计数器中的数字的平方根

Question

我想得到存储在计数器中的数字的平方根。我一直在使用计算用于求和和乘法运算的包，但我找不到类似的东西

\setcounter{squarerootofmynumber}{\value{mynumber}^{1/2}}

或者类似的东西。你知道路吗？

Answer 1

这里有四种计算数字平方根的方法（精度不同）。但是，除非结果为整数，否则不能将其存储在计数器中。

1. 这calculator包裹

   \documentclass{article}
   \usepackage{calculator}
   \newcounter{mycount}
   \setcounter{mycount}{7}
   \begin{document}
   \SQUAREROOT{\themycount}{\solution}%
   $\sqrt{\themycount}=\solution$
   \end{document}
   

2. 这fp包裹

   \documentclass{article}
   \usepackage{fp}
   \newcounter{mycount}
   \setcounter{mycount}{7}
   \begin{document}
   \FProot\solution{\themycount}{2}%
   \FPround\solution\solution{5}%
   $\sqrt{\themycount}=\solution$
   \end{document}
   

3. 这pgf包（感谢 Peter Grill 的提醒）

   \documentclass{article}
   \usepackage{pgf}
   \newcounter{mycount}
   \setcounter{mycount}{7}
   \begin{document}
   \pgfmathsetmacro{\solution}{sqrt(\themycount)}%
   $\sqrt{\themycount}=\solution$
   \end{document}
   

4. 模块l3fp​l3kernel

   \documentclass{article}
   \usepackage{expl3}
   \ExplSyntaxOn
   \cs_new_eq:NN \calculate \fp_eval:n
   \ExplSyntaxOff
   \newcounter{mycount}
   \setcounter{mycount}{7}
   \begin{document}
   $\sqrt{\themycount}=\calculate{round(sqrt(\themycount),5)}$
   \end{document}
   

所有这些例子都给出了

将结果存储在计数器中要求结果为整数。包 2-4 具有对结果进行舍入的方法，以便之后设置计数器。以下是示例l3fp：

\documentclass{article}
\usepackage{expl3}
\ExplSyntaxOn
\cs_new_eq:NN \calculate \fp_eval:n
\ExplSyntaxOff
\begin{document}
\newcounter{mycount}
\setcounter{mycount}{7}
\edef\solution{\calculate{round(sqrt(\value{mycount}),0)}}
\setcounter{mycount}{\solution}\themycount
\end{document}

Answer 2

lualatex具有良好精度的解决方案

\documentclass{minimal}
\newcounter{mycount} \setcounter{mycount}{7}
\begin{document}

\directlua{tex.print(math.sqrt(\themycount))}

\end{document}

Answer 3

使用sqrt​xintexpr包您可以计算具有任意精度的平方根。

[P]我已经更新了这个答案来说明 (v1.1)中的新可选参数和(v1.1a)\xintfloatexpr中的四舍五入积分平方根的使用。\xintiiexpr

另外，可以直接使用包中的底层宏xint 和 xintfrac. 查看文档。

\documentclass{article}
\usepackage{xintexpr}
\begin{document}

$\sqrt{17}$ with various precisions:


% Square root with 16 digits of precision:
\xintthefloatexpr sqrt(17)\relax

% If you have a LaTeX counter, use \value:
\newcounter{cnt}
\setcounter{cnt}{17}

% \xintthefloatexpr sqrt(\value{cnt})\relax

% Square root with more digits:
\xintthefloatexpr [24] sqrt(17,24)\relax
% The 24 is needed twice, once for sqrt to compute with 
%  24 digits, and once for \xintthefloatexpr not to
%  round to only 16 digits.
% The [24] requires xintexpr v1.1 or later.

% Or change globally the precision:
\xintDigits := 48;
\xintthefloatexpr sqrt(17)\relax

% There is a variant which works only with (big) integers.
% You can use choose between sqrt which truncates and sqrtr
% which rounds. The latter requires xintexpr v1.1a or later.

Integer approximation to $\sqrt{170000000000000000}$:

\xinttheiiexpr sqrt(170000000000000000)\relax{} (truncated using \verb|sqrt|)

\xinttheiiexpr sqrtr(170000000000000000)\relax{} (rounded using \verb|sqrtr|)% v1.1a or later

% This can be put in a LaTeX counter if <2^31.

A counter can not hold larger than $\number"7FFFFFFF$.

\setcounter{cnt}{\xinttheiiexpr sqrtr(170000000000000000)\relax}
The counter holds: $\thecnt\approx \sqrt{170000000000000000}$.

\setcounter{cnt}{\xinttheiiexpr sqrtr(1700000000000000000)\relax}
The counter holds $\thecnt\approx \sqrt{1700000000000000000}$.

% Rather than expressions with the function sqrt, one
% can also use directly the underlying macros provided 
% by xint and xintfrac package. See xint documentation.
\end{document}