% derivative.sty % Copyright 2019-2020 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. \NeedsTeXFormat{LaTeX2e} \RequirePackage{xparse}[2018/05/09] \ProvidesExplPackage{derivative}{2020/02/03}{0.97}{Nice and easy derivatives} %%%%% Useful conditionals %%%%% \prg_new_conditional:Npnn \__deriv_if_novalue:n #1 { T , F , TF } { \tl_if_novalue:nTF {#1} { \prg_return_true: } { \tl_if_blank:nTF {#1} { \prg_return_true: } { \prg_return_false: } } } \prg_new_conditional:Npnn \__deriv_if_novalue_and:nn #1 #2 { F, TF } { \__deriv_if_novalue:nTF {#1} { \__deriv_if_novalue:nTF {#2} { \prg_return_true: } { \prg_return_false: } } { \prg_return_false: } } \prg_new_conditional:Npnn \__deriv_show_order:N #1 { T, TF } { \quark_if_no_value:NTF #1 { \prg_return_false: } { \str_if_eq:NNTF #1 1 { \prg_return_false: } { \exp_args:NV \tl_if_novalue:nTF #1 { \prg_return_false: } { \tl_if_blank:VTF #1 { \prg_return_false: } { \prg_return_true: } } } } } \cs_new:Npn \__deriv_case:n #1 { \exp:w \__deriv_case_begin:nTF {#1} { } { } } \cs_new:Npn \__deriv_case:nT #1#2 { \exp:w \__deriv_case_begin:nTF {#1} {#2} { } } \cs_new:Npn \__deriv_case:nF #1#2 { \exp:w \__deriv_case_begin:nTF {#1} { } {#2} } \cs_new:Npn \__deriv_case:nTF #1 { \exp:w \__deriv_case_begin:nTF {#1} } \cs_new:Npn \__deriv_case_begin:nTF #1#2#3 { \__deriv_case:w #1 \c_true_bool { } \q_mark {#2} \q_mark {#3} \q_stop } \cs_new:Npn \__deriv_case:w #1#2 { \bool_if:nTF {#1} { \__deriv_case_end:nw {#2} } { \__deriv_case:w } } \cs_new:Npn \__deriv_case_end:nw #1#2#3 \q_mark #4#5 \q_stop { \exp_end: #1 #4 } %%%%% Variables for settings of odv, pdv and variants %%%%% \cs_new_protected:Npn \__deriv_auto_left:n #1 { \left #1 } \cs_new_protected:Npn \__deriv_auto_right:n #1 { \right #1 } \tl_new:N \l__deriv_dv_tmp_tl \tl_new:N \l__deriv_derivset_tl \seq_new:N \l__deriv_var_seq \seq_new:N \l__deriv_rubber_seq %%%%% Variables for odv %%%%% \seq_new:N \l__deriv_d_variant_seq \tl_new:N \l__deriv_d_order_tl %%%%% Variables for pdv and mixed order (mo) %%%%% \seq_new:N \l__deriv_p_variant_seq \tl_new:N \l__deriv_p_tmpa_tl \tl_new:N \l__deriv_p_mo_tl \tl_new:N \l__deriv_p_denom_tl \seq_new:N \l__deriv_p_var_seq \seq_new:N \l__deriv_p_order_seq \seq_new:N \l__deriv_p_mo_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_unsorted_seq \seq_new:N \l__deriv_sorted_seq \seq_new:N \l__deriv_symbol_seq \seq_new:N \l__deriv_number_seq \seq_new:N \l__deriv_rebuild_seq \int_new:N \l__deriv_tmpa_int \int_new:N \l__deriv_numerical_int \int_new:N \l__deriv_sort_counter_int \int_new:N \l__deriv_sort_max_int \int_new:N \l__deriv_position_int \int_new:N \l__deriv_rebuild_int \regex_const:Nn \c__deriv_pattern_regex { \A([\+\-]?\d*)(.*) } %%%%%% Key-val for all %%%%%% \keys_define:nn { deriv-all-settings } { 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_eq:NN \__deriv_auto_left:n \mleft \cs_set_eq:NN \__deriv_auto_right:n \mright }, scale-auto .default:n = { leftright } } %%%%% Key-val for odv and variants %%%%% \cs_new:Npn \__deriv_d_define_keys:n #1 { \keys_define:nn { deriv/d/#1 } { style-inf .code:n = { \cs_set_eq:cN { __deriv_#1_style_inf:n } ##1 }, style-frac .code:n = { \cs_set_eq:cN { __deriv_#1_style_frac:n } ##1 }, style-frac .default:n = { \frac }, style-frac-/ .code:n = { \cs_set_eq:cN { __deriv_#1_style_frac_slash:n } ##1 }, style-frac-/ .default:n = { \slashfrac }, scale-eval .choices:nn = { auto, none, big, Big, bigg, Bigg } { \tl_set_eq:cN { l__deriv_#1_scale_eval_tl } \l_keys_choice_tl }, scale-eval .default:n = { auto }, scale-eval-/ .choices:nn = { auto, none, big, Big, bigg, Bigg } { \tl_set_eq:cN { l__deriv_#1_scale_eval_slash_tl } \l_keys_choice_tl }, scale-eval-/ .default:n = { auto }, scale-fun .choices:nn = { auto, none, big, Big, bigg, Bigg } { \tl_set_eq:cN { l__deriv_#1_scale_fun_tl } \l_keys_choice_tl }, scale-fun .default:n = { auto }, scale-var .choices:nn = { auto, none, big, Big, bigg, Bigg } { \tl_set_eq:cN { l__deriv_#1_scale_var_tl } \l_keys_choice_tl }, scale-var .default:n = { auto }, scale-frac .choices:nn = { auto, none, big, Big, bigg, Bigg } { \tl_set_eq:cN { l__deriv_#1_scale_frac_tl } \l_keys_choice_tl }, scale-frac .default:n = { auto }, scale-frac-/ .choices:nn = { auto, none, big, Big, bigg, Bigg } { \tl_set_eq:cN { l__deriv_#1_scale_frac_slash_tl } \l_keys_choice_tl }, scale-frac-/ .default:n = { auto }, delims-eval .code:n = { \tl_set:cn { l__deriv_#1_delims_eval_tl } { ##1 } }, delims-eval .default:n = { .\rvert }, delims-eval-/ .code:n = { \tl_set:cn { l__deriv_#1_delims_eval_slash_tl } { ##1 } }, delims-eval-/ .default:n = { .