% File: intexgral.tex
%
% Copyright (C) 2025 Valentin Dao
%
% 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
%
%   https://www.latex-project.org/lppl.txt
%
% and version 1.3c or later is part of all distributions of LaTeX
% version 2008 or later.
%
% This work has the LPPL maintenance status `maintained'.
% 
% The Current Maintainer of this work is Valentin Dao.
%
% This work consists of the file intexgral.sty. 

\NeedsTeXFormat{LaTeX2e}
\RequirePackage{expl3}[2025-05-14]
\RequirePackage{l3keys2e}
\ProvidesExplPackage{intexgral}{2025-07-26}{1.0.0}{A LaTeX package for typesetting integrals.}

\@ifpackagelater{expl3}{2025-05-14}{}{\PackageError{expl3~version~too~old.}}

\bool_new:N \l__intexgral_pkg_invert_limits_bool
\bool_new:N \l__intexgral_pkg_deactivate_differential_bool
\bool_new:N \l__intexgral_pkg_invert_differential_bool

\keys_define:nn { intexgral } 
  {
    invert-limits .bool_set:N = \l__intexgral_pkg_invert_limits_bool,
    invert-limits .usage:n = { load },
    invert-limits .default:n = { false },

    hide-differentials .bool_set:N = \l__intexgral_pkg_deactivate_differential_bool,
    hide-differentials .usage:n = { load },
    hide-differentials .default:n = { false },

    invert-differentials .bool_set:N = \l__intexgral_pkg_invert_differential_bool,
    invert-differentials .usage:n = { load },
    invert-differentials .default:n = { false },

    italic .choice:,
      italic / true .code:n = { \PassOptionsToPackage{italic=true}{derivative} },
      italic / false .code:n = { \PassOptionsToPackage{italic=false}{derivative} },

    upright .choice:,
      upright / true .code:n = { \PassOptionsToPackage{upright=true}{derivative} },
      upright / false .code:n = { \PassOptionsToPackage{upright=false}{derivative} },
  }


\ProcessKeysPackageOptions{intexgral}

\RequirePackage{derivative}

\cs_new:Nn \__intexgral_pkg_warning_msg_header: {
  (integral~no.~\int_use:N\g__intexgral_pkg_integral_number_int\c_space_tl\msg_line_context:)
}

\msg_new:nnnn { intexgral } { diff-group-alr-def }
  { Differential~group~"\tl_trim_spaces:n{#1}"~already~defined. }
  { You~should~use~\token_to_str:N\RenewDifferentialKeyword~instead. }

\msg_new:nnnn { intexgral } { diff-group-not-def }
  { Differential~group~"\tl_trim_spaces:n{#1}"~undefined. }
  { You~should~use~\token_to_str:N\NewDifferentialKeyword~instead. }

\msg_new:nnnn { intexgral } { lim-group-alr-def }
  { Limits~group~"\tl_trim_spaces:n{#1}"~already~defined. }
  { You~should~use~\token_to_str:N\RenewLimitsKeyword~instead. }

\msg_new:nnnn { intexgral } { lim-group-not-def }
  { Limits~group~"\tl_trim_spaces:n{#1}"~undefined. }
  { You~should~use~\token_to_str:N\NewLimitsKeyword~instead. }

\msg_new:nnn { intexgral } { unknown-int-symb }
  { Unknown~integral~symbol~"\tl_trim_spaces:n{#1}"~substituted~to~\token_to_str:N\int. }

\msg_new:nnn { intexgral } { no-diff-despite-macro }
  { 
    Unknown~differentials~\__intexgral_pkg_warning_msg_header:\\
    You~used~\token_to_str:N\differentials~but~no~differentials~were~declared.
  }

\msg_new:nnn { intexgral } { semicolon-misused }
{
  Semicolon~misused~\__intexgral_pkg_warning_msg_header:\\
  The~integrand~contains~semicolon(s),~but~"int-split=true"~was~not~enabled.~\\
  As~a~precaution,~I~have~removed~~them.
}

\msg_new:nnn { intexgral } { unequal-dim }
  { 
    Inconsistent~separation~\__intexgral_pkg_warning_msg_header:\\
    The~integral~sequence~contains~#1~element(s).\\
    The~integrand~sequence~contains~#2~element(s).\\
    The~differentials~sequence~contains~#3~element(s). 
  }

\msg_new:nnn { intexgral } { no-jacobian }
  {
    No~jacobian~\__intexgral_pkg_warning_msg_header:\\
    You~asked~to~display~the~jacobian~but~it~hasn't~been~declared~for~the~corresponding~differentials. 
  }

\msg_new:nnn { intexgral } { use-glyph-instead }
  {
    Use~adapted~glyph~instead~\__intexgral_pkg_warning_msg_header:\\
    You~used~the~key~"multiple"~for~a~symbol~containing~less~than~5~regular~integrals.~You~may~want~to~use~the~font's~dedicated~glyph~instead. 
  }

\msg_new:nnn { intexgral } { missing-diff }
  {
    Missing~differentials~\__intexgral_pkg_warning_msg_header:\\
    I~have~spotted~\token_to_str:N\differentials~only~#1~times~whereas~you~declared~#2~variables.
  }

\msg_new:nnn { intexgral } { missing-var }
  {
    Too~many~differentials~\__intexgral_pkg_warning_msg_header:\\
    The~amount~of~\token_to_str:N\differentials~exceeded~that~of~the~variables.~The~subsequent~\token_to_str:N\differentials~won't~show~anything.
  }

