set_scale:nnn {dv_#1} {##1} { fun } },
scale-var .choices:nn = { auto, none, big, Big, bigg, Bigg } { \__deriv_set_scale:nnn {dv_#1} {##1} { var } },
scale-frac .choices:nn = { auto, none, big, Big, bigg, Bigg } { \__deriv_set_scale:nnn {dv_#1} {##1} { frac } },
scale-frac-/ .choices:nn = { auto, none, big, Big, bigg, Bigg } { \__deriv_set_scale:nnn {dv_#1} {##1} { frac_slash } },
delims-eval .tl_set:c = { l__deriv_dv_#1_delims_eval_tl },
delims-eval-/ .tl_set:c = { l__deriv_dv_#1_delims_eval_slash_tl },
delims-fun .tl_set:c = { l__deriv_dv_#1_delims_fun_tl },
delims-var .tl_set:c = { l__deriv_dv_#1_delims_var_tl },
delims-frac .tl_set:c = { l__deriv_dv_#1_delims_frac_tl },
delims-frac-/ .tl_set:c = { l__deriv_dv_#1_delims_frac_slash_tl },
sep-inf-ord .code:n = { \__deriv_set_rubber_length:cn { l__deriv_dv_#1_sep_inf_ord_tl } {##1} },
sep-inf-fun .code:n = { \__deriv_set_rubber_length:cn { l__deriv_dv_#1_sep_inf_fun_tl } {##1} },
sep-ord-fun .code:n = { \__deriv_set_rubber_length:cn { l__deriv_dv_#1_sep_ord_fun_tl } {##1} },
sep-frac-fun .code:n = { \__deriv_set_rubber_length:cn { l__deriv_dv_#1_sep_frac_fun_tl } {##1} },
sep-inf-var .code:n = { \__deriv_set_rubber_length:cn { l__deriv_dv_#1_sep_inf_var_tl } {##1} },
sep-var-ord .code:n = { \__deriv_set_rubber_length:cn { l__deriv_dv_#1_sep_var_ord_tl } {##1} },
sep-var-inf .code:n = { \__deriv_set_rubber_length:cn { l__deriv_dv_#1_sep_var_inf_tl } {##1} },
sep-ord-inf .code:n = { \__deriv_set_rubber_length:cn { l__deriv_dv_#1_sep_ord_inf_tl } {##1} },
sep-ord-ord .code:n = { \__deriv_set_rubber_length:cn { l__deriv_dv_#1_sep_ord_ord_tl } {##1} },
sep-ord-var .code:n = { \__deriv_set_rubber_length:cn { l__deriv_dv_#1_sep_ord_var_tl } {##1} },
sep-var-var .code:n = { \__deriv_set_rubber_length:cn { l__deriv_dv_#1_sep_var_var_tl } {##1} },
sep-eval-sb .code:n = { \__deriv_set_rubber_length:cn { l__deriv_dv_#1_sep_eval_sb_tl } {##1} },
sep-eval-sp .code:n = { \__deriv_set_rubber_length:cn { l__deriv_dv_#1_sep_eval_sp_tl } {##1} },
switch-* .bool_set:c = { l__deriv_dv_#1_switch_star_bool },
switch-/ .bool_set:c = { l__deriv_dv_#1_switch_slash_bool },
switch-sort .bool_set:c = { l__deriv_dv_#1_switch_sort_bool },
switch-! .bool_set:c = { l__deriv_dv_#1_switch_compact_bool },
fun .bool_set:c = { l__deriv_dv_#1_misc_fun_bool },
frac .bool_set:c = { l__deriv_dv_#1_misc_frac_bool },
var .clist_set:c = { l__deriv_dv_#1_misc_var_clist },
var .default:n = {all},
order .clist_set:c = { l__deriv_dv_#1_misc_order_clist },
ord .clist_set:c = { l__deriv_dv_#1_misc_order_clist },
mixed-order .tl_set:c = { l__deriv_dv_#1_misc_mixed_order_tl },
mixord .tl_set:c = { l__deriv_dv_#1_misc_mixed_order_tl },
sort-method .code:n = { \__deriv_set_sort_method:nn {#1} {##1} },
sort-numerical .choices:nn = { auto, first, last, symbolic } { \tl_set:cn { l__deriv_dv_#1_sort_numerical_tl } {##1} },
sort-abs-reverse .bool_set:c = { l__deriv_dv_#1_sort_abs_reverse_bool },
sort-number-reverse .bool_set:c = { l__deriv_dv_#1_sort_number_reverse_bool },
sort-sign-reverse .bool_set:c = { l__deriv_dv_#1_sort_sign_reverse_bool },
sort-symbol-reverse .bool_set:c = { l__deriv_dv_#1_sort_symbol_reverse_bool },