\rvert }, delims-fun .code:n = { \tl_set:cn { l__deriv_#1_delims_fun_tl } { ##1 } }, delims-fun .default:n = { () }, delims-var .code:n = { \tl_set:cn { l__deriv_#1_delims_var_tl } { ##1 } }, delims-var .default:n = { () }, delims-frac .code:n = { \tl_set:cn { l__deriv_#1_delims_frac_tl } { ##1 } }, delims-frac .default:n = { () }, delims-frac-/ .code:n = { \tl_set:cn { l__deriv_#1_delims_frac_slash_tl } { ##1 } }, delims-frac-/ .default:n = { () }, sep-inf-ord .code:n = { \__deriv_set_rubber_length:cn { l__deriv_#1_sep_inf_ord_muskip } {##1} }, sep-inf-ord .default:n = { 0 }, sep-inf-fun .code:n = { \__deriv_set_rubber_length:cn { l__deriv_#1_sep_inf_fun_muskip } {##1} }, sep-inf-fun .default:n = { 0 }, sep-ord-fun .code:n = { \__deriv_set_rubber_length:cn { l__deriv_#1_sep_ord_fun_muskip } {##1} }, sep-ord-fun .default:n = { 0 }, sep-var-ord .code:n = { \__deriv_set_rubber_length:cn { l__deriv_#1_sep_var_ord_muskip } {##1} }, sep-var-ord .default:n = { 0 }, sep-inf-var .code:n = { \__deriv_set_rubber_length:cn { l__deriv_#1_sep_inf_var_muskip } {##1} }, sep-inf-var .default:n = { 0 }, sep-eval-sb .code:n = { \__deriv_set_rubber_length:cn { l__deriv_#1_sep_eval_sb_muskip } {##1} }, sep-eval-sb .default:n = { 0 }, sep-eval-sp .code:n = { \__deriv_set_rubber_length:cn { l__deriv_#1_sep_eval_sp_muskip } {##1} }, sep-eval-sp .default:n = { 0 }, switch-* .bool_set:c = { l__deriv_#1_switch_star_bool }, switch-* .default:n = { false }, switch-/ .bool_set:c = { l__deriv_#1_switch_slash_bool }, switch-/ .default:n = { false }, misc-add-delims .multichoices:nn = { fun, var, frac } { \bool_set_true:c { l__deriv_#1_mics_##1_bool } }, misc-remove-delims .multichoices:nn = { fun, var, frac } { \bool_set_false:c { l__deriv_#1_mics_##1_bool } }, misc-remove-delims .default:n = { fun, var, frac } } \bool_lazy_or:nnT { \sys_if_engine_luatex_p: } { \sys_if_engine_xetex_p: } { \keys_define:nn { deriv/d/#1 } { style-inf .default:n = { \symnormal } } } \sys_if_engine_pdftex:T { \keys_define:nn { deriv/d/#1 } { style-inf .default:n = { \mathnormal } } } } %%%%%% Key-val for pdv and variants %%%%%% \cs_new:Npn \__deriv_p_define_keys:n #1 { \keys_define:nn { deriv/p/#1 } { style-inf .code:n = { \cs_set_eq:cN { __deriv_#1_style_inf:n } ##1 }, style-frac .code:n = { \cs_set_eq:cN { __deriv_#1_style_frac:n } ##1 }, style-frac .default:n = { \frac }, style-frac-/ .code:n = { \cs_set_eq:cN { __deriv_#1_style_frac_slash:n } ##1 }, style-frac-/ .default:n = { \slashfrac }, scale-eval .choices:nn = { auto, none, big, Big, bigg, Bigg } { \tl_set_eq:cN { l__deriv_#1_scale_eval_tl } \l_keys_choice_tl }, scale-eval .default:n = { auto }, scale-eval-/ .choices:nn = { auto, none, big, Big, bigg, Bigg } { \tl_set_eq:cN { l__deriv_#1_scale_eval_slash_tl } \l_keys_choice_tl }, scale-eval-/ .default:n = { auto }, scale-fun .choices:nn = { auto, none, big, Big, bigg, Bigg } { \tl_set_eq:cN { l__deriv_#1_scale_fun_tl } \l_keys_choice_tl }, scale-fun .default:n = { auto }, scale-var .choices:nn = { auto, none, big, Big, bigg, Bigg } { \tl_set_eq:cN { l__deriv_#1_scale_var_tl } \l_keys_choice_tl }, scale-var .default:n = { auto }, scale-frac .choices:nn = { auto, none, big, Big, bigg, Bigg } { \tl_set_eq:cN { l__deriv_#1_scale_frac_tl } \l_keys_choice_tl }, scale-frac .default:n = { auto }, scale-frac-/ .choices:nn = { auto, none, big, Big, bigg, Bigg } { \tl_set_eq:cN { l__deriv_#1_scale_frac_slash_tl } \l_keys_choice_tl }, scale-frac-/ .default:n = { auto }, delims-eval .code:n = { \tl_set:cn { l__deriv_#1_delims_eval_tl } {##1} }, delims-eval .default:n = { () }, delims-eval-/ .code:n = { \tl_set:cn { l__deriv_#1_delims_eval_slash_tl } {##1} }, delims-eval-/ .default:n = { () }, delims-fun .code:n = { \tl_set:cn { l__deriv_#1_delims_fun_tl } {##1} }, delims-fun .default:n = { () }, delims-var .code:n = { \tl_set:cn { l__deriv_#1_delims_var_tl } {##1} }, delims-var .default:n = { () }, delims-frac .code:n = { \tl_set:cn { l__deriv_#1_delims_frac_tl } {##1} }, delims-frac .default:n = { () }, delims-frac-/ .code:n = { \tl_set:cn { l__deriv_#1_delims_frac_slash_tl } {##1} }, delims-frac-/ .default:n = { () }, sep-inf-ord .code:n = { \__deriv_set_rubber_length:cn { l__deriv_#1_sep_inf_ord_muskip } {##1} }, sep-inf-ord .default:n = { 0 }, sep-inf-fun .code:n = { \__deriv_set_rubber_length:cn { l__deriv_#1_sep_inf_fun_muskip } {##1} }, sep-inf-fun .default:n = { 0 }, sep-ord-fun .code:n = { \__deriv_set_rubber_length:cn { l__deriv_#1_sep_ord_fun_muskip } {##1} }, sep-ord-fun .default:n = { 0 }, sep-inf-var .code:n = { \__deriv_set_rubber_length:cn { l__deriv_#1_sep_inf_ord_muskip } {##1} }, sep-inf-var .default:n = { 0 }, sep-var-ord .code:n = { \__deriv_set_rubber_length:cn { l__deriv_#1_sep_var_ord_muskip } {##1} }, sep-var-ord .default:n = { 0 }, sep-var-inf .code:n = { \__deriv_set_rubber_length:cn { l__deriv_#1_sep_var_inf_muskip } {##1} }, sep-var-inf .default:n = { 3 }, sep-ord-inf .code:n = { \__deriv_set_rubber_length:cn { l__deriv_#1_sep_ord_inf_muskip } {##1} }, sep-ord-inf .default:n = { 3 }, sep-eval-sb .code:n = { \__deriv_set_rubber_length:cn { l__deriv_#1_sep_eval_sb_muskip } {##1} }, sep-eval-sb .default:n = { -4 }, sep-eval-sp .code:n = { \__deriv_set_rubber_length:cn { l__deriv_#1_sep_eval_sp_muskip } {##1} }, sep-eval-sp .default:n = { -4 }, switch-* .bool_set:c = { l__deriv_#1_switch_star_bool }, switch-* .default:n = { false }, switch-/ .bool_set:c = { l__deriv_#1_switch_slash_bool }, switch-/ .default:n = { false }, misc-add-delims .multichoices:nn = { fun, var, frac } { \bool_set_true:c { l__deriv_#1_mics_##1_bool } }, misc-remove-delims .multichoices:nn = { fun, var, frac } { \bool_set_false:c { l__deriv_#1_mics_##1_bool } }, misc-remove-delims .default:n = { fun, var, frac }, sort-method .clist_set:c = { l__deriv_#1_sort_method_clist }, % måske seq sort-method .default:n = { abs, sign, symbol }, sort-numerical .choices:nn = { auto, first, last } { \tl_set_eq:cN { l__deriv_#1_sort_numerical_tl } \l_keys_choice_tl }, sort-numerical .default:n = { auto }, sort-sign-reverse .bool_set:c = { l__deriv_#1_sort_sign_reverse_bool }, sort-sign-reverse .default:n = { false }, sort-symbol-reverse .bool_set:c = { l__deriv_#1_sort_symbol_reverse_bool }, sort-symbol-reverse .default:n = { false }, sort-abs-reverse .bool_set:c = { l__deriv_#1_sort_abs_reverse_bool }, sort-abs-reverse .default:n = { false } } \bool_lazy_or:nnT { \sys_if_engine_luatex_p: } { \sys_if_engine_xetex_p: } { \keys_define:nn { deriv/p/#1 } { style-inf .default:n = { \symnormal } } } \sys_if_engine_pdftex:T { \keys_define:nn { deriv/p/#1 } { style-inf .default:n = { \mathnormal } } } } %%%%% Setting keys %%%%% \DeclareDocumentCommand{\derivset}{ m o } { \token_if_macro:NTF {#1} { \tl_set:Nx \l__deriv_derivset_tl { \cs_to_str:N #1 } } { \tl_set:Nx \l__deriv_derivset_tl { \tl_to_str:n {#1} } } \__deriv_derivset:Vn \l__deriv_derivset_tl {#2} } \cs_new_protected:Npn \__deriv_derivset:nn #1 #2 { \seq_if_in:NnTF \l__deriv_d_variant_seq {#1} { \__deriv_d_set_keys:nn {#1} {#2} } { \seq_if_in:NnTF \l__deriv_p_variant_seq {#1} { \__deriv_p_set_keys:nn {#1} {#2} } { \str_if_eq:nnTF {#1} { all } { \__deriv_all_set_keys:n {#2} } { \msg_error:nnxx { deriv } { derivative-not-defined } { \token_to_str:N #1 } { \token_to_str:N \derivset } } } } } % dv , key=val clist \cs_new_protected:Npn \__deriv_d_set_keys:nn #1 #2 { \tl_if_novalue:nTF {#2} { \keys_set:nn { deriv/d/#1 } { style-inf , style-frac , style-frac-/ , scale-eval , scale-eval-/ , scale-fun , scale-var , scale-frac , scale-frac-/ , delims-eval , delims-eval-/ , delims-fun , delims-var , delims-frac , delims-frac-/ , sep-inf-ord , sep-inf-fun , sep-ord-fun , sep-var-ord , sep-inf-var , sep-eval-sb , sep-eval-sp , switch-* , switch-/ , misc-remove-delims } } { \keys_set:nn { deriv/d/#1 } {#2} } } % key=val clist \cs_new_protected:Npn \__deriv_p_set_keys:nn #1 #2 { \tl_if_novalue:nTF {#2} { \keys_set:nn { deriv/p/#1 } { style-inf , style-frac , style-frac-/ , scale-eval , scale-eval-/ , scale-fun , scale-var , scale-frac , scale-frac-/ , delims-eval , delims-eval-/ , delims-fun , delims-var , delims-frac , delims-frac-/ , sep-inf-ord , sep-inf-fun , sep-ord-fun , sep-inf-var , sep-var-ord , sep-var-inf , sep-ord-inf , sep-eval-sb , sep-eval-sp , switch-* , switch-/ , sort-method , sort-numerical , sort-sign-reverse , sort-symbol-reverse , sort-abs-reverse , misc-remove-delims } } { \keys_set:nn { deriv/p/#1 } {#2} } } % key=val clist \cs_new_protected:Npn \__deriv_all_set_keys:n #1 { \tl_if_novalue:nTF {#1} { \keys_set:nn { deriv-all-settings } { scale-auto } } { \keys_set:nn { deriv-all-settings } {#1} } } %%%%% Declaring variants %%%%% % tl-dv , macro , key-value \cs_new_protected:Npn \deriv_d_preamble:Nnn #1 #2 #3 { \tl_set:Nx #1 { \cs_to_str:N #2 } \seq_if_in:NVF \l__deriv_d_variant_seq #1 { \seq_put_left:NV \l__deriv_d_variant_seq #1 \__deriv_d_variables:V #1 \__deriv_d_define_keys:V #1 } \__deriv_derivset:VV #1 \c_novalue_tl \tl_if_novalue:nF {#3} { \__deriv_derivset:Vn #1 {#3} } } % dv , new/delare/renew/provide , macro , inf \cs_new_protected:Npn \deriv_d_define:nnnn #1 #2 #3 #4 { \use:c { #2 DocumentCommand }{#3}{ s o m t/ m !e{\sb^} } { \group_begin: \exp_args:Nnc \bool_xor:nnTF {##4} { l__deriv_#1_switch_slash_bool } { \exp_args:Nnc \bool_xor:nnTF {##1} { l__deriv_#1_switch_star_bool } { \__deriv_odv_both:nnnnnnn {#4} {#1} {##2} {##3} {##5} {##6} {##7} } { \__deriv_odv_slash:nnnnnnn {#4} {#1} {##2} {##3} {##5} {##6} {##7} } } { \exp_args:Nnc \bool_xor:nnTF {##1} { l__deriv_#1_switch_star_bool } { \__deriv_odv_star:nnnnnnn {#4} {#1} {##2} {##3} {##5} {##6} {##7} } { \__deriv_odv_none:nnnnnnn {#4} {#1} {##2} {##3} {##5} {##6} {##7} } } \group_end: } } % tl-dv , macro , key-value \cs_new_protected:Npn \deriv_p_preamble:Nnn #1 #2 #3 { \tl_set:Nx #1 { \cs_to_str:N #2 } \seq_if_in:NVF \l__deriv_p_variant_seq #1 { \seq_put_left:NV \l__deriv_p_variant_seq #1 \__deriv_p_variables:V #1 \__deriv_p_define_keys:V #1 } \__deriv_derivset:VV #1 \c_novalue_tl \tl_if_novalue:nF {#3} { \__deriv_derivset:Vn #1 {#3} } } % dv , new/delare/renew/provide , macro , inf \cs_new_protected:Npn \deriv_p_define:nnnn #1 #2 #3 #4 { \use:c { #2 DocumentCommand }{#3}{ s o o m t/ m !e{\sb^} } { \group_begin: \exp_args:Nnc \bool_xor:nnTF {##5} { l__deriv_#1_switch_slash_bool } { \exp_args:Nnc \bool_xor:nnTF {##1} { l__deriv_#1_switch_star_bool } { \__deriv_pdv_both:nnnnnnnn {#4} {#1} {##2} {##3} {##4} {##6} {##7} {##8} } { \__deriv_pdv_slash:nnnnnnnn {#4} {#1} {##2} {##3} {##4} {##6} {##7} {##8} } } { \exp_args:Nnc \bool_xor:nnTF {##1} { l__deriv_#1_switch_star_bool } { \__deriv_pdv_star:nnnnnnnn {#4} {#1} {##2} {##3} {##4} {##6} {##7} {##8} } { \__deriv_pdv_none:nnnnnnnn {#4} {#1} {##2} {##3} {##4} {##6} {##7} {##8} } } \group_end: } } % dv \cs_new_protected:Npn \__deriv_d_variables:n #1 { \__deriv_new:nnnn { tl } {#1} { style } { inf, frac, frac_slash } \__deriv_new:nnnn { tl } {#1} { scale } { eval, eval_slash, fun, var, frac, frac_slash } \__deriv_new:nnnn { tl } {#1} { delims } { eval, eval_slash, fun, var, frac, frac_slash } \__deriv_new:nnnn { muskip } {#1} { sep } { inf_ord, inf_fun, ord_fun, var_ord, inf_var, eval_sb, eval_sp } \__deriv_new:nnnn { bool } {#1} { switch } { star, slash } \__deriv_new:nnnn { bool } {#1} { mics } { fun, var, frac } } % dv \cs_new_protected:Npn \__deriv_p_variables:n #1 { \__deriv_new:nnnn { tl } {#1} { style } { inf, frac, frac_slash } \__deriv_new:nnnn { tl } {#1} { scale } { eval, eval_slash, fun, var, frac, frac_slash } \__deriv_new:nnnn { tl } {#1} { delims } { eval, eval_slash, fun, var, frac, frac_slash } \__deriv_new:nnnn { muskip } {#1} { sep } { inf_ord, inf_fun, ord_fun, inf_var, var_ord, var_inf, ord_inf, eval_sb, eval_sp } \__deriv_new:nnnn { bool } {#1} { switch } { star, slash } \__deriv_new:nnnn { clist } {#1} { sort } { method } \__deriv_new:nnnn { tl } {#1} { sort } { numerical } \__deriv_new:nnnn { bool } {#1} { sort } { sign_reverse, symbol_reverse, abs_reverse } \__deriv_new:nnnn { bool } {#1} { mics } { fun, var, frac } } % data-type , dv , category , cs-var-list \cs_new:Npn \__deriv_new:nnnn #1 #2 #3 #4 { \seq_set_from_clist:Nn \l__deriv_var_seq {#4} \seq_map_inline:Nn \l__deriv_var_seq { \cs:w #1_new:c \cs_end: { l__deriv_#2_#3_##1_#1 } } } %%%%% Ordinary derivative definition %%%%% % inf , dv , order , function , variable , sb-point , sp-point \cs_new_protected:Npn \__deriv_odv_both:nnnnnnn #1 #2 #3 #4 #5 #6 #7 { \__deriv_set_order:Nn \l__deriv_d_order_tl {#3} \__deriv_evaluation_slash:nnnn {#2} {#6} {#7} { \__deriv_fraction_slash:nn {#2} { \use:c { __deriv_#2_style_frac_slash:n } { \__deriv_d_numerator_nofun:nn {#1} {#2} } { \__deriv_d_denominator:nnn {#1} {#2} {#5} } } \__deriv_function:nn {#2} {#4} } } % inf , dv , order , function , variable , sb-point , sp-point \cs_new_protected:Npn \__deriv_odv_star:nnnnnnn #1 #2 #3 #4 #5 #6 #7 { \__deriv_set_order:Nn \l__deriv_d_order_tl {#3} \__deriv_evaluation:nnnn {#2} {#6} {#7} { \__deriv_fraction:nn {#2} { \use:c { __deriv_#2_style_frac:n } { \__deriv_d_numerator_nofun:nn {#1} {#2} } { \__deriv_d_denominator:nnn {#1} {#2} {#5} } } \__deriv_function:nn {#2} {#4} } } % inf , dv , order , function , variable , sb-point , sp-point \cs_new_protected:Npn \__deriv_odv_slash:nnnnnnn #1 #2 #3 #4 #5 #6 #7 { \__deriv_set_order:Nn \l__deriv_d_order_tl {#3} \__deriv_evaluation_slash:nnnn {#2} {#6} {#7} { \__deriv_fraction_slash:nn {#2} { \use:c { __deriv_#2_style_frac_slash:n } { \__deriv_d_numerator_fun:nnn {#1} {#2} {#4} } { \__deriv_d_denominator:nnn {#1} {#2} {#5} } } } } % inf , dv , order , function , variable , sb-point , sp-point \cs_new_protected:Npn \__deriv_odv_none:nnnnnnn #1 #2 #3 #4 #5 #6 #7 { \__deriv_set_order:Nn \l__deriv_d_order_tl {#3} \__deriv_evaluation:nnnn {#2} {#6} {#7} { \__deriv_fraction:nn {#2} { \use:c { __deriv_#2_style_frac:n } { \__deriv_d_numerator_fun:nnn {#1} {#2} {#4} } { \__deriv_d_denominator:nnn {#1} {#2} {#5} } } } } % inf , dv , function \cs_new_protected:Npn \__deriv_d_numerator_fun:nnn #1 #2 #3 { \__deriv_insert_inf:nn {#1} {#2} \__deriv_insert_ord:Nnn \l__deriv_d_order_tl {#2} { inf_ord } \__deriv_insert_fun:Nnn \l__deriv_d_order_tl {#2} {#3} } % inf , dv \cs_new_protected:Npn \__deriv_d_numerator_nofun:nn #1 #2 { \__deriv_insert_inf:nn {#1} {#2} \__deriv_insert_ord:Nnn \l__deriv_d_order_tl {#2} { inf_ord } } % inf , dv , variable \cs_new_protected:Npn \__deriv_d_denominator:nnn #1 #2 #3 { \__deriv_insert_inf:nn {#1} {#2} \__deriv_insert_var_ord:Nnn \l__deriv_d_order_tl {#2} {#3} } %%%%% Partial derivative definition %%%%% % inf , dv , order , mixed order , function , variable , sb-point , sp-point \cs_new_protected:Npn \__deriv_pdv_both:nnnnnnnn #1 #2 #3 #4 #5 #6 #7 #8 { \__deriv_preparation:NNnnnnn \l__deriv_p_mo_tl \l__deriv_p_denom_tl {#1} {#2} {#3} {#4} {#6} \__deriv_evaluation_slash:nnnn {#2} {#7} {#8} { \__deriv_fraction_slash:nn {#2} { \use:c { __deriv_#2_style_frac_slash:n } { \__deriv_p_numerator_nofun:nn {#1} {#2} } { \__deriv_p_denominator:n {#2} } } \__deriv_function:nn {#2} {#5} } } % inf , dv , order , mixed order , function , variable , sb-point , sp-point \cs_new_protected:Npn \__deriv_pdv_star:nnnnnnnn #1 #2 #3 #4 #5 #6 #7 #8 { \__deriv_preparation:NNnnnnn \l__deriv_p_mo_tl \l__deriv_p_denom_tl {#1} {#2} {#3} {#4} {#6} \__deriv_evaluation:nnnn {#2} {#7} {#8} { \__deriv_fraction:nn {#2} { \use:c { __deriv_#2_style_frac:n } { \__deriv_p_numerator_nofun:nn {#1} {#2} } { \__deriv_p_denominator:n {#2} } } \__deriv_function:nn {#2} {#5} } } % inf , dv , order , mixed order , function , variable , sb-point , sp-point \cs_new_protected:Npn \__deriv_pdv_slash:nnnnnnnn #1 #2 #3 #4 #5 #6 #7 #8 { \__deriv_preparation:NNnnnnn \l__deriv_p_mo_tl \l__deriv_p_denom_tl {#1} {#2} {#3} {#4} {#6} \__deriv_evaluation_slash:nnnn {#2} {#7} {#8} { \__deriv_fraction_slash:nn {#2} { \use:c { __deriv_#2_style_frac_slash:n } { \__deriv_p_numerator_fun:nnn {#1} {#2} {#5} } { \__deriv_p_denominator:n {#2} } } } } % inf , dv , order , mixed order , function , variable , sb-point , sp-point \cs_new_protected:Npn \__deriv_pdv_none:nnnnnnnn #1 #2 #3 #4 #5 #6 #7 #8 { \__deriv_preparation:NNnnnnn \l__deriv_p_mo_tl \l__deriv_p_denom_tl {#1} {#2} {#3} {#4} {#6} \__deriv_evaluation:nnnn {#2} {#7} {#8} { \__deriv_fraction:nn {#2} { \use:c { __deriv_#2_style_frac:n } { \__deriv_p_numerator_fun:nnn {#1} {#2} {#5} } { \__deriv_p_denominator:n {#2} } } } }% inf , dv , function \cs_new_protected:Npn \__deriv_p_numerator_fun:nnn #1 #2 #3 { \__deriv_insert_inf:nn {#1} {#2} \__deriv_insert_ord:Nnn \l__deriv_p_mo_tl {#2} { inf_ord } \__deriv_insert_fun:Nnn \l__deriv_p_mo_tl {#2} {#3} } % inf , dv \cs_new_protected:Npn \__deriv_p_numerator_nofun:nn #1 #2 { \__deriv_insert_inf:nn {#1} {#2} \__deriv_insert_ord:Nnn \l__deriv_p_mo_tl {#2} { inf_ord } } % dv \cs_new_protected:Npn \__deriv_p_denominator:n #1 { \tl_use:N \l__deriv_p_denom_tl %{ \__deriv_insert_mskip:nn {#1} { var_inf } } } % mixed-order-tl , denom-seq , inf , dv , order , mixed order , variable \cs_new_protected:Npn \__deriv_preparation:NNnnnnn #1 #2 #3 #4 #5 #6 #7 { \seq_clear:N #2 \seq_set_from_clist:Nn \l__deriv_p_var_seq {#7} \tl_if_novalue:nTF {#5} { \seq_clear:N \l__deriv_p_order_seq } { \seq_set_from_clist:Nn \l__deriv_p_order_seq {#5} } \tl_if_novalue:nTF {#6} { \seq_set_eq:NN \l__deriv_p_mo_seq \l__deriv_p_order_seq \__deriv_adjust_mo_seq:NNN \l__deriv_p_mo_seq \l__deriv_p_var_seq \l__deriv_p_order_seq \__deriv_mixed_order:NNn #1 \l__deriv_p_mo_seq {#4} } { \tl_set:Nn #1 {#6} } \__deriv_p_build_denom:NNNnn \l__deriv_p_var_seq \l__deriv_p_order_seq #2 {#3} {#4} } \cs_new_protected:Npn \__deriv_adjust_mo_seq:NNN #1 #2 #3 { \int_set:Nn \l__deriv_vmo_int { \seq_count:N #2 - \seq_count:N #3 } \__deriv_case:nF { { \int_compare_p:nNn { \l__deriv_vmo_int } > { 0 } } { \seq_put_left:NV #1 \l__deriv_vmo_int } { \int_compare_p:nNn { \l__deriv_vmo_int } = { 0 } } { \prg_do_nothing: } } { \int_step_inline:nn { -1 * \l__deriv_vmo_int } { \seq_pop_right:NN #1 \l__deriv_p_tmpa_tl } } } % \l__deriv_p_var_seq \l__deriv_p_order_seq, denom-tl , inf , dv \cs_new_protected:Npn \__deriv_p_build_denom:NNNnn #1 #2 #3 #4 #5 { \int_zero:N \l__deriv_tmpa_int \seq_map_inline:Nn #1 { \int_incr:N \l__deriv_tmpa_int \seq_pop_left:NN #2 \l__deriv_p_tmpa_tl \tl_if_blank:nF {##1} { \tl_put_right:Nx #3 { \__deriv_insert_inf:nn {#4} {#5} \int_compare:nNnTF { \l__deriv_tmpa_int } = { \seq_count:N #1 } { \__deriv_insert_var_ord:Nnn \l__deriv_p_tmpa_tl {#5} {##1} } { \__deriv_insert_var_ord_sep:Nnn \l__deriv_p_tmpa_tl {#5} {##1} } } } } } %%%%% And the rest of the code %%%%% % inf , dv \cs_new:Npn \__deriv_insert_inf:nn #1 #2 { \exp_not:n { \use:c { __deriv_#2_style_inf:n } {#1} } } % dv , function \cs_new:Npn \__deriv_insert_fun:Nnn #1 #2 #3 { \tl_if_blank:nF {#3} { \str_if_eq:NNTF #1 1 { \__deriv_insert_mskip:nn {#2} { inf_fun } } { \__deriv_insert_mskip:nn {#2} { ord_fun } } \__deriv_function:nn {#2} {#3} } } % order, dv , variable \cs_new:Npn \__deriv_insert_var_ord:Nnn #1 #2 #3 { \tl_if_blank:nF {#3} { \__deriv_insert_mskip:nn {#2} { inf_var } \exp_not:n { \__deriv_variable:nn {#2} {#3} } \__deriv_insert_ord:Nnn #1 {#2} { var_ord } } } \cs_new:Npn \__deriv_insert_var_ord_sep:Nnn #1 #2 #3 { \tl_if_blank:nF {#3} { \__deriv_insert_mskip:nn {#2} { inf_var } \exp_not:n { \__deriv_variable:nn {#2} {#3} } \__deriv_insert_ord:Nn #1 {#2} } } % dv , name \cs_new:Npn \__deriv_insert_mskip:nn #1 #2 { \str_if_eq:vnF { l__deriv_#1_sep_#2_muskip } { 0.0mu } { \exp_args:Nc \mskip { l__deriv_#1_sep_#2_muskip } } } % order , dv , name \cs_new:Npn \__deriv_insert_ord:Nnn #1 #2 #3 { \__deriv_show_order:NT #1 { \sp { \__deriv_insert_mskip:nn {#2} {#3} \tl_use:N #1 } } } % order , dv , name \cs_new:Npn \__deriv_insert_ord:Nn #1 #2 { \__deriv_show_order:NTF #1 { \sp { \__deriv_insert_mskip:nn {#2} { var_ord } \tl_use:N #1 } \__deriv_insert_mskip:nn {#2} { ord_inf } } { \__deriv_insert_mskip:nn {#2} { var_inf } } } % order , order-list \cs_new:Npn \__deriv_set_order:Nn #1 #2 { \tl_if_novalue:nTF {#2} { \tl_set:Nn #1 { 1 } } { \tl_set:Nn #1 {#2} } } % muskip , length \cs_new:Npn \__deriv_set_rubber_length:Nn #1 #2 { \seq_set_split:Nnn \l__deriv_rubber_seq { , } { #2 } \exp_args:NNf \muskip_set:Nn #1 { \seq_use:Nnnn \l__deriv_rubber_seq { mu plus } { mu plus } { mu minus } mu } } %%%%% Scale, delimiters, evaluation %%%%% % dv , function \cs_new:Npn \__deriv_function:nn #1 #2 { \bool_set_false:c { l__deriv_#1_mics_var_bool } \bool_if:cTF { l__deriv_#1_mics_fun_bool } { \bool_set_false:c { l__deriv_#1_mics_fun_bool } \__deriv_add_delims:nnn {#1} { fun } {#2} } { #2 } } % dv , variable \cs_new:Npn \__deriv_variable:nn #1 #2 { \bool_if:cTF { l__deriv_#1_mics_var_bool } { \bool_set_false:c { l__deriv_#1_mics_var_bool } \__deriv_add_delims:nnn {#1} { var } {#2} } { \__deriv_handle_double_sp:n {#2} } } % variable \cs_new:Npn \__deriv_handle_double_sp:n #1 { \tl_set:Nn \l_tmpa_tl {#1} \str_set:Nn \l_tmpa_str {#1} \str_if_in:NnTF \l_tmpa_str { ^ } { \exp_args:Nf \str_if_eq:nnTF { \tl_item:Nn \l_tmpa_tl {-2} } { ^ } { {#1} } { \exp_args:Nf \str_if_eq:nnTF { \tl_item:Nn \l_tmpa_tl {-4} } { ^ } { {#1} } { #1 } } } {#1} } % dv , code-for-fraction \cs_new:Npn \__deriv_fraction:nn #1 #2 { \bool_if:cTF { l__deriv_#1_mics_frac_bool } { \bool_set_false:c { l__deriv_#1_mics_frac_bool } \__deriv_add_delims:nnn {#1} { frac } {#2} } { #2 } } % dv , code-for-fraction \cs_new:Npn \__deriv_fraction_slash:nn #1 #2 { \bool_if:cTF { l__deriv_#1_mics_frac_bool } { \bool_set_false:c { l__deriv_#1_mics_frac_bool } \__deriv_add_delims:nnn {#1} { frac_slash } {#2} } { #2 } } % dv , sub , sup , code-for-fraction \cs_new:Npn \__deriv_evaluation:nnnn #1 #2 #3 #4 { \__deriv_if_novalue_and:nnTF {#2} {#3} { #4 } { \__deriv_add_delims:nnn {#1} { eval } {#4} \__deriv_if_novalue:nF {#2} { \sb{ \__deriv_insert_mskip:nn {#1} { eval_sb } #2 } } \__deriv_if_novalue:nF {#3} { \sp{ \__deriv_insert_mskip:nn {#1} { eval_sp } #3 } } } } % dv , sub , sup , code-for-fraction \cs_new:Npn \__deriv_evaluation_slash:nnnn #1 #2 #3 #4 { \__deriv_if_novalue_and:nnTF {#2} {#3} { #4 } { \__deriv_add_delims:nnn {#1} { eval_slash } {#4} \__deriv_if_novalue:nF {#2} { \sb{ \__deriv_insert_mskip:nn {#1} { eval_sb } #2 } } \__deriv_if_novalue:nF {#3} { \sp{ \__deriv_insert_mskip:nn {#1} { eval_sp } #3 } } } } % dv , name , value \cs_new:Npn \__deriv_add_delims:nnn #1 #2 #3 { \__deriv_scale_left:nn {#1} {#2} {#3} \__deriv_scale_right:nn {#1} {#2} } % dv , name \cs_new:Npn \__deriv_scale_left:nn #1 #2 { \exp_args:Nv \str_case:nnF { l__deriv_#1_scale_#2_tl } { { auto } { \__deriv_scale_auto:Nnnn \__deriv_auto_left:n {#1} {#2} { 1 } } { none } { \__deriv_scale_none:nnn {#1} {#2} { 1 } } } { \__deriv_scale_big:nnnn {#1} {#2} { 1 } { l } } } % dv , name \cs_new:Npn \__deriv_scale_right:nn #1 #2 { \exp_args:Nv \str_case:nnF { l__deriv_#1_scale_#2_tl } { { auto } { \__deriv_scale_auto:Nnnn \__deriv_auto_right:n {#1} {#2} { 2 } } { none } { \__deriv_scale_none:nnn {#1} {#2} { 2 } } } { \__deriv_scale_big:nnnn {#1} {#2} { 2 } { r } } } % left/right , dv , name, number \cs_new:Npn \__deriv_scale_auto:Nnnn #1 #2 #3 #4 { #1 \tl_item:cn { l__deriv_#2_delims_#3_tl } { #4 } } % dv , name , number \cs_new:Npn \__deriv_scale_none:nnn #1 #2 #3 { \str_if_eq:cNF { l__deriv_#1_delims_#2_tl } . { \tl_item:cn { l__deriv_#1_delims_#2_tl } { #3 } } } % dv , name , number , l/r \cs_new:Npn \__deriv_scale_big:nnnn #1 #2 #3 #4 { \tl_use:c { \tl_use:c { l__deriv_#1_scale_#2_tl } #4 } { \tl_item:cn { l__deriv_#1_delims_#2_tl } { #3 } } } %%%%% Calculation of mixed order %%%%% % mixed-order-tl , mixed-order-seq , dv \cs_new:Npn \__deriv_mixed_order:NNn #1 #2 #3 { \__deriv_replace:NN \l__deriv_input_seq #2 \__deriv_seq_counting:N \l__deriv_input_seq \__deriv_combine_seq:N \l__deriv_unsorted_seq \__deriv_sort:NNn \l__deriv_sorted_seq \l__deriv_unsorted_seq {#3} \__deriv_output:NNNn #1 \l__deriv_sorted_seq \l__deriv_numerical_int {#3} } % input-seq , mixed-order-seq \cs_new_protected:Npn \__deriv_replace:NN #1 #2 { \tl_set:Nf \l__deriv_input_tl { \seq_use:Nn #2 { , } } \tl_remove_all:Nn \l__deriv_input_tl { ~ } \tl_replace_all:Nnn \l__deriv_input_tl { -- } { , } \tl_replace_all:Nnn \l__deriv_input_tl { - } { ,- } \tl_replace_all:Nnn \l__deriv_input_tl { + } { , } \exp_args:NNV \seq_set_from_clist:Nn #1 \l__deriv_input_tl } % input-seq \cs_new_protected:Npn \__deriv_seq_counting:N #1 { \seq_clear:N \l__deriv_symbol_seq \seq_clear:N \l__deriv_number_seq \seq_map_inline:Nn #1 { \__deriv_extract:NNn \l__deriv_sym_tmpa_tl \l__deriv_num_tmpa_tl {##1} \seq_if_in:NVTF \l__deriv_symbol_seq \l__deriv_sym_tmpa_tl { \__deriv_update_seq:NN \l__deriv_sym_tmpa_tl \l__deriv_num_tmpa_tl } { \__deriv_add_to_seq:NN \l__deriv_sym_tmpa_tl \l__deriv_num_tmpa_tl } } } % sym-tl , num-tl , seq-item \cs_new_protected:Npn \__deriv_extract:NNn #1 #2 #3 { \regex_extract_once:NnN \c__deriv_pattern_regex {#3} \l__deriv_extract_seq \seq_pop_right:NN \l__deriv_extract_seq #1 \seq_pop_right:NN \l__deriv_extract_seq #2 \exp_args:NV \str_case:nn #2 { { } { \tl_set:Nn #2 { 1 } } { - } { \tl_set:Nn #2 { -1 } } } } % unsorted-seq \cs_new:Npn \__deriv_combine_seq:N #1 { \seq_clear:N #1 \seq_map_inline:Nn \l__deriv_symbol_seq { \seq_pop_left:NN \l__deriv_number_seq \l__deriv_num_tmpa_tl \__deriv_eval_term:NNn #1 \l__deriv_num_tmpa_tl {##1} } } % unsorted-seq , num-tl, seq-item \cs_new_protected:Npn \__deriv_eval_term:NNn #1 #2 #3 { \__deriv_case:nF { { \tl_if_empty_p:n {#3} } { \int_set:Nn \l__deriv_numerical_int {#2} } { \int_compare_p:nNn {#2} = { 1 } } { \seq_put_left:Nn #1 {#3} } { \int_compare_p:nNn {#2} = { 0 } } { \prg_do_nothing: } { \int_compare_p:nNn {#2} = { -1 } } { \seq_put_left:Nn #1 { -#3 } } } { \seq_put_left:No #1 { #2 #3 } } } % sym-tl , num-tl \cs_new_protected:Npn \__deriv_add_to_seq:NN #1 #2 { \seq_put_left:NV \l__deriv_symbol_seq #1 \seq_put_left:NV \l__deriv_number_seq #2 } % sym-tl , num-tl \cs_new_protected:Npn \__deriv_update_seq:NN #1 #2 { \__deriv_get_position:NN \l__deriv_position_int #1 \__deriv_rebuild_seq:NNN \l__deriv_number_seq \l__deriv_position_int #2 } % position-int , sym-tl \cs_new:Npn \__deriv_get_position:NN #1 #2 { \int_zero:N #1 \seq_map_inline:Nn \l__deriv_symbol_seq { \int_incr:N #1 \exp_args:NV \tl_if_eq:nnT #2 {##1} { \seq_map_break: } } } % num-seq , position-int , num-tl \cs_new_protected:Npn \__deriv_rebuild_seq:NNN #1 #2 #3 { \int_zero:N \l__deriv_rebuild_int \seq_clear:N \l__deriv_rebuild_seq \seq_map_inline:Nn #1 { \int_incr:N \l__deriv_rebuild_int \int_compare:nNnTF \l__deriv_rebuild_int = #2 { \tl_set:Nf \l__deriv_num_tmpb_tl { \int_eval:n { ##1 + #3 } } \seq_put_right:NV \l__deriv_rebuild_seq \l__deriv_num_tmpb_tl } { \seq_put_right:Nn \l__deriv_rebuild_seq {##1} } } \seq_set_eq:NN #1 \l__deriv_rebuild_seq } % sorted-seq , unsorted-seq , dv \cs_new_protected:Npn \__deriv_sort:NNn #1 #2 #3 { \int_set:Nn \l__deriv_sort_max_int { \clist_count:c { l__deriv_#3_sort_method_clist } } \seq_sort:Nn #2 { \__deriv_extract:NNn \l__deriv_sym_tmpa_tl \l__deriv_num_tmpa_tl {##1} \__deriv_extract:NNn \l__deriv_sym_tmpb_tl \l__deriv_num_tmpb_tl {##2} \int_zero:N \l__deriv_sort_counter_int \__deriv_sort_method:n {#3} } \seq_set_eq:NN #1 #2 } % dv \cs_new_protected:Npn \__deriv_sort_method:n #1 { \int_incr:N \l__deriv_sort_counter_int \exp_args:Nf \str_case:nn { \clist_item:cn { l__deriv_#1_sort_method_clist } { \l__deriv_sort_counter_int } } { { sign } { \__deriv_sort_sign:n {#1} } { symbol } { \__deriv_sort_symbol:n {#1} } { abs } { \__deriv_sort_abs:n {#1} } } } % dv \cs_new_protected:Npn \__deriv_sort_sign:n #1 { \__deriv_case:nF { { \tl_if_head_eq_charcode_p:VN \l__deriv_num_tmpb_tl - && ! \tl_if_head_eq_charcode_p:VN \l__deriv_num_tmpa_tl - } { \__deriv_sort_reverse:nnn {#1} { sign } { same } } { \tl_if_head_eq_charcode_p:VN \l__deriv_num_tmpa_tl - && ! \tl_if_head_eq_charcode_p:VN \l__deriv_num_tmpb_tl - } { \__deriv_sort_reverse:nnn {#1} { sign } { swapped } } } { \int_compare:nNnTF { \l__deriv_sort_counter_int } = { \l__deriv_sort_max_int } { \sort_return_same: } { \__deriv_sort_method:n {#1} } } } % dv \cs_new_protected:Npn \__deriv_sort_symbol:n #1 { \__deriv_case:nF { { \int_compare_p:nNn { \tl_count:N \l__deriv_sym_tmpa_tl } > { \tl_count:N \l__deriv_sym_tmpb_tl } } { \__deriv_sort_reverse:nnn {#1} { symbol } { same } } { \int_compare_p:nNn { \tl_count:N \l__deriv_sym_tmpa_tl } < { \tl_count:N \l__deriv_sym_tmpb_tl } } { \__deriv_sort_reverse:nnn {#1} { symbol } { swapped } } } { \int_compare:nNnTF { \l__deriv_sort_counter_int } = { \l__deriv_sort_max_int } { \sort_return_same: } { \__deriv_sort_method:n {#1} } } } % dv \cs_new_protected:Npn \__deriv_sort_abs:n #1 { \__deriv_case:nF { { \int_compare_p:nNn { \int_abs:n \l__deriv_num_tmpa_tl } > { \int_abs:n \l__deriv_num_tmpb_tl } } { \__deriv_sort_reverse:nnn {#1} { abs } { same } } { \int_compare_p:nNn { \int_abs:n \l__deriv_num_tmpa_tl } < { \int_abs:n \l__deriv_num_tmpb_tl } } { \__deriv_sort_reverse:nnn {#1} { abs } { swapped } } } { \int_compare:nNnTF { \l__deriv_sort_counter_int } = { \l__deriv_sort_max_int } { \sort_return_same: } { \__deriv_sort_method:n {#1} } } } % dv , sort-method , same/swapped \cs_new_protected:Npn \__deriv_sort_reverse:nnn #1 #2 #3 { \exp_args:Nc \bool_xor:nnTF { l__deriv_#1_sort_#2_reverse_bool } { \str_if_eq_p:nn {#3} { same } } { \sort_return_same: } { \sort_return_swapped: } } % mixed-order-tl , sorted-seq , numerical-term, dv \cs_new_protected:Npn \__deriv_output:NNNn #1 #2 #3 #4 { \tl_set:Nf #1 { \seq_use:Nn #2 { + } } \int_compare:nNnF {#3} = { 0 } { \tl_if_empty:NTF #1 { \tl_put_left:NV #1 #3 } { \exp_args:Nv \str_case:nnF { l__deriv_#4_sort_numerical_tl } { { last } { \tl_put_right:Nx #1 { + \int_use:N #3 } } { first } { \tl_put_left:Nx #1 { \int_use:N #3 + } } } { \bool_if:nTF { \tl_if_head_eq_charcode_p:VN #1 - } { \tl_put_left:NV #1 #3 } { \tl_put_right:Nx #1 { + \int_use:N #3 } } } } } \tl_replace_all:Nnn #1 { +- } { - } \tl_if_empty:NT #1 { \tl_set:Nn #1 { 0 } } } %%%%% Declaring Variant %%%%% \DeclareDocumentCommand{\NewOdvVariant}{ m m o } { \cs_if_exist:NTF #1 { \msg_error:nnxx { deriv } { command-already-defined } { \token_to_str:N #1 } { \token_to_str:N \NewOdvVariant } } { \deriv_d_preamble:Nnn \l__deriv_dv_tmp_tl {#1} {#3} \deriv_d_define:Vnnn \l__deriv_dv_tmp_tl { New } {#1} {#2} } } \DeclareDocumentCommand{\RenewOdvVariant}{ m m o } { \cs_if_exist:NTF #1 { \deriv_d_preamble:Nnn \l__deriv_dv_tmp_tl {#1} {#3} \deriv_d_define:Vnnn \l__deriv_dv_tmp_tl { Renew } {#1} {#2} } { \msg_error:nnxx { deriv } { command-not-defined } { \token_to_str:N #1 } { \token_to_str:N \RenewOdvVariant } } } \DeclareDocumentCommand{\ProvideOdvVariant}{ m m o } { \cs_if_exist:NF #1 { \deriv_d_preamble:Nnn \l__deriv_dv_tmp_tl {#1} {#3} \deriv_d_define:Vnnn \l__deriv_dv_tmp_tl { Provide } {#1} {#2} } } \DeclareDocumentCommand{\DeclareOdvVariant}{ m m o } { \deriv_d_preamble:Nnn \l__deriv_dv_tmp_tl {#1} {#3} \deriv_d_define:Vnnn \l__deriv_dv_tmp_tl { Declare } {#1} {#2} } \DeclareDocumentCommand{\NewPdvVariant}{ m m o } { \cs_if_exist:NTF #1 { \msg_error:nnxx { deriv } { command-already-defined } { \token_to_str:N #1 } { \token_to_str:N \NewPdvVariant } } { \deriv_p_preamble:Nnn \l__deriv_dv_tmp_tl {#1} {#3} \deriv_p_define:Vnnn \l__deriv_dv_tmp_tl { New } {#1} {#2} } } \DeclareDocumentCommand{\RenewPdvVariant}{ m m o } { \cs_if_exist:NTF #1 { \deriv_p_preamble:Nnn \l__deriv_dv_tmp_tl {#1} {#3} \deriv_p_define:Vnnn \l__deriv_dv_tmp_tl { Renew } {#1} {#2} } { \msg_error:nnxx { deriv } { command-already-defined } { \token_to_str:N #1 } { \token_to_str:N \RenewPdvVariant } } } \DeclareDocumentCommand{\ProvidePdvVariant}{ m m o } { \cs_if_exist:NF #1 { \deriv_p_preamble:Nnn \l__deriv_dv_tmp_tl {#1} {#3} \deriv_p_define:Vnnn \l__deriv_dv_tmp_tl { Provide } {#1} {#2} } } \DeclareDocumentCommand{\DeclarePdvVariant}{ m m o } { \deriv_p_preamble:Nnn \l__deriv_dv_tmp_tl {#1} {#3} \deriv_p_define:Vnnn \l__deriv_dv_tmp_tl { Declare } {#1} {#2} } %%%%% slash frac %%%%% \DeclareDocumentCommand{\slashfrac}{ o m m } { \tl_if_novalue:nTF {#1} { \__deriv_slashfrac_auto:nn {#2} {#3} } { \str_case:nnF {#1} { { auto } { \__deriv_slashfrac_auto:nn {#2} {#3} } { none } { \__deriv_slashfrac_none:nn {#2} {#3} } } { \__deriv_slashfrac_scale:nnn {#1} {#2} {#3} } } } % numerator , denominator \cs_new_protected:Npn \__deriv_slashfrac_auto:nn #1 #2 { \__deriv_auto_left:n . \kern-\nulldelimiterspace {#1} \middle/ {#2} \__deriv_auto_right:n . \kern-\nulldelimiterspace } % numerator , denominator \cs_new_protected:Npn \__deriv_slashfrac_none:nn #1 #2 { {#1} / {#2} } % scale , numerator , denominator \cs_new_protected:Npn \__deriv_slashfrac_scale:nnn #1 #2 #3 { \cs:w #1 l \cs_end: . {#2} \cs:w #1 \cs_end: / {#3} \cs:w #1 r \cs_end: . } %%%%% Generate variants %%%%% \cs_generate_variant:Nn \tl_if_head_eq_charcode_p:nN { V } \cs_generate_variant:Nn \__deriv_set_rubber_length:Nn { c } \cs_generate_variant:Nn \__deriv_p_variables:n { V } \cs_generate_variant:Nn \__deriv_d_variables:n { V } \cs_generate_variant:Nn \deriv_p_define:nnnn { V } \cs_generate_variant:Nn \deriv_d_define:nnnn { V } \cs_generate_variant:Nn \__deriv_derivset:nn { V, VV } \cs_generate_variant:Nn \__deriv_p_define_keys:n { V } \cs_generate_variant:Nn \__deriv_d_define_keys:n { V } %%%%% Messages %%%%% \msg_new:nnnn { deriv } { command-already-defined } { Command~'#1'~already~defined! } { You~have~used~#2~with~a~command~that~already~has~a~definition. \\ The~existing~definition~of~'#1'~will~not~be~altered. } \msg_new:nnnn { deriv } { derivative-not-defined } { Derivative~'#1'~is~not~defined! } { You~have~used~#2~with~a~derivative~that~was~never~defined. } \msg_new:nnnn { deriv } { command-not-defined } { Command~'#1'~not~yet~defined! } { You~have~used~#2~with~a~derivative~that~was~never~defined. } %%%%% Declaring derivatives %%%%% \bool_lazy_or:nnT { \sys_if_engine_luatex_p: } { \sys_if_engine_xetex_p: } { \DeclareOdvVariant{\odv}{d}[style-inf = \symup] \DeclareOdvVariant{\mdv}{D}[style-inf = \symup] \DeclareOdvVariant{\fdv}{\delta} \DeclareOdvVariant{\adv}{\Delta} \DeclareOdvVariant{\jdv}{\partial}[misc-add-delims = {fun, var}] \DeclarePdvVariant{\pdv}{\partial}[sep-inf-ord=1, sep-ord-fun=-2] } \sys_if_engine_pdftex:T { \DeclareOdvVariant{\odv}{d}[style-inf = \mathrm] \DeclareOdvVariant{\mdv}{D}[style-inf = \mathrm] \DeclareOdvVariant{\fdv}{\delta} \DeclareOdvVariant{\adv}{\Delta}[style-inf = \mathrm] \DeclareOdvVariant{\jdv}{\partial}[misc-add-delims = {fun, var}] \DeclarePdvVariant{\pdv}{\partial}[sep-inf-ord=1, sep-ord-fun=-2] } \derivset{all} \endinput