\msg_new:nnnn { intexgral } { int-symb-alr-def }
  { Integral~symbol~\tl_trim_spaces:n{#1}~already~defined }
  { You~should~use~\token_to_str:N\RenewIntegralSymbol~instead. }

\msg_new:nnnn { intexgral } { int-symb-not-def }
  { Integral~symbol~\tl_trim_spaces:n{#1}~undefined }
  { You~should~use~\token_to_str:N\NewIntegralSymbol~instead. }

\cs_new_protected:Npn \__intexgral_pkg_mathchoice:nnnn #1#2#3#4 {
  \mathchoice{#1}{#2}{#3}{#4}
}
\cs_generate_variant:Nn \regex_if_match:nnTF { nVTF }
\cs_generate_variant:Nn \__intexgral_pkg_new_limits_group:nn { nV }
\cs_generate_variant:Nn \str_if_eq:nnTF { neTF } 
\cs_generate_variant:Nn \str_if_eq:nnF { neF }
\cs_generate_variant:Nn \__intexgral_pkg_parse_variable:nn { oo }

\tl_new:N \l__intexgral_pkg_integrand_tl
\tl_new:N \l__intexgral_pkg_integral_symbol_tl
\tl_new:N \l__intexgral_pkg_lower_limit_tl
\tl_new:N \l__intexgral_pkg_upper_limit_tl
\tl_new:N \l__intexgral_pkg_limits_style_tl
\tl_new:N \l__intexgral_pkg_differentials_options_i_tl
\tl_new:N \l__intexgral_pkg_differentials_options_ii_tl
\tl_new:N \l__intexgral_pkg_vectorial_differential_style_tl
\tl_new:N \l__intexgral_pkg_independent_differential_options_tl
\tl_new:N \l__intexgral_pkg_domain_char_tl
\tl_new:N \l__intexgral_pkg_domain_dimension_tl
\tl_const:Nn \c__intexgral_pkg_left_bracket_tl { [ }
\tl_const:Nn \c__intexgral_pkg_right_bracket_tl { ] }

\tl_set_eq:NN \l__intexgral_pkg_integral_symbol_tl \int 
\tl_set:Nn \l__intexgral_pkg_vectorial_differential_style_tl { \vec }

\bool_new:N \l__intexgral_pkg_manual_differentials_bool
\bool_new:N \l__intexgral_pkg_custom_variables_bool
\bool_new:N \l__intexgral_pkg_separate_integral_bool
\bool_new:N \l__intexgral_pkg_vectorial_differentials_bool
\bool_new:N \l__intexgral_pkg_jacobian_bool
\bool_new:N \l__intexgral_pkg_starred_differential_bool
\bool_new:N \l__intexgral_pkg_has_order_bool
\bool_new:N \l__intexgral_pkg_has_var_bool

\bool_set_false:N \l__intexgral_pkg_vectorial_differentials_bool
\bool_set_false:N \l__intexgral_pkg_manual_differentials_bool
\bool_set_false:N \l__intexgral_pkg_custom_variables_bool
\bool_set_false:N \l__intexgral_pkg_separate_integral_bool
\bool_set_false:N \l__intexgral_pkg_has_order_bool
\bool_set_false:N \l__intexgral_pkg_has_var_bool

\clist_new:N \g__intexgral_pkg_independent_differential_options_clist
\clist_new:N \l__intexgral_pkg_variable_i_clist
\clist_new:N \l__intexgral_pkg_variable_ii_clist
\clist_new:N \l__intexgral_pkg_var_index_clist

\seq_new:N \l__intexgral_pkg_integrand_seq
\seq_new:N \l__intexgral_pkg_integral_symbol_seq
\seq_new:N \l__intexgral_pkg_jacobian_seq
\seq_new:N \l__intexgral_pkg_differential_seq
\seq_new:N \l__intexgral_pkg_limits_seq
\seq_new:N \l__intexgral_pkg_upper_limits_seq
\seq_new:N \l__intexgral_pkg_lower_limits_seq
\seq_new:N \l__intexgral_pkg_differential_var_i_seq
\seq_new:N \l__intexgral_pkg_differential_var_ii_seq
\seq_new:N \l__intexgral_pkg_differential_order_i_seq
\seq_new:N \l__intexgral_pkg_differential_order_ii_seq
\seq_new:N \l__intexgral_pkg_domain_seq

\prop_new:N \g__intexgral_pkg_limits_keyword_prop
\prop_new:N \g__intexgral_pkg_differential_group_keyword_prop

\int_new:N \l__intexgral_pkg_integral_sequence_int
\int_gzero_new:N \g__intexgral_pkg_integral_number_int

\cs_new_protected:Npn \__intexgral_pkg_new_integral_symbol:n #1 {
  \tl_new:c { c__intexgral_pkg_#1_symbol_tl }
  \cs_if_exist:cTF { #1 }
    { \tl_set_eq:cc { c__intexgral_pkg_#1_symbol_tl } { #1 } }
    { 
      \msg_warning:nne { intexgral } { unknown-int-symb } { \token_to_str:N #1 }
      \tl_set_eq:cc { c__intexgral_pkg_#1_symbol_tl } { int }
    }
}

