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新的数学公式装饰三角形

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新的数学公式装饰三角形

我想要两个新的装饰三角形。这是用于编写有关数学公式中的 B 方法的练习。

例子

答案1

这是这些符号的简单实现。我不确定这个 B 方法是什么，所以我将它们设为关系符号，\mathrel这样它们的行为就类似于amsmath和\vartriangleleft符号\vartriangleright。

\documentclass{article}
\usepackage{amsmath,amssymb}
\usepackage{trimclip}
\newlength{\trianglewidth}
\newlength{\pluswidth}
\settowidth{\trianglewidth}{\(\vartriangleleft\)}
\settowidth{\pluswidth}{\(+\)}
\newcommand{\lefttrianglebar}{%
    \mathrel{\makebox[\trianglewidth]{%
        \makebox[\trianglewidth]{\(\vartriangleleft\)}%
        \hspace*{-\trianglewidth}%
        \makebox[\trianglewidth]{\(-\)}%
    }}%
}
\newcommand{\righttrianglebar}{%
    \mathrel{\makebox[\trianglewidth]{%
        \makebox[\trianglewidth]{\(-\)}%
        \hspace*{-\trianglewidth}%
        \makebox[\trianglewidth]{\(\vartriangleright\)}%
    }}%
}
\newcommand{\lefttriangleplus}{%
    \mathrel{\makebox[\trianglewidth]{%
        \makebox[\trianglewidth]{\(<\)}%
        \hspace*{-.333\pluswidth}%
        \raisebox{.3\height}{\clipbox{.3\width{} .3\height}{\(+\)}}%
    }}%
}
\newcommand{\righttriangleplus}{%
    \mathrel{\makebox[\trianglewidth]{%
        \raisebox{.3\height}{\clipbox{.3\width{} .3\height}{\(+\)}}%
        \hspace*{-.333\pluswidth}%
        \makebox[\trianglewidth]{\(>\)}%
    }}%
}
\begin{document}
\( A \vartriangleleft  B \qquad A \vartriangleright B \)

\( A \lefttrianglebar  B \qquad A \righttrianglebar  B \)

\( A \lefttriangleplus B \qquad A \righttriangleplus B \)
\end{document}

附录

@barbarabeeton 指出，带横线的三角形符号作为 Unicode 符号存在，并包含在 STIX 字体中。使用该stix包，可以像以下示例一样获取它们。

\documentclass{article}
\usepackage{stix}
\begin{document}
\begin{tabular}{ll}
    \( A \vartriangleleft  B \) & \( A \vartriangleright B \) \\
    \( A \rsub             B \) & \( A \dsub             B \)
\end{tabular}
\end{document}

不过我觉得它们看起来有点太大了。也许最好把它们缩小一点，以便更好地与其他三角形符号相配。

答案2

由于问题中的图像在内部使用了不同的颜色相同的符号我提出了一个灵活的界面，允许人们选择特定的设置（通过 Ti钾Z 样式）用于三角形和“内部特征”（可以为空、加号或水平线）。下面定义的运算符表现为二元关系（ ）。左或右三角形顶点位于数学轴的高度（即与分数条、和符号\mathrel处于同一级别）。我实现了两个接口：\cdots+=

  • 详细的：采用一个可选参数，该参数由在（例如）\myTriangle中执行的 PGF 密钥组成；/tikz/my triangle\myTriangle[orientation=right, inner feature type=+, append style={fill=yellow}, append inner feature style={draw=red}]

  • 简洁的一个：\mytriangle[triangle opts][inner feature opts]{l}{+}或\mytriangle[triangle opts][inner feature opts]{r}{-}，等等（如果最后一个参数为空或空白，则三角形将为空）。

下面的示例中说明了这两个接口。“内部特征”的颜色是brown默认的，因为这是问题中的颜色。只需修改以下行即可更改此默认设置：

set inner feature style={draw=brown, line cap=round, line width=0.3pt}

您可以选择默认的Ti钾使用我代码中第一个命令中定义的键，独立设置三角形和内部特征所需的 Z 设置\tikzset。 可以在 的可选参数中使用完全相同的选项\myTriangle。

\documentclass[border=0.5mm]{standalone}
\usepackage{tikz}
\usepackage{xparse} % for the interface allowing concise syntax (\mytriangle)

\makeatletter
\newif\ifmy@triangle@orientation@left
\newif\ifmy@triangle@twosides