sort-lexical-reverse .bool_set:c = { l__deriv_dv_#1_sort_lexical_reverse_bool },
}
}
% variant, value
\cs_new:Npn \__deriv_set_sort_method:nn #1 #2
{
\seq_clear:c { l__deriv_dv_#1_sort_method_seq }
\seq_set_from_clist:Nn \l__deriv_tmpa_seq {#2}
\seq_map_indexed_inline:Nn \l__deriv_tmpa_seq
{
\str_case:nn {##2}
{
{ sign } { \seq_put_right:cn { l__deriv_dv_#1_sort_method_seq } { \__deriv_sort_sign:n } }
{ symbol } { \seq_put_right:cn { l__deriv_dv_#1_sort_method_seq } { \__deriv_sort_symbol:n } }
{ abs } { \seq_put_right:cn { l__deriv_dv_#1_sort_method_seq } { \__deriv_sort_abs:n } }
{ number } { \seq_put_right:cn { l__deriv_dv_#1_sort_method_seq } { \__deriv_sort_number:n } }
{ lexical } { \seq_put_right:cn { l__deriv_dv_#1_sort_method_seq } { \__deriv_sort_lexical:n } }
}
\int_compare:nNnT {##1} = { 3 } { \seq_map_break: }
}
}
% variant, value, name
\cs_new:Npn \__deriv_set_style_var:nnn #1 #2 #3
{
\str_case:nnF {#2}
{
{ single-single } { \tl_set:cn { l__deriv_#1_style_var#3_tl } { \__deriv_build_var_single_single:NNNnn } }
{ single-right } { \tl_set:cn { l__deriv_#1_style_var#3_tl } { \__deriv_build_var_single_right:NNNnn } }
{ single-mixed } { \tl_set:cn { l__deriv_#1_style_var#3_tl } { \__deriv_build_var_single_mixed:NNNnn } }
{ multiple-right } { \tl_set:cn { l__deriv_#1_style_var#3_tl } { \__deriv_build_var_multiple_right:NNNnn } }
{ multiple-left } { \tl_set:cn { l__deriv_#1_style_var#3_tl } { \__deriv_build_var_multiple_left:NNNnn } }
{ multiple-mixed } { \tl_set:cn { l__deriv_#1_style_var#3_tl } { \__deriv_build_var_multiple_mixed:NNNnn } }
}
{
\msg_error:nnxx { deriv } { differential-option-not-defined }
{#2} {'#2'}
}
}
% dv_variant, scale, name
\cs_new:Npn \__deriv_set_scale:nnn #1 #2 #3
{
\str_case:nnF {#2}
{
{ auto } { \tl_set:cn { l__deriv_#1_scale_#3_tl } { \__deriv_scale_auto:nnn } }
{ none } { \tl_set:cn { l__deriv_#1_scale_#3_tl } { \__deriv_scale_none:nnn } }
}
{ \tl_set:cn { l__deriv_#1_scale_#3_tl } { \__deriv_scale_big:nnnn {#2} } }
}
% muskip, tl
\cs_new:Npn \__deriv_set_rubber_length:Nn #1 #2
{
\regex_match:NnTF \c__deriv_cs_numbers_regex {#2}
{
\str_case:nnF {#2}
{
{ 0 } { \tl_clear:N #1 }
{ 0,0 } { \tl_clear:N #1 }
{ 0,0,0 } { \tl_clear:N #1 }
}
{
\seq_set_split:Nnn \l__deriv_rubber_seq { , } {#2}
\tl_set:Nf #1 { \seq_use:Nnnn \l__deriv_rubber_seq { mu plus } { mu plus } { mu minus } mu }
\tl_put_left:Nn #1 { \mskip }
}
}
{ \tl_set:Nn #1 {#2} }
}
%%%%%% Key-val: derivatives %%%%%%
% variant
\cs_new:Npn \__deriv_i_define_keys:n #1
{
\keys_define:nn { deriv/i/#1 }
{
style-inf .tl_set:c = { l__deriv_i_#1_style_inf_tl },
style-var .code:n = { \__deriv_set_style_var:nnn {i_#1} {##1} {} },
style-var-* .code:n = { \__deriv_set_style_var:nnn {i_#1} {##1} { _star } },
scale-var .choices:nn = { auto, none, big, Big, bigg, Bigg } { \__deriv_set_scale:nnn {i_#1} {##1} { var } },
scale-var-* .choices:nn = { auto, none, big, Big, bigg, Bigg } { \__deriv_set_scale:nnn {i_#1} {##1} { var_slash } },
delims-var .tl_set:c = { l__deriv_i_#1_delims_var_tl },
delims-var-* .tl_set:c = { l__deriv_i_#1_delims_var_star_tl },