\cs_new_protected:Nn \__intexgral_pkg_check_sequence_size: {
  \int_compare:nNnTF 
    { \seq_count:N \l__intexgral_pkg_integral_symbol_seq }
    =
    { \seq_count:N \l__intexgral_pkg_integrand_seq }
      {
        \int_compare:nNnF
          { \seq_count:N \l__intexgral_pkg_integrand_seq }
          =
          { \seq_count:N \l__intexgral_pkg_differential_seq }
            {
              \msg_warning:nneee { intexgral } { unequal-dim } 
                { \seq_count:N \l__intexgral_pkg_integral_symbol_seq }
                { \seq_count:N \l__intexgral_pkg_integrand_seq       }
                { \seq_count:N \l__intexgral_pkg_differential_seq    }
            }
      }
      {
        \msg_warning:nneee { intexgral } { unequal-dim } 
          { \seq_count:N \l__intexgral_pkg_integral_symbol_seq }
          { \seq_count:N \l__intexgral_pkg_integrand_seq       }
          { \seq_count:N \l__intexgral_pkg_differential_seq    }
      }
}

\cs_new_protected:Npn \__intexgral_pkg_set_limits:nn #1#2 {
  \bool_if:NTF \l__intexgral_pkg_invert_limits_bool
    {
      \tl_set:Nn \l__intexgral_pkg_lower_limit_tl { #2 }
      \tl_set:Nn \l__intexgral_pkg_upper_limit_tl { #1 }
    }
    {
      \tl_set:Nn \l__intexgral_pkg_lower_limit_tl { #1 }
      \tl_set:Nn \l__intexgral_pkg_upper_limit_tl { #2 }
    }
}

\cs_new_protected:Npn \__intexgral_pkg_parse_integral_symbol: { 
  \tl_use:N \l__intexgral_pkg_integral_symbol_tl
  \tl_use:N \l__intexgral_pkg_limits_style_tl
  \c_math_subscript_token
    { \l__intexgral_pkg_lower_limit_tl }
  \c_math_superscript_token 
    { \l__intexgral_pkg_upper_limit_tl } 
}

\cs_new_protected:Nn \__intexgral_pkg_integral_preconfiguration: {
  \int_gincr:N \g__intexgral_pkg_integral_number_int

  \cs_new_protected:Npn \differentials {
    \seq_if_empty:NTF \l__intexgral_pkg_differential_seq
      { \msg_warning:nn { intexgral } { missing-var } }
      {
        \bool_if:NTF \l__intexgral_pkg_invert_differential_bool
          {
            \seq_gpop_left:NN \l__intexgral_pkg_differential_seq \l_tmpa_tl
            \tl_use:N \l_tmpa_tl
            \seq_if_empty:NF \l__intexgral_pkg_jacobian_seq
              { 
                \seq_gpop_left:NN \l__intexgral_pkg_jacobian_seq \l_tmpb_tl
                \tl_use:N \l_tmpb_tl
              }
          }
          {
            \seq_if_empty:NF \l__intexgral_pkg_jacobian_seq
              { 
                \seq_gpop_left:NN \l__intexgral_pkg_jacobian_seq \l_tmpb_tl
                \tl_use:N \l_tmpb_tl
              }
            \seq_gpop_left:NN \l__intexgral_pkg_differential_seq \l_tmpa_tl
            \tl_use:N \l_tmpa_tl
          }
      }
  }

  \bool_if:NTF \l__intexgral_pkg_separate_integral_bool
    { \seq_set_split:NnV \l__intexgral_pkg_integrand_seq { ; } \l__intexgral_pkg_integrand_tl }
    { 
      \tl_if_in:NnT \l__intexgral_pkg_integrand_tl { ; } 
        { 
          \msg_warning:nn { intexgral } { semicolon-misused } 
          \tl_remove_all:Nn \l__intexgral_pkg_integrand_tl { ; }
        }
    }

  \seq_if_empty:NT \l__intexgral_pkg_integral_symbol_seq 
    {
      \seq_put_right:Nn \l__intexgral_pkg_integral_symbol_seq 
        { \__intexgral_pkg_parse_integral_symbol: }
    }

  \seq_if_empty:NT \l__intexgral_pkg_integrand_seq
    {
      \seq_put_right:NV \l__intexgral_pkg_integrand_seq \l__intexgral_pkg_integrand_tl
    }

  \__intexgral_pkg_parse_differentials:

  \bool_if:NTF \l__intexgral_pkg_jacobian_bool 
    {
      \seq_if_empty:NT \l__intexgral_pkg_jacobian_seq
        { \msg_warning:nn { intexgral } { no-jacobian } }
    }
    { \seq_clear:N \l__intexgral_pkg_jacobian_seq }

  \regex_if_match:nVTF { \c{differentials}+ } \l__intexgral_pkg_integrand_tl 
    { \bool_set_true:N \l__intexgral_pkg_manual_differentials_bool }
    { \bool_set_false:N \l__intexgral_pkg_manual_differentials_bool }

  \bool_if:NT \l__intexgral_pkg_manual_differentials_bool
    { 
      \regex_count:nVN { \c{differentials} } \l__intexgral_pkg_integrand_tl \l_tmpa_int
      \int_set:Nn \l_tmpb_int { \seq_count:N \l__intexgral_pkg_differential_seq }
      \int_compare:nNnT 
        { \l_tmpa_int }
        <
        { \l_tmpb_int }
        { \msg_warning:nnee { intexgral } { missing-diff } { \l_tmpa_int } { \seq_count:N \l__intexgral_pkg_differential_seq } }
    }

  \bool_if:NT \l__intexgral_pkg_separate_integral_bool
    { \__intexgral_pkg_check_sequence_size: }
}