\tikzset{
  my triangle/.is family,
  my triangle/.cd,
  set style/.style={style/.style={#1}}, % store for future use
  append style/.style={style/.append style={#1}},
  set style={draw=black, line width=0.3pt},
  inner feature type/.store in=\my@triangle@feature@type,
  inner feature type={},
  set inner feature style/.style={inner feature style/.style={#1}},
  append inner feature style/.style={inner feature style/.append style={#1}},
  set inner feature style={draw=brown, line cap=round, line width=0.3pt},
  orientation/.is choice,
  orientation/left/.code={\my@triangle@orientation@lefttrue},
  orientation/right/.code={\my@triangle@orientation@leftfalse},
  orientation=left,
  transform/.style={},  % semi-private: use only if you understand how it works
}

% Command from egreg (https://tex.stackexchange.com/a/499972/73317)
\newcommand{\math@param}[3]{%
  \fontdimen#3
  \ifx#1\displaystyle\textfont#2
  \else\ifx#1\textstyle\textfont#2
  \else\ifx#1\scriptstyle\scriptfont#2
  \else\scriptscriptfont#2 \fi\fi\fi
}

% #1: Either \my@triangle@left or \my@triangle@right
\newcommand*{\my@triangle@wrap}[1]{%
  \ifx\my@triangle@feature@type\empty
    \my@triangle@twosidesfalse
  \else
    \if\my@triangle@feature@type -%
      \my@triangle@twosidesfalse
    \else
      \if\my@triangle@feature@type +%
        \my@triangle@twosidestrue
      \else
        \errmessage{%
          Unexpected triangle feature type: '\my@triangle@feature@type'}%
      \fi
    \fi
  \fi
  \mathrel{\mathpalette#1\relax}%
}

\newcommand*{\my@triangle@width}{2} % multiple of the math axis height
\newdimen\my@height

% #1: math style
% #2: unused
\newcommand*{\my@triangle@left}[2]{%
  \my@height=\math@param{#1}{2}{22}% height of the math axis
  \begin{tikzpicture}[scale=\my@height/1cm, my triangle/transform]
    \path[my triangle/style, draw=none]
      (0,1) -- (\my@triangle@width,2) -- (\my@triangle@width,0) -- cycle;

    \ifx\my@triangle@feature@type\empty
    \else
      \begin{scope}[every path/.append style={my triangle/inner feature style}]
        \if\my@triangle@feature@type -
          \path (0,1) -- (\my@triangle@width,1);
        \else
          \if\my@triangle@feature@type +
            \path (\my@[email protected], 1) -- (\my@triangle@width+0.5, 1)
                  (\my@triangle@width, 0.5) -- (\my@triangle@width, 1.5);
          \fi
        \fi
      \end{scope}
    \fi

    \path[my triangle/style, fill=none]
      (\my@triangle@width,0) -- (0,1) -- (\my@triangle@width,2)
      \ifmy@triangle@twosides \else --cycle \fi;
  \end{tikzpicture}%
}

\newcommand*{\my@triangle@right}{%
  \tikzset{my triangle/transform/.append style={xscale=-1}}%
  \my@triangle@left
}

% #1: PGF keys executed in '/tikz/my triangle'
\newcommand*{\myTriangle}[1][]{%
  \begingroup
    \tikzset{my triangle/.cd, #1}%
    \expandafter\expandafter\expandafter\my@triangle@wrap
    \ifmy@triangle@orientation@left
      \expandafter\my@triangle@left
    \else
      \expandafter\my@triangle@right
    \fi
  \endgroup
}
\makeatother

% Offer an interface that allows concise syntax
\ExplSyntaxOn
\msg_new:nnn { mytriangle } { invalid-orientation-arg }
  { Invalid~value~for~triangle~orientation:~'#1'. }
\msg_new:nnn { mytriangle } { invalid-feature-type }
  { Invalid~feature~type:~'#1'. }

\tl_new:N \l__mytriangle_orientation_tl
\tl_new:N \l__mytriangle_feature_type_tl

% #1: passed to '/tikz/my triangle/append style'
% #2: passed to '/tikz/my triangle/append inner feature style'
% #3: orientation ('l', 'r')
% #4: inner feature type ('' or ' ', '-', '+')
\NewDocumentCommand \mytriangle { O{} O{} m m }
  {
    \str_case_e:nnF {#3}
      {
        { l } { \tl_set:Nn \l__mytriangle_orientation_tl { left } }
        { r } { \tl_set:Nn \l__mytriangle_orientation_tl { right } }
      }
      { \msg_error:nnn { mytriangle } { invalid-orientation-arg } {#3} }

