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authorKarl Berry <karl@freefriends.org>2022-01-07 22:29:40 +0000
committerKarl Berry <karl@freefriends.org>2022-01-07 22:29:40 +0000
commitdb5f35c7db6319d4ca6369052b1a492c8729bfc7 (patch)
tree75c6f8e3f40f7393bfdecbb68e4d15d6ac254d03 /Master/texmf-dist/tex/latex/pascaltriangle
parent9977ee10493897ac7eb7e02d347eb83e70cdc4e0 (diff)
pascaltriangle (7jan22)
git-svn-id: svn://tug.org/texlive/trunk@61523 c570f23f-e606-0410-a88d-b1316a301751
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+%%% ----------------------------------------------------------------------------
+%%% 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