sep-begin .code:n = { \__deriv_set_rubber_length:cn { l__deriv_i_#1_sep_begin_tl } {##1} },
sep-inf-ord .code:n = { \__deriv_set_rubber_length:cn { l__deriv_i_#1_sep_inf_ord_tl } {##1} },
sep-inf-var .code:n = { \__deriv_set_rubber_length:cn { l__deriv_i_#1_sep_inf_var_tl } {##1} },
sep-ord-inf .code:n = { \__deriv_set_rubber_length:cn { l__deriv_i_#1_sep_ord_inf_tl } {##1} },
sep-ord-var .code:n = { \__deriv_set_rubber_length:cn { l__deriv_i_#1_sep_ord_var_tl } {##1} },
sep-var-ord .code:n = { \__deriv_set_rubber_length:cn { l__deriv_i_#1_sep_var_ord_tl } {##1} },
sep-var-inf .code:n = { \__deriv_set_rubber_length:cn { l__deriv_i_#1_sep_var_inf_tl } {##1} },
sep-var-var .code:n = { \__deriv_set_rubber_length:cn { l__deriv_i_#1_sep_var_var_tl } {##1} },
sep-ord-ord .code:n = { \__deriv_set_rubber_length:cn { l__deriv_i_#1_sep_ord_ord_tl } {##1} },
sep-end .code:n = { \__deriv_set_rubber_length:cn { l__deriv_i_#1_sep_end_tl } {##1} },
switch-* .bool_set:c = { l__deriv_i_#1_switch_star_bool },
var .clist_set:c = { l__deriv_i_#1_misc_var_clist },
var .default:n = {all},
order .clist_set:c = { l__deriv_i_#1_misc_order_clist },
ord .clist_set:c = { l__deriv_i_#1_misc_order_clist },
}
}
%%%%% Setting keys %%%%%
\DeclareDocumentCommand{\derivset}{ m o }
{
\str_if_eq:nnTF {#1} { all }
{
\__deriv_set_default:nnn { all } {#2} { all }
\keys_set:nn { deriv/all/all } { default }
}
{
\tl_set:Nx \l__deriv_derivset_tl { \cs_to_str:N #1 }
\deriv_set_keys:Vn \l__deriv_derivset_tl {#2}
}
}
% dv, keyval
\cs_new_protected:Npn \deriv_set_keys:nn #1 #2
{
\seq_if_in:NnTF \l__deriv_dv_variant_seq {#1}
{ \__deriv_set_default:nnn {#1} {#2} { dv } }
{
\seq_if_in:NnTF \l__deriv_i_variant_seq {#1}
{ \__deriv_set_default:nnn {#1} {#2} { i } }
{
\msg_error:nnxx { deriv } { derivative-not-defined }
{ \token_to_str:N #1 }
{ \token_to_str:N \derivset }
}
}
}
% keyval, dv/i, variant
\cs_new_protected:Npn \deriv_local_keys:nnn #1 #2 #3
{
\tl_if_novalue:nTF {#1}
{
\bool_if:cT { l__deriv_#2_#3_local_keys_bool }
{
\keys_set:nn { deriv/#2/#3 } { default }
\bool_set_false:c { l__deriv_#2_#3_local_keys_bool }
}
}
{
\bool_if:cTF { l__deriv_#2_#3_local_keys_bool }
{ \keys_set:nn { deriv/#2/#3 } { default, #1 } }
{ \keys_set:nn { deriv/#2/#3 } {#1} }
\bool_set_true:c { l__deriv_#2_#3_local_keys_bool }
}
}
%%%%% Declaring variants %%%%%
% tl-dv, macro, inf, keyval, dv/i
\cs_new_protected:Npn \deriv_preamble:NNnnn #1 #2 #3 #4 #5
{
\tl_set:Nx #1 { \cs_to_str:N #2 }
\tl_if_novalue:nTF {#4}
{ \__deriv_preamble_aux:Vnn #1 { style-inf={#3} } {#5} }
{ \__deriv_preamble_aux:Vnn #1 { style-inf={#3}, #4} {#5} }
}
% variant, key-value, dv/i
\cs_new_protected:Npn \__deriv_preamble_aux:nnn #1 #2 #3
{
\seq_if_in:cnF { l__deriv_#3_variant_seq } {#1}
{
\seq_put_left:cn { l__deriv_#3_variant_seq } {#1}
\use:c { __deriv_#3_variables:n } {#1}
\use:c { __deriv_#3_define_keys:n } {#1}
}
\prop_set_eq:cc { l__deriv_#3_#1_user_keys_prop } { c__deriv_#3_pkg_keys_prop }
\__deriv_set_default:nnn {#1} {#2} {#3}
}
% data-type, variant, category, cs-var-list
\cs_new:Npn \__deriv_new:nnnn #1 #2 #3 #4
{
\seq_set_from_clist:Nn \l__deriv_new_var_seq {#4}
\seq_map_inline:Nn \l__deriv_new_var_seq
