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Diffstat (limited to 'Master/texmf-dist/tex')
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diff --git a/Master/texmf-dist/tex/latex/pascaltriangle/pascaltriangle.sty b/Master/texmf-dist/tex/latex/pascaltriangle/pascaltriangle.sty new file mode 100644 index 00000000000..6c4be46ac37 --- /dev/null +++ b/Master/texmf-dist/tex/latex/pascaltriangle/pascaltriangle.sty @@ -0,0 +1,397 @@ +%%% ---------------------------------------------------------------------------- +%%% pascaltriangle: Typeset Pascal triangle figure with LaTeX3 +%%% Author : Nan Geng <nangeng@nwafu.edu.cn> +%%% Repository: https://github.com/registor/pascaltriangle or https://gitee.com/nwafu_nan/pascaltriangle +%%% License : The LaTeX Project Public License 1.3c +%%% ---------------------------------------------------------------------------- + +\NeedsTeXFormat{LaTeX2e} +\RequirePackage{expl3} +\ProvidesExplPackage{pascaltriangle}{2022-01-07}{v1.0.0} + {Typeset Pascal triangle figure with LaTeX3} + +\RequirePackage{xparse} + +%% \tl_if_eq:NnTF 与texlive 2020的兼容性设置 +\cs_if_exist:NF \tl_if_eq:NnTF + { + \tl_new:N \l__tblr_backport_b_tl + \prg_new_protected_conditional:Npnn \tl_if_eq:Nn #1 #2 { T, F, TF } + { + \group_begin: + \tl_set:Nn \l__tblr_backport_b_tl {#2} + \exp_after:wN + \group_end: + \if_meaning:w #1 \l__tblr_backport_b_tl + \prg_return_true: + \else: + \prg_return_false: + \fi: + } + \prg_generate_conditional_variant:Nnn \tl_if_eq:Nn { c } { TF, T, F } + } + +\cs_if_exist:NF \seq_map_indexed_function:NN + { + \cs_set_eq:NN \seq_map_indexed_function:NN \seq_indexed_map_function:NN + } + +%% 解决TikZ库无法在Expl3中载入问题 +\RequirePackage {amsmath, tikz, etoolbox} +\ExplSyntaxOff +\patchcmd +{\tcb@input@library@in} + {% + \input\tcbpkgprefix#1\relax% + } + {% + \@pushfilename + \input\tcbpkgprefix#1\relax% + \@popfilename + } + {}{} + +\patchcmd +{\pgfutil@InputIfFileExists} + {\input #1} + {% + \@pushfilename + \xdef\@currname{#1}% + \input #1 % + \@popfilename + } + {}{} +\ExplSyntaxOn +\usetikzlibrary{shapes.geometric} + +%% 定义变量 +\bool_new:N \l__pascal_num_cell_bool % 是否绘制行列号 +\bool_new:N \l__pascal_binom_cell_bool % 是否仅绘制二项式表达式 + +\tl_new:N \l__pascal_cell_color_tl % 单元格填充颜色 +\tl_new:N \l__pascal_shift_col_pt_tl % 列变换坐标 +\tl_new:N \l__pascal_shift_row_pt_tl % 行变换坐标 +\tl_new:N \l__pascal_font_size_tl % 文件大小 + +\int_new:N \l__pascal_shape_type_int % 形状(1---等腰，2---直角) +\int_new:N \l__pascal_row_idx_int % 行索引(从0计数) +\int_new:N \l__pascal_col_idx_int % 列索引(从0计数) +\int_new:N \l__pascal_row_top_int % 各列最大行数 +\int_new:N \l__pascal_total_idx_int % 索引总数 +\int_new:N \l__pascal_fill_row_int % 填充行号(最大值与当前列数有关，从顶向下从0计数) +\int_new:N \l__pascal_fill_col_int % 填充列号(从0计数) + +\dim_new:N \l__pascal_cell_radius_dim % 单元格大小(中心到顶点的半径) + +%% 选项设计 +\keys_define:nn { pascal } + { + % 是否需要行列编号 + withnum .bool_set:N = \l__pascal_num_cell_bool, + withnum .default:n = true, + withnum .initial:n = false, + + % 是否仅绘制二项式表达式 + binom .bool_set:N = \l__pascal_binom_cell_bool, + binom .default:n = true, + binom .initial:n = false, + + % 形状选择(iso---等腰三角形, rt---直角三角形) + shape .choice:, + shape .value_required:n = true, + shape .choices:nn = + { iso, rt } + { \int_set_eq:NN \l__pascal_shape_type_int \l_keys_choice_int }, + shape .initial:n = iso, + + % 单元格半径(中心到顶点) + radius .dim_set:N = \l__pascal_cell_radius_dim, + radius .initial:n = 0.5cm, + + % 文字大小 + fontsize .tl_set:N = \l__pascal_font_size_tl, + fontsize .initial:n = \small, + + % 要填充单元格行数(按列从顶向下，从0开始计数) + fillr .int_set:N = \l__pascal_fill_row_int, + fillr .initial:n = 1 , + % 要填充单元格列数(从左向右，从0开始计数) + fillc .int_set:N = \l__pascal_fill_col_int, + fillc .initial:n = 1 , + fillrc .meta:n = { fillr = #1 , fillc = #1 }, + + unknown .code:n = { \__pascal_error:n { unknown-option } } + } + +\msg_new:nnn { pascal } { unknown-option } + { package~ option~ "\l_keys_key_tl"~ is~ unknown. } + +%% 参数设置用户接口 +\NewDocumentCommand \pascalset { m } + { \keys_set:nn { pascal } {#1} } + +%% 利用LaTeX3的fact阶乘计算函数计算组合数 +\cs_set:Npn \__pascal_binomcoeff:nn #1#2 + { + \fp_eval:n { fact(#1) / (fact(#2) * fact(#1 - #2)) } + } + +%% 组合数计算用户接口 +\NewDocumentCommand{\binomc}{m m} + { + \__pascal_binomcoeff:nn{#1}{#2} + } + +%% 绘制Pascal三角形 +%% 注意":"无法使用造成极坐标不能用的问题，以下网站给出了解决方案 +%% https://tex.stackexchange.com/questions/501333/how-to-use-colon-as-part-of-tikz-syntax-while-in-explsyntaxon-environment +%% 将":"用\c_colon_str代替 + +%% 根据形状类型计算列变换坐标(极坐标) +\cs_set:Npn \__pascal_shift_col_pt:n #1 + { + \int_case:nn { \l__pascal_shape_type_int } + { + {1}{ + \tl_set:Nn \l__pascal_shift_col_pt_tl { -60 \c_colon_str + \fp_eval:n {sqrt(3) * \l__pascal_cell_radius_dim * #1}pt + } + } + {2}{ + \tl_set:Nn \l__pascal_shift_col_pt_tl { -45 \c_colon_str + \fp_eval:n {2 * \l__pascal_cell_radius_dim * #1}pt + } + } + } + } + +%% 根据形状类型计算行变换坐标(极坐标) +\cs_set:Npn \__pascal_shift_row_pt:n #1 + { + \int_case:nn { \l__pascal_shape_type_int } + { + {1}{ + \tl_set:Nn \l__pascal_shift_row_pt_tl { -120 \c_colon_str + \fp_eval:n {sqrt(3) * \l__pascal_cell_radius_dim * #1}pt + } + } + {2}{ + \tl_set:Nn \l__pascal_shift_row_pt_tl { -90 \c_colon_str + \fp_eval:n {sqrt(2) * \l__pascal_cell_radius_dim * #1}pt + } + } + } + } + +%% 正六边形闭合路径代码 +\cs_set:Npn \__pascal_hex_cell: + { + (30 \c_colon_str \fp_eval:n{\l__pascal_cell_radius_dim}pt) -- + (90 \c_colon_str \fp_eval:n{\l__pascal_cell_radius_dim}pt) -- + (150 \c_colon_str \fp_eval:n{\l__pascal_cell_radius_dim}pt) -- + (210 \c_colon_str \fp_eval:n{\l__pascal_cell_radius_dim}pt) -- + (270 \c_colon_str \fp_eval:n{\l__pascal_cell_radius_dim}pt) -- + (330 \c_colon_str \fp_eval:n{\l__pascal_cell_radius_dim}pt) -- + cycle (90 \c_colon_str 0) + } + +%% 正方形闭合路径代码 +\cs_set:Npn \__pascal_square_cell: + { + (45 \c_colon_str \fp_eval:n{\l__pascal_cell_radius_dim}pt) -- + (134 \c_colon_str \fp_eval:n{\l__pascal_cell_radius_dim}pt) -- + (225 \c_colon_str \fp_eval:n{\l__pascal_cell_radius_dim}pt) -- + (-45 \c_colon_str \fp_eval:n{\l__pascal_cell_radius_dim}pt) -- + cycle (90 \c_colon_str 0) + } + +%% 绘制行列编号标记单元格 +\cs_set:Npn \__pascal_num_draw:nnn #1#2#3 + { + \int_case:nn { \l__pascal_shape_type_int } + { + {1}{% 正六边形 + \int_compare:nNnT { #1 } = {0}% 最左列 + { + \int_compare:nNnT { #2 } = { #3 - 1 }% 最底行 + { + \begin{scope}[shift={(-150\c_colon_str {\fp_eval:n{3*\l__pascal_cell_radius_dim}pt})}] + \draw[dashed, top~color=gray!10,bottom~color=gray!20] + \__pascal_hex_cell: + node[rotate=-45] {$m,n$}; + \end{scope} + } + } + \int_compare:nNnT { #1 } = { 0 }% 最左列 + { + \begin{scope}[shift={(-180\c_colon_str {\fp_eval:n{sqrt(3)*\l__pascal_cell_radius_dim}pt})}] + \draw[dashed, top~color=gray!10,bottom~color=gray!20] + \__pascal_hex_cell: + node{$(\int_eval:n {#2})$}; + \end{scope} + } + \int_compare:nNnT { #2 } = { #3 - 1 }% 最底行 + { + \begin{scope}[shift={(-120\c_colon_str {\fp_eval:n{sqrt(3)*\l__pascal_cell_radius_dim}pt})}] + \draw[dashed, top~color=gray!10,bottom~color=gray!20] + \__pascal_hex_cell: + node {$(\int_eval:n {#1})$}; + \end{scope} + } + } + {2}{% 正方形 + \int_compare:nNnT { #1 } = {0}% 最左列 + { + \int_compare:nNnT { #2 } = { #3 - 1 }% 最底行 + { + \begin{scope}[shift={(-135\c_colon_str {\fp_eval:n{2*\l__pascal_cell_radius_dim}pt})}] + \draw[dashed, top~color=gray!10,bottom~color=gray!20] + \__pascal_square_cell: + node[scale=0.8,rotate=-45] {$m,n$}; + \end{scope} + } + } + \int_compare:nNnT { #1 } = { 0 }% 最左列 + { + \begin{scope}[shift={(-180\c_colon_str {\fp_eval:n{sqrt(2)*\l__pascal_cell_radius_dim}pt})}] + \draw[dashed, top~color=gray!10,bottom~color=gray!20] + \__pascal_square_cell: + node{$(\int_eval:n {#2})$}; + \end{scope} + } + \int_compare:nNnT { #2 } = { #3 - 1 }% 最底行 + { + \begin{scope}[shift={(-90\c_colon_str {\fp_eval:n{sqrt(2)*\l__pascal_cell_radius_dim}pt})}] + \draw[dashed, top~color=gray!10,bottom~color=gray!20] + \__pascal_square_cell: + node {$(\int_eval:n {#1})$}; + \end{scope} + } + } + } + } + +%% 绘制三角形单元格 +\cs_set:Npn \__pascal_cell_draw:nn #1#2 + { + \int_case:nn { \l__pascal_shape_type_int } + { + {1}{% 正六边形 + \draw[top~color=\l__pascal_cell_color_tl!20,bottom~color=\l__pascal_cell_color_tl!60] + \__pascal_hex_cell: + \bool_if:NTF \l__pascal_binom_cell_bool + { + node {$\binom{\int_eval:n {#1}}{\int_eval:n {#2}}$}; + } + { + node {$\__pascal_binomcoeff:nn {#1}{#2}$}; + } + } + {2}{% 正方形 + \draw[top~color=\l__pascal_cell_color_tl!20,bottom~color=\l__pascal_cell_color_tl!60] + \__pascal_square_cell: + \bool_if:NTF \l__pascal_binom_cell_bool + { + node {$\binom{\int_eval:n {#1}}{\int_eval:n {#2}}$}; + } + { + node {$\__pascal_binomcoeff:nn {#1}{#2}$}; + } + } + } + } + +%% 绘制Pascal三角形 +% 等腰三角形的绘制原理参考了 https://texample.net/tikz/examples/pascal-triangle/ +% Author: M.H. Ahmadi +\cs_set:Npn \__pascal_triangle_draw:n #1 + { + % 设置正常单元格为灰色 + \tl_set:Nn \l__pascal_cell_color_tl {gray} + % 记录绘制列数 + \int_set:Nn \l_tmpa_int {#1} + + % 使用TikZ绘制 + \begin{tikzpicture}[font=\l__pascal_font_size_tl] + % 列循环 + \int_step_inline:nn {\l_tmpa_int} + { + % 调整为从0计数，以便于后续计算 + \int_set:Nn \l__pascal_col_idx_int { ##1 - 1 } + + % 计算列变换坐标(极坐标) + \__pascal_shift_col_pt:n {\l__pascal_col_idx_int} + + % 用scope环境变换各列到指定位置 + \begin{scope}[shift={(\l__pascal_shift_col_pt_tl)}] + % 计算每列最多行数 + \int_set:Nn \l__pascal_row_top_int {\l_tmpa_int - ##1 + 1} + + % 行循环 + \int_step_inline:nn { \l__pascal_row_top_int } + { + % 调整为从0计数，以便于后续计算 + \int_set:Nn \l__pascal_row_idx_int { ####1 - 1 } + + % 计算组合数计算中的行数 + \int_zero:N \l__pascal_total_idx_int + \int_add:Nn \l__pascal_total_idx_int { \l__pascal_row_idx_int } + \int_add:Nn \l__pascal_total_idx_int { \l__pascal_col_idx_int } + + % 为指定行设置绘制颜色 + \int_case:nn { \l__pascal_col_idx_int } + { + {0}{ + \tl_set:Nn \l__pascal_cell_color_tl { pink } + } + {1}{ + \tl_set:Nn \l__pascal_cell_color_tl { yellow } + } + {2}{ + \tl_set:Nn \l__pascal_cell_color_tl { blue } + } + {3}{ + \tl_set:Nn \l__pascal_cell_color_tl { green } + } + {\l__pascal_fill_col_int - 1}{ + \int_compare:nNnTF{\l__pascal_row_idx_int} < { \l__pascal_fill_row_int + 1 } + {\tl_set:Nn \l__pascal_cell_color_tl { purple }} + {\tl_set:Nn \l__pascal_cell_color_tl { gray }} + } + {\l__pascal_fill_col_int}{ + \int_compare:nNnTF{\l__pascal_row_idx_int} = { \l__pascal_fill_row_int } + {\tl_set:Nn \l__pascal_cell_color_tl { purple }} + {\tl_set:Nn \l__pascal_cell_color_tl { gray }} + } + } + + % 计算行变换坐标(极坐标) + \__pascal_shift_row_pt:n {\l__pascal_row_idx_int} + % 用scope环境变换各行到指定位置 + \begin{scope}[shift={(\l__pascal_shift_row_pt_tl)}] + % 是否绘制行列编号 + \bool_if:NT \l__pascal_num_cell_bool + { + \__pascal_num_draw:nnn { \l__pascal_col_idx_int } + { \l__pascal_row_idx_int } + { \l__pascal_row_top_int } + } + % 绘制一个单元格 + \__pascal_cell_draw:nn{\l__pascal_total_idx_int}{\l__pascal_col_idx_int} + \end{scope} + } + \end{scope} + } + \end{tikzpicture} + } + +%% 绘制Pascal三角形用户接口 +\NewDocumentCommand{\pascal}{O{} m} + { + \IfNoValueF{#1}{ \keys_set:nn { pascal } {#1} } + \group_begin: + \__pascal_triangle_draw:n{#2} + \group_end: + } + +\endinput |