\cs_new_protected:Nn \__intexgral_pkg_print_integral: {

  \seq_log:N \l__intexgral_pkg_differential_seq

  \__intexgral_pkg_integral_preconfiguration:

  \seq_log:N \l__intexgral_pkg_differential_seq

  \int_step_inline:nn { \seq_count:N \l__intexgral_pkg_integral_symbol_seq }
    {
      \seq_item:Nn \l__intexgral_pkg_integral_symbol_seq { ##1 }

      \bool_if:NT \l__intexgral_pkg_invert_differential_bool
        { 
          \bool_if:NF \l__intexgral_pkg_manual_differentials_bool
            { 
              \bool_if:NF \l__intexgral_pkg_deactivate_differential_bool
                { \seq_item:Nn \l__intexgral_pkg_differential_seq { ##1 } }
              \bool_if:NT \l__intexgral_pkg_jacobian_bool
                { \seq_item:Nn \l__intexgral_pkg_jacobian_seq { ##1 } }
            } 
        }

      \seq_item:Nn \l__intexgral_pkg_integrand_seq { ##1 }

      \bool_if:NT \l__intexgral_pkg_vectorial_differentials_bool
        {
          \bool_if:NTF \l__intexgral_pkg_separate_integral_bool
            { \cdot }
            {
              \int_compare:nNnT { ##1 } = { 1 }
                { \cdot }
            }
        }

      \bool_if:NF \l__intexgral_pkg_invert_differential_bool
        { 
          \bool_if:NF \l__intexgral_pkg_manual_differentials_bool
            { 
              \bool_if:NT \l__intexgral_pkg_jacobian_bool
                { \seq_item:Nn \l__intexgral_pkg_jacobian_seq { ##1 } }
              \bool_if:NF \l__intexgral_pkg_deactivate_differential_bool
                { \seq_item:Nn \l__intexgral_pkg_differential_seq { ##1 } }
            } 
        }
    }
}

\cs_new_protected:Npn \__intexgral_pkg_new_limits_group:nn #1#2 {
  \prop_put:Nnn \g__intexgral_pkg_limits_keyword_prop { #1 } { #2 }
}

\cs_new_protected:Npn \__intexgral_pkg_new_differential_group:nnn #1#2#3 {
  \prop_put:Nnn \g__intexgral_pkg_differential_group_keyword_prop 
    { #1 } { #2 }
  \tl_if_blank:nF { #3 }
    {
      \clist_set:Nn \l_tmpa_clist { #3 }
      \seq_set_from_clist:cN { g__#1_jacobian_seq } \l_tmpa_clist
    }
}

\cs_new:Npn \__intexgral_pkg_parse_integral_limit:n #1 {
  \prop_if_in:NnTF \g__intexgral_pkg_limits_keyword_prop { #1 }
    { \prop_item:Nn \g__intexgral_pkg_limits_keyword_prop { #1 } }
    { #1 }
}

\cs_new:Npn \__intexgral_pkg_differentials:nn #1#2 {
  \bool_if:NTF \l__intexgral_pkg_starred_differential_bool
    { \odif*[#1]{#2} }
    { \odif[#1]{#2} }
}

\cs_new_protected:Npn \__intexgral_pkg_extract_differential_order:n #1 {
  \regex_extract_once:nnNT { order \s* = \s* \{ \s* (\d+ (?: \s* , \s* \d+ )* ) \s* \} } 
    { #1 } \l__intexgral_pkg_differential_order_i_seq
    { \bool_set_true:N \l__intexgral_pkg_has_order_bool }
    \clist_set:Ne \l_tmpa_clist 
      { \seq_item:Nn \l__intexgral_pkg_differential_order_i_seq { 2 } }
    \seq_set_from_clist:NN \l__intexgral_pkg_differential_order_ii_seq \l_tmpa_clist
}

\cs_new_protected:Npn \__intexgral_pkg_extract_differential_var:n #1 {
  \regex_extract_once:nnNTF
    { var\s*=\s*(none|all|\{\s*(\d+(?:\s*,\s*\d+)*\s*)\}) }
    { #1 }
    \l__intexgral_pkg_differential_var_i_seq
    { \bool_set_true:N \l__intexgral_pkg_has_var_bool }
    { 
      \str_if_in:nnT { #1 } { var }
        { 
          \seq_put_left:Nn \l__intexgral_pkg_differential_var_i_seq { var } 
          \bool_set_true:N \l__intexgral_pkg_has_var_bool
        } 
    }
  \clist_set:Ne \l_tmpa_clist { \seq_item:Nn \l__intexgral_pkg_differential_var_i_seq { 3 } }
  \seq_set_from_clist:NN \l__intexgral_pkg_differential_var_ii_seq \l_tmpa_clist
}

\cs_new_protected:Npn \__intexgral_pkg_remove_differential_order_and_var:n #1 {
  \tl_set:Nn \l__intexgral_pkg_independent_differentials_options_tl { #1 }
  \regex_replace_all:nnN
    {
      order \s* = \s* \{ \s* \d+ ( \s* , \s* \d+ )* \} \s*,?
      |
      [^-] var (?: \s* = \s* (?: none | all | \{ \s* \d+ (?: \s* , \s* \d+ )* \s* \} ) )? ,?
    }
    {  }
    \l__intexgral_pkg_independent_differentials_options_tl
}