{ \cs:w #1_new:c \cs_end: { l__deriv_#2_#3_##1_#1 } }
}
% variant
\cs_new_protected:Npn \__deriv_dv_variables:n #1
{
\__deriv_new:nnnn { tl } {dv_#1} { style } { inf, var, var_star, var_slash, var_compact, var_star_slash, var_star_compact, var_slash_compact, frac, frac_slash, frac_compact, frac_slash_compact }
\__deriv_new:nnnn { tl } {dv_#1} { scale } { eval, eval_slash, fun, var, frac, frac_slash }
\__deriv_new:nnnn { tl } {dv_#1} { delims } { eval, eval_slash, fun, var, frac, frac_slash }
\__deriv_new:nnnn { tl } {dv_#1} { sep } { inf_ord, inf_fun, ord_fun, frac_fun, inf_var, var_ord, var_var, var_inf, ord_ord, ord_inf, ord_var, eval_sb, eval_sp }
\__deriv_new:nnnn { bool } {dv_#1} { switch } { star, slash, compact, sort }
\__deriv_new:nnnn { seq } {dv_#1} { sort } { method }
\__deriv_new:nnnn { tl } {dv_#1} { sort } { numerical }
\__deriv_new:nnnn { bool } {dv_#1} { sort } { abs_reverse, sign_reverse, symbol_reverse, number_reverse, lexical_reverse }
\__deriv_new:nnnn { bool } {dv_#1} { misc } { fun, frac }
\__deriv_new:nnnn { clist } {dv_#1} { misc } { var }
\__deriv_new:nnnn { clist } {dv_#1} { misc } { order }
\__deriv_new:nnnn { tl } {dv_#1} { misc } { mixed_order }
\__deriv_new:nnnn { prop } {dv_#1} { user } { keys }
\__deriv_new:nnnn { bool } {dv_#1} { local } { keys }
}
% variant
\cs_new_protected:Npn \__deriv_i_variables:n #1
{
\__deriv_new:nnnn { tl } {i_#1} { style } { inf, var, var_star }
\__deriv_new:nnnn { tl } {i_#1} { scale } { var, var_star }
\__deriv_new:nnnn { tl } {i_#1} { delims } { var, var_star }
\__deriv_new:nnnn { tl } {i_#1} { sep } { begin, inf_ord, inf_var, ord_inf, ord_var, var_inf, var_var, ord_ord, end }
\__deriv_new:nnnn { bool } {i_#1} { switch } { star }
\__deriv_new:nnnn { bool } {i_#1} { mics } { fun, var, frac }
\__deriv_new:nnnn { clist } {i_#1} { misc } { order }
\__deriv_new:nnnn { prop } {i_#1} { user } { keys }
\__deriv_new:nnnn { bool } {i_#1} { local } { keys }
}
% variant, keyval, dv/i
\cs_new_protected:Npn \__deriv_set_default:nnn #1 #2 #3
{
\tl_if_novalue:nTF {#2}
{ \prop_set_eq:cc { l__deriv_#3_#1_user_keys_prop } { c__deriv_#3_pkg_keys_prop } }
{ \prop_put_from_keyval:cn { l__deriv_#3_#1_user_keys_prop } {#2} }
\__deriv_set_default_auxi:cnn { l__deriv_#3_#1_user_keys_prop } {#1} {#3}
\keys_set:nn { deriv/#3/#1 } { default }
}
% prop-key-val, variant, dv/i
\cs_new_protected:Npn \__deriv_set_default_auxi:Nnn #1 #2 #3
{ \__deriv_set_default_auxii:fnn { \prop_to_keyval:N #1 } {#2} {#3} }
% key-val, variant, dv/i
\cs_new_protected:Npn \__deriv_set_default_auxii:nnn #1 #2 #3
{ \keys_define:nn { deriv/#3/#2 } { default .meta:n = {#1} } }
% new/delare/renew/provide, variant, macro
\cs_new_protected:Npn \deriv_dv_define:Nnn #1 #2 #3
{
\exp_args:Nne #1 {#3}{ s o m t/ t! m !e{\char_generate:nn {`_}{8}^} }
{
\group_begin:
\deriv_local_keys:nnn {##2} { dv } {#2}
\exp_args:Nnc \bool_xor:nnTF {##5} {l__deriv_dv_#2_switch_compact_bool}
{%compact = true
\exp_args:Nnc \bool_xor:nnTF {##4} { l__deriv_dv_#2_switch_slash_bool }
{% slash = true
\exp_args:Nnc \bool_xor:nnTF {##1} { l__deriv_dv_#2_switch_star_bool }
{% star and slash + compact