    \tl_if_blank:nTF {#4}
      { \tl_clear:N \l__mytriangle_feature_type_tl }
      {
        \str_case_e:nnF {#4}
          {
            { - } { \tl_set:Nn \l__mytriangle_feature_type_tl { - } }
            { + } { \tl_set:Nn \l__mytriangle_feature_type_tl { + } }
          }
          { \msg_error:nnn { mytriangle } { invalid-feature-type } {#4} }
      }

    \myTriangle
      [
        append~style={#1}, append~inner~feature~style={#2},
        orientation/.expand~once=\l__mytriangle_orientation_tl,
        inner~feature~type/.expand~once=\l__mytriangle_feature_type_tl,
      ]
  }
\ExplSyntaxOff

\begin{document}

$\begin{array}{@{}l@{}}
a \mytriangle{l}{} b \mytriangle{l}{-} c \mytriangle{l}{+} d
\\
a \mytriangle{r}{} b \mytriangle{r}{-} c \mytriangle{r}{+} d
\\
a \myTriangle[append style={fill=yellow}, inner feature type=-] b
\mytriangle[fill=cyan!60!green][draw=black]{l}{+}
\mytriangle[fill=cyan][draw=yellow]{l}{-}
\mytriangle[fill=red]{l}{+}
\\
a \myTriangle[orientation=right, append style={draw=orange!50!red, fill=yellow},
              inner feature type=+, append inner feature style={draw=cyan}] b
\mytriangle[fill=cyan!60!green][draw=black]{r}{}
\mytriangle[fill=cyan][draw=yellow]{r}{-}
\mytriangle[fill=red]{r}{+}
\end{array}$

\end{document}

在此处输入图片描述

带有下标和上标的示例：

$\begin{array}{@{}l@{}}
M \mytriangle{l}{ } N
  ^{{\alpha \mytriangle{l}{-} \beta}^{\gamma \mytriangle{l}{+} \delta}}
  _{{\varepsilon \mytriangle{l}{-} \delta}_{\eta \mytriangle{l}{+} \kappa}}
\\[1ex]
M \mytriangle{r}{ } N
  ^{{\alpha \mytriangle{r}{-} \beta}^{\gamma \mytriangle{r}{+} \delta}}
  _{{\varepsilon \mytriangle{r}{-} \delta}_{\eta \mytriangle{r}{+} \kappa}}
\end{array}$

在此处输入图片描述

答案3

几何符号：的工作l3draw。

\documentclass{article}
\usepackage{amsmath,xparse,l3draw}

\ExplSyntaxOn

\fp_new:N \l__pbmc_triangle_fp

\cs_new_protected:Nn \pmbc_triangle_right:
 {
  \draw_begin:
  \draw_linewidth:n { \l__pmbc_triangle_fp }
  \draw_cap_round:
  \draw_join_round:
  \draw_path_moveto:n { 0.0ex , 0.5ex }
  \draw_path_lineto:n { 1.0ex , 0.0ex }
  \draw_path_lineto:n { 1.0ex , 1.0ex }
  \draw_path_close:
  \draw_path_use_clear:n { stroke }
  \draw_end:
 }
\cs_new_protected:Nn \pmbc_triangle_left:
 {
  \draw_begin:
  \draw_linewidth:n { \l__pmbc_triangle_fp }
  \draw_cap_round:
  \draw_join_round:
  \draw_path_moveto:n { 0.0ex , 0.0ex }
  \draw_path_lineto:n { 1.0ex , 0.5ex }
  \draw_path_lineto:n { 0.0ex , 1.0ex }
  \draw_path_close:
  \draw_path_use_clear:n { stroke }
  \draw_end:
 }
\cs_new_protected:Nn \pmbc_triangle_minus_right:
 {
  \draw_begin:
  \draw_linewidth:n { \l__pmbc_triangle_fp }
  \draw_cap_round:
  \draw_join_round:
  \draw_path_moveto:n { 1.0ex , 0.5ex }
  \draw_path_lineto:n { 0.0ex , 0.5ex }
  \draw_path_lineto:n { 1.0ex , 1.0ex }
  \draw_path_lineto:n { 1.0ex , 0.0ex }
  \draw_path_lineto:n { 0.0ex , 0.5ex }
  \draw_path_close:
  \draw_path_use_clear:n { stroke }
  \draw_end:
 }
\cs_new_protected:Nn \pmbc_triangle_minus_left:
 {
  \draw_begin:
  \draw_linewidth:n { \l__pmbc_triangle_fp }
  \draw_cap_round:
  \draw_join_round:
  \draw_path_moveto:n { 0.0ex , 0.5ex }
  \draw_path_lineto:n { 1.0ex , 0.5ex }
  \draw_path_lineto:n { 0.0ex , 1.0ex }
  \draw_path_lineto:n { 0.0ex , 0.0ex }
  \draw_path_lineto:n { 1.0ex , 0.5ex }
  \draw_path_close:
  \draw_path_use_clear:n { stroke }
  \draw_end:
 }
\cs_new_protected:Nn \pmbc_triangle_plus_right:
 {
  \draw_begin:
  \draw_linewidth:n { \l__pmbc_triangle_fp }
  \draw_cap_round:
  \draw_join_round:
  \draw_path_moveto:n { 1.0ex , 1.0ex }
  \draw_path_lineto:n { 0.0ex , 0.5ex }
  \draw_path_lineto:n { 1.0ex , 0.0ex }
  \draw_path_use_clear:n { stroke }
  \draw_path_moveto:n { 1.0ex , 0.2ex }
  \draw_path_lineto:n { 1.0ex , 0.8ex }
  \draw_path_use_clear:n { stroke }
  \draw_path_moveto:n { 0.7ex, 0.5ex }
  \draw_path_lineto:n { 1.3ex, 0.5ex }
  \draw_path_use_clear:n { stroke }
  \draw_end:
 }
\cs_new_protected:Nn \pmbc_triangle_plus_left:
 {
  \draw_begin:
  \draw_linewidth:n { \l__pmbc_triangle_fp }
  \draw_cap_round:
  \draw_join_round:
  \draw_path_moveto:n { 0.0ex , 1.0ex }
  \draw_path_lineto:n { 1.0ex , 0.5ex }
  \draw_path_lineto:n { 0.0ex , 0.0ex }
  \draw_path_use_clear:n { stroke }
  \draw_path_moveto:n { 0.0ex , 0.2ex }
  \draw_path_lineto:n { 0.0ex , 0.8ex }
  \draw_path_use_clear:n { stroke }
  \draw_path_moveto:n { -0.3ex, 0.5ex }
  \draw_path_lineto:n { +0.3ex, 0.5ex }
  \draw_path_use_clear:n { stroke }
  \draw_end:
 }