\cs_new_protected:Npn \__intexgral_pkg_parse_variable:nn #1#2 {
  \clist_set:Nn \l_tmpa_clist { #2 } 
  \seq_set_from_clist:NN \l_tmpa_seq \l_tmpa_clist
  \bool_if:NTF \l__intexgral_pkg_separate_integral_bool
    {
      \__intexgral_pkg_extract_differential_order:n { #1 }
      \__intexgral_pkg_extract_differential_var:n { #1 }
      \__intexgral_pkg_remove_differential_order_and_var:n { #1 }
      \seq_map_indexed_inline:Nn \l_tmpa_seq {
        \tl_put_right:Ne \l__intexgral_pkg_differentials_options_ii_tl
          { \l__intexgral_pkg_independent_differentials_options_tl }
        \bool_if:NT \l__intexgral_pkg_has_order_bool 
          { 
            \tl_put_right:Ne \l__intexgral_pkg_differentials_options_ii_tl 
              { order=\seq_item:Nn \l__intexgral_pkg_differential_order_ii_seq { ##1 }, }
          }
        \bool_if:NT \l__intexgral_pkg_has_var_bool
          {
            \int_compare:nNnTF 
            { \seq_count:N \l__intexgral_pkg_differential_var_i_seq }
            =
            { 1 }
            { \tl_put_right:Nn \l__intexgral_pkg_differentials_options_ii_tl { var } }
            {
              \str_if_eq:neF { none } 
                { \seq_item:Nn \l__intexgral_pkg_differential_var_i_seq { 2 } }
                  {
                    \str_if_eq:neTF { all } 
                      { \seq_item:Nn \l__intexgral_pkg_differential_var_i_seq { 2 } }
                      { 
                        \tl_put_right:Nn \l__intexgral_pkg_differentials_options_ii_tl 
                        { var } 
                      }
                      {
                        \seq_if_in:NnT \l__intexgral_pkg_differential_var_ii_seq { ##1 }
                          {
                            \seq_pop_left:NN \l__intexgral_pkg_differential_var_ii_seq \l_tmpa_tl
                            \tl_put_right:Nn \l__intexgral_pkg_differentials_options_ii_tl 
                              { var, }
                          }
                      }
                  }
            }
          }
        \seq_put_right:Ne \l__intexgral_pkg_differential_seq
          { 
            \__intexgral_pkg_differentials:nn
              { \l__intexgral_pkg_differentials_options_ii_tl }
              { \seq_item:Nn \l_tmpa_seq { ##1 } }
          }
        \tl_clear:N \l__intexgral_pkg_differentials_options_ii_tl
      }
    }
    {
      \seq_put_right:Nn \l__intexgral_pkg_differential_seq 
        { 
          \__intexgral_pkg_differentials:nn { #1 } { #2 } 
        }
    }
}


\cs_new_protected:Npn \__intexgral_pkg_parse_differentials: {
  \bool_if:NTF \l__intexgral_pkg_vectorial_differentials_bool
    {
      \clist_map_inline:Nn \l__intexgral_pkg_variable_i_clist
        { 
          \clist_put_right:Nn \l__intexgral_pkg_variable_ii_clist 
            { \l__intexgral_pkg_vectorial_differential_style_tl{##1} }
        }
      \bool_if:NTF \l__intexgral_pkg_custom_variables_bool
        {
          \__intexgral_pkg_parse_variable:oo
            { \l__intexgral_pkg_differentials_options_i_tl }
            { \l__intexgral_pkg_variable_ii_clist }
        }
        {
          \__intexgral_pkg_parse_variable:oo
            { \l__intexgral_pkg_differentials_options_i_tl }
            { \vec{r} }
        }
      
    }
    {
      \bool_if:NTF \l__intexgral_pkg_custom_variables_bool
        {
          \__intexgral_pkg_parse_variable:oo
            { \l__intexgral_pkg_differentials_options_i_tl }
            { \l__intexgral_pkg_variable_i_clist }
        }
        {
          \__intexgral_pkg_parse_variable:oo
            { \l__intexgral_pkg_differentials_options_i_tl }
            { x }
        }
    }
}

\cs_new_protected:Npn \__intexgral_pkg_parse_limits:n #1 {
  \tl_set:Nn \l_tmpa_tl { #1 }
  \seq_clear:N \l__intexgral_pkg_lower_limits_seq
  \seq_clear:N \l__intexgral_pkg_upper_limits_seq
  \seq_set_split:NnV \l__intexgral_pkg_limits_seq { ; } \l_tmpa_tl
}

\cs_new_protected:Nn \__intexgral_pkg_set_limits_regular: {
  \seq_map_inline:Nn \l__intexgral_pkg_limits_seq
    {
      \clist_set:Ne \l_tmpa_clist 
        { \__intexgral_pkg_parse_integral_limit:n { ##1 } }
      \seq_put_right:Ne \l__intexgral_pkg_lower_limits_seq 
        { \clist_item:Nn \l_tmpa_clist { 1 } }
      \seq_put_right:Ne \l__intexgral_pkg_upper_limits_seq 
        { \clist_item:Nn \l_tmpa_clist { 2 } }
    }
}