% \msg_error:nnxx { deriv } { differential-options-incompatible }
% {'slash','star'~and~'compact'} {'slash','star'~and~'compact'}
\__deriv_dv_star_slash_compact:nnnnn {dv_#2} {##3} {##6} {##7} {##8}
}
{% slash only + compact
% \msg_error:nnxx { deriv } { differential-options-incompatible }
% {'slash'~and~'compat'} {'slash'~and~'compact'}
\__deriv_dv_slash_compact:nnnnn {dv_#2} {##3} {##6} {##7} {##8}
}
}
{% slash = false
\exp_args:Nnc \bool_xor:nnTF {##1} { l__deriv_dv_#2_switch_star_bool }
{% star only + compact
\__deriv_dv_star_compact:nnnnn {dv_#2} {##3} {##6} {##7} {##8}
}
{% no star no slash + compact
\__deriv_dv_compact:nnnnn {dv_#2} {##3} {##6} {##7} {##8}
}
}
}
{% compact = false
\exp_args:Nnc \bool_xor:nnTF {##4} { l__deriv_dv_#2_switch_slash_bool }
{% slash = true
\exp_args:Nnc \bool_xor:nnTF {##1} { l__deriv_dv_#2_switch_star_bool }
{% star and slash
\__deriv_dv_star_slash:nnnnn {dv_#2} {##3} {##6} {##7} {##8}
}
{% slash only
\__deriv_dv_slash:nnnnn {dv_#2} {##3} {##6} {##7} {##8}
}
}
{% slash = false
\exp_args:Nnc \bool_xor:nnTF {##1} { l__deriv_dv_#2_switch_star_bool }
{% star only
\__deriv_dv_star:nnnnn {dv_#2} {##3} {##6} {##7} {##8}
}
{% no star no slash
\__deriv_dv_none:nnnnn {dv_#2} {##3} {##6} {##7} {##8}
}
}
}
\group_end:
}
}
% new/delare/renew/provide, variant, macro
\cs_new_protected:Npn \deriv_i_define:Nnn #1 #2 #3
{
#1 {#3}{ s o m }
{
\group_begin:
\deriv_local_keys:nnn {##2} { i } {#2}
\exp_args:Nnc \bool_xor:nnTF {##1} { l__deriv_i_#2_switch_star_bool }
{ \__deriv_inf_star:nn {i_#2} {##3} }
{ \__deriv_inf_none:nn {i_#2} {##3} }
\group_end:
}
}
%%%%% derivative definition %%%%%
% variant, function, variable, sb-point, sp-point
\cs_new_protected:Npn \__deriv_dv_star_slash:nnnnn #1 #2 #3 #4 #5
{
star~slash
\__deriv_dv_preparation:Nnnn \l__deriv_dv_denom_tl {#1} {#3} {_star_slash}
\__deriv_evaluation_slash:nnnn {#1} {#4} {#5}
{
\__deriv_fraction_slash:nn {#1}
{
\use:c { __deriv_#1_style_frac_slash:nn }
{ \__deriv_dv_numerator_nofun:n {#1} }
{ \__deriv_dv_denominator:n {#1} }
}
\__deriv_insert_fun:nnn {#1} {#2} { frac_fun }
}
}
% variant, function, variable, sb-point, sp-point
\cs_new_protected:Npn \__deriv_dv_star:nnnnn #1 #2 #3 #4 #5
{ % star
\__deriv_dv_preparation:Nnnn \l__deriv_dv_denom_tl {#1} {#3} {_star}
\__deriv_evaluation:nnnn {#1} {#4} {#5}
{
\__deriv_fraction:nn {#1}
{
\use:c { __deriv_#1_style_frac:nn }
{ \__deriv_dv_numerator_nofun:n {#1} }
{ \__deriv_dv_denominator:n {#1} }
}
\__deriv_insert_fun:nnn {#1} {#2} { frac_fun }
}
}
% variant, function, variable, sb-point, sp-point
\cs_new_protected:Npn \__deriv_dv_slash:nnnnn #1 #2 #3 #4 #5
{ % slash
\__deriv_dv_preparation:Nnnn \l__deriv_dv_denom_tl {#1} {#3} {_slash}
\__deriv_evaluation_slash:nnnn {#1} {#4} {#5}
{
\__deriv_fraction_slash:nn {#1}
{
\use:c { __deriv_#1_style_frac_slash:nn }
{ \__deriv_dv_numerator_fun:nn {#1} {#2} }
{ \__deriv_dv_denominator:n {#1} }
}
}
}
% variant, function, variable, sb-point, sp-point
\cs_new_protected:Npn \__deriv_dv_none:nnnnn #1 #2 #3 #4 #5
{ % none
\__deriv_dv_preparation:Nnnn \l__deriv_dv_denom_tl {#1} {#3} {}
\__deriv_evaluation:nnnn {#1} {#4} {#5}
{
\__deriv_fraction:nn {#1}
{
