\def a variable for sqrt with parameters

Question

I tried to define variables with the sqrt command but couldn't get the result printed .

\def \radius {sqrt(4^2+2^2)}
\draw (4,3) node [right] {$The radius is \radius for x=4, y=2$};

The \draw shows "Theradiusissqrt(4^2+2^2)forx=4,y=2" instead of "The radius is 4.47 for x=4, y=2".

Also, I tried to \def the variable with pass-ins like below:

\def \my_radius#1#2 {sqrt(#1^2+#2^2)}   % r=4.47
\draw (4,0) node [right] {$My_radius is \my_radius{4}{2}\ for x=4, y=2$};

It didn't show the result. What would be the right code for these two examples? Btw, I am using the TeXnicCenter IDE, how do I debug/print by not using \draw?

Answer 1

You can use apnum package for evaluating expressions. The following example is in plain TeX:

\input tikz
\input apnum
\apFRAC=2
\evaldef\radius{\SQRT{4^2+2^2}}
\tikzpicture
\draw (4,0) node [right] {The radius is \radius\ for $x=4, y=2$};
\endtikzpicture
\bye

In OpTeX, you can use \expr macro, which evaluates the expression by Lua.

\edef\radius{\expr[2]{math.sqrt(4^2+2^2)}}
The radius is \radius\ for $x=4, y=2$.
\bye

You can use "variables" \x and \y with variable values too:

\def\my_radius{\expr[2]{math.sqrt(\x^2+\y^2)}}
\def\x{4} \def\y{2}
The radius is \my_radius\ for $x=\x, y=\y$.
% prints: The radius is 4.47 for x = 4, y = 2.
\def\x{7} \def\y{1}
The radius is \my_radius\ for $x=\x, y=\y$.
% prints: The radius is 7.07 for x = 7, y = 1.
\bye

Note that OpTeX allows to define the control sequence \my_radius directly. On the other hand, if you say \def\my_radius in LaTeX, then you define a macro \my with obligatory separator _radius. It isn't what you want.

Answer 2

With expl3

\documentclass[tikz,border=5mm]{standalone}
\begin{document}
\ExplSyntaxOn
\NewDocumentCommand \radius { m m }{
    The~radius~is~  
    $\fp_eval:n {round(sqrt(#1^2+#2^2),2)}$~
    for~$x=#1$,~$y=#2$
    }
\ExplSyntaxOff
\begin{tikzpicture}
    \draw (4,3) node [right] {\radius{4}{2}};
\end{tikzpicture}
\end{document}

With pgf, in the pgfmanual documentation section 94.3.8 Miscellaneous functions

\documentclass[tikz,border=5mm]{standalone}
\begin{document}
\begin{tikzpicture}
    \draw (4,3) node [right] {The radius is $\pgfmathparse{veclen(4,2)}\pgfmathresult$ for $x=4$, $y=2$ };
\end{tikzpicture}
\end{document}

Answer 3

With LaTeX released October 2023, you can define your own function for \fpeval calculations.

\documentclass{article}
\usepackage{tikz}
\ExplSyntaxOn
\fp_new_function:n { pythadd }
\fp_set_function:nnn { pythadd } { a,b } { sqrt(a^2+b^2) }
\ExplSyntaxOff
\newcommand{\radius}[2]{%
  The radius is $\fpeval{round(pythadd(#1,#2),2)}$
  for $x=#1$ and $y=#2$%
}
\begin{document}
\begin{tikzpicture}
  \draw (0,0) circle [radius=\fpeval{pythadd(4,2)}mm];
  \draw (1,0) node [right] {\radius{4}{2}};
\end{tikzpicture}
\end{document}

With previous releases you can do the same with a macro

\documentclass{article}
\usepackage{tikz}
\newcommand{\pythadd}[2]{sqrt((#1)^2+(#2)^2)}
\newcommand{\radius}[2]{%
  The radius is $\fpeval{round(\pythadd{#1}{#2},2)}$
  for $x=#1$ and $y=#2$%
}
\begin{document}
\begin{tikzpicture}
  \draw (0,0) circle [radius=\fpeval{\pythadd{4}{2}}mm];
  \draw (1,0) node [right] {\radius{4}{2}};
\end{tikzpicture}
\end{document}