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如何制作定制的$\sum$运算符？

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如何制作定制的$\sum$运算符？

我如何创建以下符号？

\circlearrowleft或\circlearrowright以操作员为中心\sum。

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編輯：

所以，

在\usepackage{esint}包中，\ointclockwise以及\ointctrclockwise；如何添加closed\circlearrowleft或closed \circlearrowright？我们会用到吗tikz？

有没有类似\clockwise和的\ctrclockwise命令？

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答案1

这是一种可能性。只有文本和显示样式，我希望您不需要在下标、上标或小分数中使用它们。

\documentclass{article}
\usepackage{amsmath,amssymb,graphicx}

\makeatletter
\newcommand*{\sumcirclearrowleft}{%
  \DOTSB
  \mathop{
    \mathchoice
      {\rlap{\kern.25em\rotatebox[origin=c]{-90}{$\circlearrowleft$}}{\sum}}
      {\vcenter{\rlap{\kern.2em\rotatebox[origin=c]{-90}{$\scriptscriptstyle\circlearrowleft$}}}{\sum}}
      {\sum}{\sum}
  }\slimits@
}

\newcommand*{\sumcirclearrowright}{%
  \DOTSB
  \mathop{
    \mathchoice
      {\rlap{\kern.25em\rotatebox[origin=c]{90}{$\circlearrowright$}}{\sum}}
      {\vcenter{\rlap{\kern.2em\rotatebox[origin=c]{90}{$\scriptscriptstyle\circlearrowright$}}}{\sum}}
      {\sum}{\sum}
  }\slimits@
}
\makeatother

\begin{document}

$\sumcirclearrowleft\displaystyle\sumcirclearrowleft$

$\sumcirclearrowright\displaystyle\sumcirclearrowright$

$\sumcirclearrowleft_{i=1}^n
\displaystyle\sumcirclearrowleft_{i=1}^n$

\end{document}

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带封闭圆圈的替代版本

我找到了一个 TikZ 版本（仍然只能在文本和显示样式中使用），其中有 Qrrbrbirlbel 的代码https://tex.stackexchange.com/a/95263/4427（修改的）。

\documentclass{article}
\usepackage{amsmath,amssymb,tikz}
\usetikzlibrary{arrows.meta,bending}

\makeatletter
\tikzset{
    /qrr/circle arrow/.cd,
    start angle/.initial={},
    delta angle/.initial={},
    end angle/.initial={},
    arrows/.estore in=\qrr@ca@arrow,
    arrows=-
}
\pgfdeclareshape{circle arrow}{
    \inheritsavedanchors[from=circle] \inheritanchorborder[from=circle]
    \inheritanchor[from=circle]{north}      \inheritanchor[from=circle]{north west}
    \inheritanchor[from=circle]{north east} \inheritanchor[from=circle]{center}
    \inheritanchor[from=circle]{west}       \inheritanchor[from=circle]{east}
    \inheritanchor[from=circle]{mid}        \inheritanchor[from=circle]{mid west}
    \inheritanchor[from=circle]{mid east}   \inheritanchor[from=circle]{base}
    \inheritanchor[from=circle]{base west}  \inheritanchor[from=circle]{base east}
    \inheritanchor[from=circle]{south}      \inheritanchor[from=circle]{south west}
    \inheritanchor[from=circle]{south east}
    \backgroundpath{
        \pgfkeysgetvalue{/qrr/circle arrow/start angle}\qrr@ca@s
        \pgfkeysgetvalue{/qrr/circle arrow/end angle}\qrr@ca@e
        \pgfkeysgetvalue{/qrr/circle arrow/delta angle}\qrr@ca@d
        \ifx\qrr@ca@s\pgfutil@empty%
            \pgfmathsetmacro\qrr@ca@s{\qrr@ca@e-\qrr@ca@d}%
        \else
            \ifx\qrr@ca@e\pgfutil@empty%
                \pgfmathsetmacro\qrr@ca@e{\qrr@ca@s+\qrr@ca@d}%
            \fi%
        \fi
        \pgfpathmoveto{\pgfpointadd{\centerpoint}{\pgfpointpolar{\qrr@ca@s}{\radius}}}%
        \pgfpatharc{\qrr@ca@s}{\qrr@ca@e}{\radius}%
        \pgfkeys{/tikz/arrows/.expand once=\qrr@ca@arrow}%
    }
}
\tikzset{% the first two styles are internal, they do not work alone!
    turn left/.style={
      /tikz/shape=circle arrow,
      /qrr/circle arrow/arrows={->[flex']},
      /qrr/circle arrow/delta angle=370
    },
    turn right/.style={
      /tikz/shape=circle arrow,
      /qrr/circle arrow/arrows={<[flex']-},
      /qrr/circle arrow/delta angle=370},
    turn left east/.style  = {/tikz/turn left,  /qrr/circle arrow/start angle=20},
    turn right west/.style = {/tikz/turn right, /qrr/circle arrow/start angle=160},
}

\newcommand*{\sumcirclearrowleft}{%
  \DOTSB
  \mathop{\mathpalette\sumcirclearrow@{left east}}
  \slimits@
}
\newcommand*{\sumcirclearrowright}{%
  \DOTSB
  \mathop{\mathpalette\sumcirclearrow@{right west}}
  \slimits@
}
\newcommand{\sumcirclearrow@}[2]{%
  \sbox\z@{$\m@th#1\sum$}%
  \dimen@=.14\wd\z@
  \makecirclearrow@{#2}
  {\sum}%
}

\newcommand{\makecirclearrow@}[1]{%
  \rlap{\kern\dimen@$\m@th\vcenter{\hbox{%
    \begin{tikzpicture}[
      >={Classical TikZ Rightarrow[width=2pt]},
    ]
    \node[draw,inner sep=\dimen@,turn #1] {};
    \end{tikzpicture}%
  }}$}%
}

\makeatother

\begin{document}

$\sumcirclearrowleft\displaystyle\sumcirclearrowleft$

$\sumcirclearrowright\displaystyle\sumcirclearrowright$

$\sumcirclearrowleft_{i=1}^n
\displaystyle\sumcirclearrowleft_{i=1}^n$

\end{document}

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答案2

适用于所有数学风格的替代方法......