\use:c { __deriv_#1_style_frac:nn }
{ \__deriv_dv_numerator_fun:nn {#1} {#2} }
{ \__deriv_dv_denominator:n {#1} }
}
}
}
% variant, function, variable, sb-point, sp-point
\cs_new_protected:Npn \__deriv_dv_compact:nnnnn #1 #2 #3 #4 #5
{ % compact
% prepare denom_tl from variable
\__deriv_dv_preparation:Nnnn \l__deriv_dv_denom_tl {#1} {#3} {_compact}
\__deriv_evaluation:nnnn {#1} {#4} {#5}
{
\__deriv_fraction_compact:nn {#1}
{
\use:c { __deriv_#1_style_frac_compact:nn }
{ \l__deriv_dv_denom_tl }
{ \__deriv_dv_no_numerator_fun:nn {#1} {#2} }
}
}
}
% variant, function, variable, sb-point, sp-point
\cs_new_protected:Npn \__deriv_dv_star_compact:nnnnn #1 #2 #3 #4 #5
{ %star~compact
%
\__deriv_dv_preparation:Nnnn \l__deriv_dv_denom_tl {#1} {#3} {_star_compact}
\__deriv_evaluation:nnnn {#1} {#4} {#5}
{
\__deriv_fraction_compact:nn {#1}
{
\use:c { __deriv_#1_style_frac_compact:nn }
{ \l__deriv_dv_denom_tl }
{ }
}
\__deriv_insert_fun:nnn {#1} {#2} { frac_fun }
}
}
% variant, function, variable, sb-point, sp-point
\cs_new_protected:Npn \__deriv_dv_slash_compact:nnnnn #1 #2 #3 #4 #5
{ %slash~compact
%
\__deriv_dv_preparation:Nnnn \l__deriv_dv_denom_tl {#1} {#3} {_slash_compact}
\__deriv_evaluation:nnnn {#1} {#4} {#5}
{
\__deriv_fraction_slash_compact:nn {#1}
{
\use:c { __deriv_#1_style_frac_slash_compact:nn }
{ \l__deriv_dv_denom_tl }
{ \__deriv_dv_no_numerator_fun:nn {#1} {#2} }
}
}
}
% variant, function, variable, sb-point, sp-point
\cs_new_protected:Npn \__deriv_dv_star_slash_compact:nnnnn #1 #2 #3 #4 #5
{ %star~slash~compact
%
\__deriv_dv_preparation:Nnnn \l__deriv_dv_denom_tl {#1} {#3} {_star_slash_compact}
\__deriv_evaluation:nnnn {#1} {#4} {#5}
{
\__deriv_fraction_slash_compact:nn {#1}
{
\use:c { __deriv_#1_style_frac_slash_compact:nn }
{ \l__deriv_dv_denom_tl }
{ }
}
\__deriv_insert_fun:nnn {#1} {#2} { frac_fun }
}
}
% variant, function
\cs_new_protected:Npn \__deriv_dv_numerator_fun:nn #1 #2
{
\__deriv_insert_inf:n {#1}
\__deriv_show_order:cTF { l__deriv_#1_misc_mixed_order_tl }
{
\__deriv_insert_ord:cnn { l__deriv_#1_misc_mixed_order_tl } {#1} { inf_ord }
\__deriv_insert_fun:nnn {#1} {#2} { ord_fun }
}
{ \__deriv_insert_fun:nnn {#1} {#2} { inf_fun } }
}
% variant, function
\cs_new_protected:Npn \__deriv_dv_no_numerator_fun:nn #1 #2
{
\__deriv_insert_fun:nnn {#1} {#2} { ord_fun }
}
% variant
\cs_new_protected:Npn \__deriv_dv_numerator_nofun:n #1
{
\__deriv_insert_inf:n {#1}
\__deriv_show_order:cT { l__deriv_#1_misc_mixed_order_tl }
{ \__deriv_insert_ord:cnn { l__deriv_#1_misc_mixed_order_tl } {#1} { inf_ord } }
}
% dv
\cs_new_protected:Npn \__deriv_dv_denominator:n #1
{ \tl_use:N \l__deriv_dv_denom_tl }
% denom-tl, variant, variable, if star
\cs_new_protected:Npn \__deriv_dv_preparation:Nnnn #1 #2 #3 #4
{
\tl_clear:N #1
\seq_set_from_clist:Nn \l__deriv_dv_var_seq {#3}
\seq_set_from_clist:Nc \l__deriv_dv_order_seq { l__deriv_#2_misc_order_clist }
\tl_use:c { l__deriv_#2_style_var#4_tl } \l__deriv_dv_var_seq \l__deriv_dv_order_seq #1 {#2} {#4}
}
% var_seq, order_seq, denom-tl, variant, if star
\cs_new_protected:Npn \__deriv_build_var_multiple_right:NNNnn #1 #2 #3 #4 #5
{
\int_set:Nn \l__deriv_var_count_int { \seq_count:N #1 }
