How can I get the value of the f(1/2) is 11/4 not 2.75 when I use \pgfmathprintnumber\pgfmathresult?

Question

This is my code

\documentclass[12pt,a4paper]{article}
\usepackage[left=2cm, right=2cm, top=2cm, bottom=2cm]{geometry}
\usepackage{pgfplots} 
\pgfplotsset{compat=1.18}
\usepackage{tikz}
\usepackage{amsmath}
\begin{document}
\begin{tikzpicture}[%
        declare function={a=1;b=-1;c=3;
      f(\x)=a*\x*\x+b*\x+c;x1=-b/(2*a);}
      ]
 \pgfmathparse{f(x1)}%
    $ f\left(\dfrac{1}{2}\right)=
    \pgfmathprintnumber\pgfmathresult$
\end{tikzpicture}
\end{document} 

I got f\left(\dfrac{1}{2}\right) = 2.75. How can I get the value of the f(1/2) is 11/4 not 2.75?

Answer 1

You can use /pgf/number format/frac and /pgf/number format/frac whole to control the format.

If you want 'proper' fractions in which the fractional part is less than unity, use /pgf/number format/frac whole=true rather than /pgf/number format/frac whole=false or omit the setting altogether.

\documentclass[12pt]{article}
\usepackage{tikz} 
\usetikzlibrary{fpu}
\usepackage{amsmath}
\begin{document}
\begin{tikzpicture}[%
  declare function={%
      a=1;b=-1;c=3;
      f(\x)=a*\x*\x+b*\x+c;
      x1=-b/(2*a);
    }
  ]
  \pgfkeys{%
    /pgf/number format/frac,
    % comment the next line to get e.g. 2 3/4 rather than 11/4
    % and 3 rather than 3/1
    /pgf/number format/frac whole=false,
  }
   \pgfmathparse{f(x1)}%
   $ f\left(\dfrac{1}{2}\right)=
   \pgfmathprintnumber\pgfmathresult$
\end{tikzpicture}
\end{document} 

But note that you could just as soon use \frac{11}{4} in this case since the function always returns the same result. If you alter c, however, the result may be printed as a decimal because no fractional equivalent will be available.

Also, according to the manual, a function should always use return. (But it doesn't seem to mind.)