修订的解决方案（闭合圆圈箭头）

这有点牵强，所以我将我原来的解决方案保留在下面。原作者希望结果中的圆圈箭头部分是一个封闭的（而不是开放的）圆圈。理想情况下，可以找到这样的字形并将其用于替代另一个。但是，找不到这样的字形。我可以通过叠加来制作一个，但仅限于\displaystyle，所以我不得不使用额外的技巧来将其缩放为相关的数学样式。因此，我认为这种方法并不理想。

\documentclass{scrartcl}
\usepackage{stackengine,scalerel,graphicx,amssymb,amsmath,wasysym}
\newsavebox\closedcircleleft
\newsavebox\closedcircleright
\savestack\closedcircleleft{\stackinset{c}{}{c}{}{$\Circle$}{$\circlearrowleft$}}
\savestack\closedcircleright{\stackinset{c}{}{c}{}{$\Circle$}{$\circlearrowright$}}
\DeclareMathOperator*{\sumcirclearrowleft}{%
  \ThisStyle{\mathop{\ensurestackMath{\stackinset{c}{-1.5\LMpt}{c}{}{%
  \rotatebox[origin=lb]{-90}{$\SavedStyle\scalerel*{\closedcircleleft}{%
  i}$}}{\SavedStyle\sum}}}}}
\DeclareMathOperator*{\sumcirclearrowright}{%
  \ThisStyle{\mathop{\ensurestackMath{\stackinset{c}{-1.5\LMpt}{c}{}{%
  \rotatebox[origin=lb]{90}{$\SavedStyle\scalerel*{\closedcircleright}{%
  i}$}}{\SavedStyle\sum}}}}}
\begin{document}
$\displaystyle\sumcirclearrowleft_i^n
\textstyle\sumcirclearrowleft_i^n
\scriptstyle\sumcirclearrowleft_i^n
\scriptscriptstyle\sumcirclearrowleft_i^n$
\medskip

$\displaystyle\sumcirclearrowright_i^n
\textstyle\sumcirclearrowright_i^n
\scriptstyle\sumcirclearrowright_i^n
\scriptscriptstyle\sumcirclearrowright_i^n$
\end{document}

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原始解决方案（空心圆形箭头）

\documentclass{scrartcl}
\usepackage{stackengine,scalerel,graphicx,amssymb,amsmath}
\DeclareMathOperator*{\sumcirclearrowleft}{%
  \ThisStyle{\mathop{\ensurestackMath{\stackinset{c}{-1.7\LMpt}{c}{.4pt}{%
  \rotatebox[origin=lb]{-90}{$\SavedStyle\circlearrowleft$}}{\SavedStyle\sum}}}}}
\DeclareMathOperator*{\sumcirclearrowright}{%
  \ThisStyle{\mathop{\ensurestackMath{\stackinset{c}{-1.7\LMpt}{c}{.1pt}{%
  \rotatebox[origin=lb]{90}{$\SavedStyle\circlearrowright$}}{\SavedStyle\sum}}}}}
\begin{document}

$\displaystyle\sumcirclearrowleft_i^n
\textstyle\sumcirclearrowleft_i^n
\scriptstyle\sumcirclearrowleft_i^n
\scriptscriptstyle\sumcirclearrowleft_i^n$
\medskip

$\displaystyle\sumcirclearrowright_i^n
\textstyle\sumcirclearrowright_i^n
\scriptstyle\sumcirclearrowright_i^n
\scriptscriptstyle\sumcirclearrowright_i^n$

\end{document}

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如果你喜欢较小的圆形箭头，

\documentclass{scrartcl}
\usepackage{stackengine,scalerel,graphicx,amssymb,amsmath}
\DeclareMathOperator*{\sumcirclearrowleft}{%
  \ThisStyle{\mathop{\ensurestackMath{\stackinset{c}{-1.5\LMpt}{c}%
    {\dimexpr.9pt-.3\LMpt}{%
  \rotatebox[origin=lb]{-90}{$\SavedStyle_\circlearrowleft$}}{\SavedStyle\sum}}}}}
\DeclareMathOperator*{\sumcirclearrowright}{%
  \ThisStyle{\mathop{\ensurestackMath{\stackinset{c}{-1.5\LMpt}{c}{.2pt}{%
  \rotatebox[origin=lb]{90}{$\SavedStyle_\circlearrowright$}}{\SavedStyle\sum}}}}}
\begin{document}

$\displaystyle\sumcirclearrowleft_i^n
\textstyle\sumcirclearrowleft_i^n
\scriptstyle\sumcirclearrowleft_i^n
\scriptscriptstyle\sumcirclearrowleft_i^n$
\medskip

$\displaystyle\sumcirclearrowright_i^n
\textstyle\sumcirclearrowright_i^n
\scriptstyle\sumcirclearrowright_i^n
\scriptscriptstyle\sumcirclearrowright_i^n$

\end{document}

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