\__deriv_adjust_ord_seq:NN \l__deriv_var_count_int #2
\str_if_eq:cNT { l__deriv_#4_misc_mixed_order_tl } 1
{ \__deriv_mixed_order:cNn { l__deriv_#4_misc_mixed_order_tl } #2 {#4} }
\__deriv_var_bool_seq:cNN { l__deriv_#4_misc_var_clist } \l__deriv_tmpa_seq \l__deriv_var_count_int
\seq_map_indexed_inline:Nn #1
{
\seq_pop_left:NN #2 \l__deriv_tmpa_tl
\seq_pop_left:NN \l__deriv_tmpa_seq \l__deriv_tmpb_tl
\tl_put_right:Nx #3
{
\__deriv_insert_inf:n {#4}
\__deriv_insert_mskip:nn {#4} { inf_var }
\__deriv_insert_var:Nnnn \l__deriv_tmpb_tl {##2} {#4} {#5}
\__deriv_show_order:NTF \l__deriv_tmpa_tl
{
\__deriv_insert_ord:Nnn \l__deriv_tmpa_tl {#4} { var_ord }
\int_compare:nNnF {##1} = { \l__deriv_var_count_int }
{ \__deriv_insert_mskip:nn {#4} { ord_inf } }
}
{
\int_compare:nNnF {##1} = { \l__deriv_var_count_int }
{ \__deriv_insert_mskip:nn {#4} { var_inf } }
}
}
}
}
% var_seq, order_seq, denom-tl, variant, if star
\cs_new_protected:Npn \__deriv_build_var_single_single:NNNnn #1 #2 #3 #4 #5
{
\int_set:Nn \l__deriv_var_count_int { \seq_count:N #1 }
\tl_set:Nf \l__deriv_tmpa_tl { \seq_use:Nn #1 { \__deriv_insert_mskip:nn {#4} { var_var } } }
\__deriv_var_bool_seq:cNN { l__deriv_#4_misc_var_clist } \l__deriv_tmpa_seq \l__deriv_var_count_int
\int_set:Nn \l__deriv_tmpa_int { \seq_count:N #2 }
\seq_map_indexed_inline:Nn #2
{
\tl_put_right:Nx \l__deriv_tmpb_tl
{
\exp_not:n {##2}
\int_compare:nNnF {##1} = { \l__deriv_tmpa_int }
{ \__deriv_insert_mskip:nn {#4} { ord_ord } }
}
}
\seq_pop_left:NN \l__deriv_tmpa_seq \l__deriv_tmpc_tl
\tl_put_right:Nx #3
{
\__deriv_insert_inf:n {#4}
\__deriv_insert_mskip:nn {#4} { inf_var }
\__deriv_insert_var:NVnn \l__deriv_tmpc_tl \l__deriv_tmpa_tl {#4} {#5}
\__deriv_show_order:NT \l__deriv_tmpb_tl
{ \__deriv_insert_ord:Nnn \l__deriv_tmpb_tl {#4} { var_ord } }
}
\str_if_eq:cNT { l__deriv_#4_misc_mixed_order_tl } 1
{ \tl_set_eq:cN { l__deriv_#4_misc_mixed_order_tl } \l__deriv_tmpb_tl }
}
% var_seq, order_seq, denom-tl, variant
\cs_new_protected:Npn \__deriv_build_var_single_right:NNNnn #1 #2 #3 #4 #5
{
\int_set:Nn \l__deriv_var_count_int { \seq_count:N #1 }
\__deriv_adjust_ord_seq:NN \l__deriv_var_count_int #2
\str_if_eq:cNT { l__deriv_#4_misc_mixed_order_tl } 1
{ \__deriv_mixed_order:cNn { l__deriv_#4_misc_mixed_order_tl } #2 {#4} }
\__deriv_var_bool_seq:cNN { l__deriv_#4_misc_var_clist } \l__deriv_tmpa_seq \l__deriv_var_count_int
\tl_put_right:Nx #3
{
\__deriv_insert_inf:n {#4}
\__deriv_insert_mskip:nn {#4} { inf_var }
}
\seq_map_indexed_inline:Nn #1
{
\seq_pop_left:NN #2 \l__deriv_tmpa_tl
\seq_pop_left:NN \l__deriv_tmpa_seq \l__deriv_tmpb_tl
\tl_put_right:Nx #3
{
\__deriv_insert_var:Nnnn \l__deriv_tmpb_tl {##2} {#4} {#5}
\__deriv_show_order:NTF \l__deriv_tmpa_tl
{
\__deriv_insert_ord:Nnn \l__deriv_tmpa_tl {#4} { var_ord }
\int_compare:nNnF {##1} = { \l__deriv_var_count_int }
{ \__deriv_insert_mskip:nn {#4} { ord_var } }
}
{}
\int_compare:nNnF {##1} = { \l__deriv_var_count_int }
{ \__deriv_insert_mskip:nn {#4} { var_var } }
}
}
}
% var_seq, order_seq
\cs_new_protected:Npn \__deriv_adjust_ord_seq:NN #1 #2
{
\int_set:Nn \l__deriv_vmo_int { #1 - \seq_count:N #2 }