\cs_new_protected:Npn \__intexgral_pkg_set_limits_starred: {
  \seq_map_indexed_inline:Nn \l__intexgral_pkg_limits_seq
    {
      \clist_set:Ne \l_tmpa_clist { \__intexgral_pkg_parse_integral_limit:n { ##2 } }
      \bool_if:NTF \l__intexgral_pkg_invert_limits_bool
        {
          \tl_set:Ne \l__intexgral_pkg_lower_limit_tl
          {
            \clist_item:Nn \l_tmpa_clist { 2 }
            \tex_mathpunct:D,
            \clist_item:Nn \l_tmpa_clist { 1 }
          }
        }
        {
          \tl_set:Ne \l__intexgral_pkg_lower_limit_tl
          {
            \clist_item:Nn \l_tmpa_clist { 1 }
            \tex_mathpunct:D,
            \clist_item:Nn \l_tmpa_clist { 2 }
          }
        }
          \bool_if:NTF \l__intexgral_pkg_invert_limits_bool
            { \seq_put_right:Ne \l__intexgral_pkg_upper_limits_seq }
            { \seq_put_right:Ne \l__intexgral_pkg_lower_limits_seq }
        { 
          \str_case_e:nnF { \clist_item:Nn \l_tmpa_clist { 1 } }
            {
              { -\infty } { \tex_left:D \c__intexgral_pkg_right_bracket_tl }
            }
            { \tex_left:D \c__intexgral_pkg_left_bracket_tl }
          \tl_use:N \l__intexgral_pkg_lower_limit_tl
          \str_case_e:nnF { \clist_item:Nn \l_tmpa_clist { 2 } }
            {
              { +\infty } { \tex_right:D \c__intexgral_pkg_left_bracket_tl }
            }
            { \tex_right:D \c__intexgral_pkg_right_bracket_tl }
          }
    }
}

\cs_new_protected:Nn \__intexgral_pkg_generate_integral_sequence: {
  \int_set:Nn \l__intexgral_pkg_integral_sequence_int
    {
      \seq_if_empty:NTF \l__intexgral_pkg_lower_limits_seq
        { \seq_count:N \l__intexgral_pkg_upper_limits_seq }
        { \seq_count:N \l__intexgral_pkg_lower_limits_seq }
    }
  \bool_if:NTF \l__intexgral_pkg_separate_integral_bool
    {
      \int_step_inline:nn { \l__intexgral_pkg_integral_sequence_int }
        {
          \seq_put_right:Nn \l__intexgral_pkg_integral_symbol_seq
            {
              \__intexgral_pkg_set_limits:nn
                { \seq_item:Nn \l__intexgral_pkg_lower_limits_seq { ##1 } }
                { \seq_item:Nn \l__intexgral_pkg_upper_limits_seq { ##1 } }
              \__intexgral_pkg_parse_integral_symbol:
            }
        }
    }
    {
      \seq_put_right:Nn \l__intexgral_pkg_integral_symbol_seq
        {
          \int_step_inline:nn { \l__intexgral_pkg_integral_sequence_int }
            {
              \__intexgral_pkg_set_limits:nn
                { \seq_item:Nn \l__intexgral_pkg_lower_limits_seq { ##1 } }
                { \seq_item:Nn \l__intexgral_pkg_upper_limits_seq { ##1 } }
              \__intexgral_pkg_parse_integral_symbol:
            }
        }
    }
}

\keys_define:nn { integral } { 

  % LIMITS

  int-split .bool_set:N = \l__intexgral_pkg_separate_integral_bool,

  limits .code:n = 
    {
      \__intexgral_pkg_parse_limits:n { #1 }
      \__intexgral_pkg_set_limits_regular:
      \__intexgral_pkg_generate_integral_sequence:
    },

  limits* .code:n = 
    {
      \__intexgral_pkg_parse_limits:n { #1 }
      \__intexgral_pkg_set_limits_starred:
      \__intexgral_pkg_generate_integral_sequence:
    },

  limits-mode .choice:,
    limits-mode / limits .code:n =
      { \tl_set_eq:NN \l__intexgral_pkg_limits_style_tl \tex_limits:D },
    limits-mode / nolimits .code:n =
      { \tl_set_eq:NN \l__intexgral_pkg_limits_style_tl \tex_nolimits:D },
  limits-mode .default:n = { nolimits },

  lower-lim .tl_set:N = \l__intexgral_pkg_lower_limit_tl,

  upper-lim .tl_set:N = \l__intexgral_pkg_upper_limit_tl,

  int-symb .tl_set:N = \l__intexgral_pkg_integral_symbol_tl,

  % SYMBOL SHORTCUT

  nint .code:n =
    {
      \int_compare:nNnT { #1 } < { 5 }
        { \msg_warning:nn { intexgral } { use-glyph-instead } }

      \tl_clear:N \l__intexgral_pkg_integral_symbol_tl

      \int_step_inline:nn { #1 }
        {
          \tl_put_right:Nn \l__intexgral_pkg_integral_symbol_tl
            { \c__intexgral_pkg_int_symbol_tl }
          \int_compare:nNnT { ##1 } < { #1 }
            {
              \tl_put_right:Nn \l__intexgral_pkg_integral_symbol_tl
                { 
                  \__intexgral_pkg_mathchoice:nnnn
                    { \tex_mkern:D -12mu \scan_stop: } 
                    { \tex_mkern:D -8mu \scan_stop: } 
                    { \tex_mkern:D -4mu \scan_stop: } 
                    { \tex_mkern:D -2mu \scan_stop: } 
                }
            }
        }
    },

  single .meta:n = 
    { 
      int-symb=\c__intexgral_pkg_int_symbol_tl, 
      lower-lim=#1
    },

  double .meta:n = 
    { 
      int-symb=\c__intexgral_pkg_iint_symbol_tl, 
      lower-lim=#1
    },

  triple .meta:n = 
    { 
      int-symb=\c__intexgral_pkg_iiint_symbol_tl, 
      lower-lim=#1
    },

  quadruple .meta:n = 
    { 
      int-symb=\c__intexgral_pkg_iiiint_symbol_tl, 
      lower-lim=#1
    },

  contour .meta:n = 
    { 
      int-symb=\c__intexgral_pkg_oint_symbol_tl, 
      lower-lim=#1
    },

  surface .meta:n = 
    { 
      int-symb=\c__intexgral_pkg_oiint_symbol_tl, 
      lower-lim=#1
    },

  volume .meta:n = 
    { 
      int-symb=\c__intexgral_pkg_oiiint_symbol_tl, 
      lower-lim=#1
    },