\NewDocumentCommand{\BMright}{}
 {
  \mathrel
   {
    \fp_set:Nn \l__pmbc_triangle_fp { 0.08ex }
    \text{\kern0.1ex \pmbc_triangle_right: \kern0.1ex}
   }
 }
\NewDocumentCommand{\BMleft}{}
 {
  \mathrel
   {
    \fp_set:Nn \l__pmbc_triangle_fp { 0.08ex }
    \text{\kern0.1ex \pmbc_triangle_left: \kern0.1ex}
   }
 }
\NewDocumentCommand{\BMminusright}{}
 {
  \mathrel
   {
    \fp_set:Nn \l__pmbc_triangle_fp { 0.08ex }
    \text{\kern0.1ex \pmbc_triangle_minus_right: \kern0.1ex}
   }
 }
\NewDocumentCommand{\BMminusleft}{}
 {
  \mathrel
   {
    \fp_set:Nn \l__pmbc_triangle_fp { 0.08ex }
    \text{\kern0.1ex \pmbc_triangle_minus_left: \kern0.1ex}
   }
 }
\NewDocumentCommand{\BMplusright}{}
 {
  \mathrel
   {
    \fp_set:Nn \l__pmbc_triangle_fp { 0.08ex }
    \text{\kern0.1ex \pmbc_triangle_plus_right: \kern-0.2ex}
    \mkern2mu\nonscript\mkern-2mu
   }
 }
\NewDocumentCommand{\BMplusleft}{}
 {
  \mathrel
   {
    \fp_set:Nn \l__pmbc_triangle_fp { 0.08ex }
    \mkern2mu\nonscript\mkern-2mu
    \text{\kern-0.2ex \pmbc_triangle_plus_left: \kern0.1ex}
   }
 }

\ExplSyntaxOff

\begin{document}

$a \BMright b \BMleft c$

$a \BMminusright b \BMminusleft c$

$a \BMplusright b \BMplusleft c$

$\scriptstyle a \BMplusright b \BMplusleft c$

\LARGE $a \BMright b \BMleft c$

\end{document}

在此处输入图片描述

答案4

您可以定义

\def\lefttrianglebar   {\mathbin{{\vartriangleleft}\mkern-14mu{-}}}
\def\righttrianglebar  {\mathbin{{-}\mkern-14mu{\vartriangleright}}}
\def\lefttriangleplus  {\mathbin{{<}\mkern-7mu{+}}}
\def\righttriangleplus {\mathbin{+\mkern-7mu>}}

你可以尝试这个：

test: $a \lefttrianglebar b, c_{\righttrianglebar}$
\bye

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