\int_compare:nNnF { \l__deriv_vmo_int } = { 0 }
{
\int_compare:nNnTF { \l__deriv_vmo_int } < { 0 }
{ \int_step_inline:nn { -1*\l__deriv_vmo_int } { \seq_pop_right:NN #2 \l__deriv_tmpa_tl } }
{ \int_step_inline:nn { \l__deriv_vmo_int } { \seq_put_right:Nn #2 { 1 } } }
}
}
% avd-clist, bool-seq, count
\cs_new_protected:Npn \__deriv_var_bool_seq:NNN #1 #2 #3
{
\seq_clear:N #2
\clist_if_in:NnTF #1 { all }
{ \exp_args:NNf \seq_set_from_clist:Nn #2 { \prg_replicate:nn {#3} { \c_true_bool , } } }
{
\clist_if_in:NnTF #1 { none }
{ \exp_args:NNf \seq_set_from_clist:Nn #2 { \prg_replicate:nn {#3} { \c_false_bool , } } }
{
\int_step_inline:nn {#3}
{
\clist_if_in:NnTF #1 {##1}
{ \seq_put_right:Nn #2 { \c_true_bool } }
{ \seq_put_right:Nn #2 { \c_false_bool } }
}
}
}
}
% ord-seq, var-seq
\cs_new_protected:Npn \__deriv_adjust_trailing_ord:NN #1 #2
{
\seq_clear:N \l__deriv_tmpa_seq
\int_set:Nn \l__deriv_vmo_int { \seq_count:N #2 - \seq_count:N #1 }
\int_compare:nNnT { \l__deriv_vmo_int } < { 0 }
{
\int_step_inline:nn { -1*\l__deriv_vmo_int }
{ \seq_pop_right:NN #1 \l__deriv_tmpa_tl }
}
\int_step_inline:nn { \seq_count:N #1 }
{
\seq_pop_right:NN #1 \l__deriv_tmpa_tl
\str_if_eq:VnF \l__deriv_tmpa_tl { 1 }
{
\seq_put_right:NV #1 \l__deriv_tmpa_tl
\prg_break:
}
}
}
%%%%% infinisimal definition %%%%%
% variant, variable
\cs_new:Npn \__deriv_inf_none:nn #1 #2
{
\__deriv_i_preparation:Nnnn \l__deriv_i_denom_tl {#1} {#2} { }
\__deriv_i_print:Nn \l__deriv_i_denom_tl {#1}
}
% variant, variable
\cs_new:Npn \__deriv_inf_star:nn #1 #2
{
\__deriv_i_preparation:Nnnn \l__deriv_i_denom_tl {#1} {#2} { _star }
\__deriv_i_print:Nn \l__deriv_i_denom_tl {#1}
}
% print-tl, variant
\cs_new:Npn \__deriv_i_print:Nn #1 #2
{
\__deriv_insert_mskip:nn {#2} { begin }
\tl_use:N #1
\__deriv_insert_mskip:nn {#2} { end }
}
% print-tl, variant, variable, if star
\cs_new_protected:Npn \__deriv_i_preparation:Nnnn #1 #2 #3 #4
{
\tl_clear:N #1
\seq_set_from_clist:Nn \l__deriv_i_var_seq {#3}
\seq_set_from_clist:Nc \l__deriv_i_order_seq { l__deriv_#2_misc_order_clist }
\tl_use:c { l__deriv_#2_style_var#4_tl } \l__deriv_i_var_seq \l__deriv_i_order_seq #1 {#2} {#4}
}
% var-seq, order-seq, print-tl, variant, if star
\cs_new_protected:Npn \__deriv_build_var_single_mixed:NNNnn #1 #2 #3 #4 #5
{
\int_set:Nn \l__deriv_var_count_int { \seq_count:N #1 }
\__deriv_var_bool_seq:cNN { l__deriv_#4_misc_var_clist } \l__deriv_add_var_bool_seq \l__deriv_var_count_int
\__deriv_adjust_trailing_ord:NN #2 #1
\int_set:Nn \l__deriv_tmpa_int { \seq_count:N #2 }
\seq_map_indexed_inline:Nn #1
{
\seq_pop_left:NN \l__deriv_add_var_bool_seq \l__deriv_tmpa_tl
\tl_put_right:Nx \l__deriv_tmpb_tl
{
\__deriv_insert_var:Nnnn \l__deriv_tmpa_tl {##2} {#4} {#5}
\int_compare:nNnF {##1} = { \l__deriv_var_count_int }
{ \__deriv_insert_mskip:nn {#4} { var_var } }
}
}
\seq_map_indexed_inline:Nn #2
{
\tl_put_right:Nx \l__deriv_tmpc_tl
{
\exp_not:n {##2}
\int_compare:nNnF {##1} = { \l__deriv_tmpa_int }
{ \__deriv_insert_mskip:nn {#4} { ord_ord } }
}
}
\tl_put_right:Nx #3
{
\__deriv_insert_inf:n {#4}
\sb
{
\__deriv_insert_mskip:nn {#4} { inf_var }
\exp_not:V \l__deriv_tmpb_tl
}