  % LIMITS SHORTCUTS

  domain .code:n = 
    {
      \tl_set:Nn \l_tmpa_tl { #1 }
      \seq_set_split:NnV \l__intexgral_pkg_domain_seq { * } \l_tmpa_tl
      \seq_map_inline:Nn \l__intexgral_pkg_domain_seq
        {
          \tl_if_empty:NF \l__intexgral_pkg_lower_limit_tl
            { \tl_put_right:Nn \l__intexgral_pkg_lower_limit_tl { \times } }
          \tl_set:Ne \l__intexgral_pkg_domain_char_tl 
            { \exp_args:Ne \str_uppercase:n { \tl_head:n { ##1 } } }
          \tl_set:Ne \l__intexgral_pkg_domain_dimension_tl
            { \tl_tail:n { ##1 } }
          \tl_put_right:Ne \l__intexgral_pkg_lower_limit_tl 
            {  
              \exp_not:N \mathbb { \l__intexgral_pkg_domain_char_tl }
              \c_math_superscript_token { \l__intexgral_pkg_domain_dimension_tl } 
            }
        }
    },

  boundary .code:n =
    { \tl_set:Nn \l__intexgral_pkg_lower_limit_tl { \partial #1 } },

  % DIFFERENTIALS

  variable .code:n = 
    {
      \bool_set_true:N \l__intexgral_pkg_custom_variables_bool
      \str_if_eq:nnTF { #1 } { none }
        { \bool_set_true:N \l__intexgral_pkg_deactivate_differential_bool }
        { 
          \prop_get:NnNTF \g__intexgral_pkg_differential_group_keyword_prop { #1 } \l_tmpa_tl
            {
              \clist_set:NV \l__intexgral_pkg_variable_i_clist \l_tmpa_tl
              \seq_if_exist:cT { g__#1_jacobian_seq }
                { \seq_set_eq:Nc \l__intexgral_pkg_jacobian_seq { g__#1_jacobian_seq } }
            }
            { \clist_set:Nn \l__intexgral_pkg_variable_i_clist { #1 } }
        }
    },

  jacobian .bool_set:N = \l__intexgral_pkg_jacobian_bool,

  diff-vec .bool_set:N = \l__intexgral_pkg_vectorial_differentials_bool,

  diff-vec-style .tl_set:N = \l__intexgral_pkg_vectorial_differential_style_tl,

  diff-symb .code:n = 
    { 
      \cs_set:Npn \__intexgral_pkg_differentials:nn ##1##2 {
        \bool_if:NTF \l__intexgral_pkg_starred_differential_bool
          { #1*[##1]{##2} }
          { #1[##1]{##2} }
      }
    },

  diff-star .bool_set:N = \l__intexgral_pkg_starred_differential_bool,

  diff-options .tl_set:N = \l__intexgral_pkg_differentials_options_i_tl,

}

\NewDocumentCommand{\NewLimitsKeyword}{ m m }{
  \prop_get:NnNTF \g__intexgral_pkg_limits_keyword_prop { #1 } \l_tmpa_tl
    { \msg_error:nnn { intexgral } { lim-group-alr-def } { #1 } }
    {
      \bool_if:NTF \l__intexgral_pkg_invert_limits_bool
        {
          \clist_set:Nn \l_tmpa_clist { #2 }
          \clist_reverse:N \l_tmpa_clist
          \__intexgral_pkg_new_limits_group:nV { #1 } \l_tmpa_clist
        }
        { \__intexgral_pkg_new_limits_group:nn { #1 } { #2 } }
    }
}

\NewDocumentCommand{\RenewLimitsKeyword}{ m m }{
  \prop_pop:NnNTF \g__intexgral_pkg_limits_keyword_prop { #1 } \l_tmpa_tl
    {
      \bool_if:NTF \l__intexgral_pkg_invert_limits_bool
        {
          \clist_set:Nn \l_tmpa_clist { #2 }
          \clist_reverse:N \l_tmpa_clist
          \__intexgral_pkg_new_limits_group:nV { #1 } \l_tmpa_clist
        }
        { \__intexgral_pkg_new_limits_group:nn { #1 } { #2 } }
    }
    { \msg_error:nnn { intexgral } { lim-group-not-def } }
}

\NewDocumentCommand{\ProvideLimitsKeyword}{ m m }{
  \prop_get:NnNF \g__intexgral_pkg_limits_keyword_prop { #1 } \l_tmpa_tl
    {
      \bool_if:NTF \l__intexgral_pkg_invert_limits_bool
        {
          \clist_set:Nn \l_tmpa_clist { #2 }
          \clist_reverse:N \l_tmpa_clist
          \__intexgral_pkg_new_limits_group:nV { #1 } \l_tmpa_clist
        }
        { \__intexgral_pkg_new_limits_group:nn { #1 } { #2 } }
    }
}

\NewDocumentCommand{\DeclareLimitsKeyword}{ m m }{
  \prop_pop:NnNT \g__intexgral_pkg_limits_keyword_prop { #1 } \l_tmpa_tl
    {
      \bool_if:NTF \l__intexgral_pkg_invert_limits_bool
        {
          \clist_set:Nn \l_tmpa_clist { #2 }
          \clist_reverse:N \l_tmpa_clist
          \__intexgral_pkg_new_limits_group:nV { #1 } \l_tmpa_clist
        }
        { \__intexgral_pkg_new_limits_group:nn { #1 } { #2 } }
    }
}

\NewDocumentCommand{\NewDifferentialKeyword}{ m m o }{
  \prop_get:NnNTF \g__intexgral_pkg_differential_group_keyword_prop { #1 } \l_tmpa_tl
    { \msg_error:nnn { intexgral } { diff-group-alr-def } { #1 } }
    { \__intexgral_pkg_new_differential_group:nnn { #1 } { #2 } { #3 } }
}

\NewDocumentCommand{\RenewDifferentialKeyword}{ m m o }{
  \prop_pop:NnNTF \g__intexgral_pkg_differential_group_keyword_prop { #1 } \l_tmpa_tl
    { 
      \seq_clear:c { g__#1_jacobian_seq }
      \__intexgral_pkg_new_differential_group:nnn { #1 } { #2 } { #3 } 
    }
    { \msg_error:nnn { intexgral } { diff-group-alr-def } { #1 } }
}

\NewDocumentCommand{\ProvideDifferentialKeyword}{ m m o }{
  \prop_get:NnNF \g__intexgral_pkg_differential_group_keyword_prop { #1 } \l_tmpa_tl
    { \__intexgral_pkg_new_differential_group:nnn { #1 } { #2 } { #3 } }
}

\NewDocumentCommand{\DeclareDifferentialKeyword}{ m m o }{
  \prop_pop:NnNT \g__intexgral_pkg_differential_group_keyword_prop { #1 } \l_tmpa_tl
    { 
      \seq_clear:c { g__#1_jacobian_seq }
      \__intexgral_pkg_new_differential_group:nnn { #1 } { #2 } { #3 } 
    }
}

\NewDocumentCommand{\NewIntegralSymbol}{ m }{
  \tl_if_exist:cTF { c__intexgral_pkg_#1_symbol_tl } 
    { \msg_error:nnn { intexgral } { int-symb-alr-def } { #1 } }
    { 
      \AtBeginDocument{ 
        \__intexgral_pkg_new_integral_symbol:n { #1 } 
      } 
    }
}

\@onlypreamble\NewIntegralSymbol

\NewIntegralSymbol{int}
\NewIntegralSymbol{iint}
\NewIntegralSymbol{iiint}
\NewIntegralSymbol{iiiint}
\NewIntegralSymbol{oint}
\NewIntegralSymbol{oiint}
\NewIntegralSymbol{oiiint}
\NewIntegralSymbol{idotsint}
\NewIntegralSymbol{intclockwise}
\NewIntegralSymbol{awint}
\NewIntegralSymbol{varointclockwise}
\NewIntegralSymbol{ointctrclockwise}
\NewIntegralSymbol{sumint}
\NewIntegralSymbol{intbar}
\NewIntegralSymbol{intBar}
\NewIntegralSymbol{fint}
\NewIntegralSymbol{cirfnint}
\NewIntegralSymbol{rppolint}
\NewIntegralSymbol{scpolint}
\NewIntegralSymbol{npolint}
\NewIntegralSymbol{pointint}
\NewIntegralSymbol{sqint}
\NewIntegralSymbol{intlarhk}
\NewIntegralSymbol{intx}
\NewIntegralSymbol{intcap}
\NewIntegralSymbol{intcup}
\NewIntegralSymbol{upint}
\NewIntegralSymbol{lowint}
\NewIntegralSymbol{inttop}
\NewIntegralSymbol{intbottom}
\NewIntegralSymbol{intextender}

\NewLimitsKeyword{ab}{a, b}
\NewLimitsKeyword{real}{-\infty, +\infty}
\NewLimitsKeyword{positive}{0, +\infty}
\NewLimitsKeyword{negative}{-\infty, 0}
\NewLimitsKeyword{unit}{0, 1}
\NewLimitsKeyword{circle}{0, 2\pi}
\NewLimitsKeyword{scircle}{0, \pi}
\NewLimitsKeyword{qcircle}{0, \frac{\pi}{2}}
\NewLimitsKeyword{height}{0, H}
\NewLimitsKeyword{radius}{0, R}
\NewLimitsKeyword{length}{0, L}
\NewLimitsKeyword{time}{0, T}

\NewDifferentialKeyword{cartesian}{x, y, z}
\NewDifferentialKeyword{polar}{r, \theta}[r]
\NewDifferentialKeyword{cylindrical}{r, \theta, z}[r]
\NewDifferentialKeyword{spherical}{r, \theta, \phi}[r^2, \sin\theta]

\NewDocumentCommand{\integral}{ O{} m }{
  \keys_set:nn { integral } { #1 }
  \tl_set:Nn \l__intexgral_pkg_integrand_tl { #2 }
  \__intexgral_pkg_print_integral:
  \cs_undefine:N \differentials
}

\ExplSyntaxOff

% End of file intexgral.sty