Divide integers and get a floating point number (for a pstricks coordinate)

Question

I'm making a picture with pstricks and would like to plot points whose coordinates are fractions a/c, b/c, where a, b, and c run over certain ranges. I tried using \numexpr but it rounds down. I wouldn't use \dimexpr, as I assume that a dimension (ending with pt or suchlike) isn't welcome as a pstricks coordinate. I tried using pgf but I can't get the syntax to work:

\documentclass{article}
\usepackage{amsmath}
\usepackage{pstricks,pst-node,multido}
\RequirePackage{pgf}%
\begin{document}

\psset{xunit=5cm,yunit=5cm}
\begin{pspicture}(0,0)(1,1)
\multido{\iC=1+1}{5}{%
  \multido{\iA=0+1}{\iC}{%
    \multido{\iB=0+1}{\iC}{%
      \pscircle*(\pgfmathparse{\iA/\iC},\pgfmathparse{\iB/\iC}){0.02}
    }
  }
}
\end{pspicture}
\end{document}

Desired output (produced using TikZ, which works for this 5x5 example but runs out TeX's memory on the larger scales I want to use).

Answer 1

\documentclass{article}
\usepackage{pstricks,multido}
\begin{document}

\psset{xunit=5cm,yunit=5cm}
\begin{pspicture}(0,0)(1,1)
\multido{\iC=1+1}{5}{%
    \multido{\iA=0+1}{\iC}{%
        \multido{\iB=0+1}{\iC}{%
            \psdot(!\iA\space \iC\space div \iB\space \iC\space div)
        }%
    }%
}%
\end{pspicture}
\end{document}

or

\documentclass{article}
\usepackage{pstricks,multido,pst-calculate}
\begin{document}

\psset{unit=8}
\begin{pspicture}(2,2)
\multido{\iC=1+1}{20}{%
    \multido{\iA=0+1}{\numexpr\iC+1}{%
        \multido{\iB=0+1}{\numexpr\iC+1}{%
            \psdot[dotscale=0.5](\pscalculate{\iA/\iC},\pscalculate{\iB/\iC})
        }%
    }%
}%
\end{pspicture}
\end{document}

Answer 2

You forgot to invoke \pgfmathresult.

\documentclass{article}
\usepackage{amsmath}
\usepackage{pstricks,pst-node,multido}
\RequirePackage{pgf}%
\begin{document}

\psset{xunit=5cm,yunit=5cm}
\begin{pspicture}(0,0)(1,1)
\multido{\iC=1+1}{5}{%
  \multido{\iA=0+1}{\iC}{%
    \multido{\iB=0+1}{\iC}{%
    \pgfmathparse{\iA/\iC}\xdef\myx{\pgfmathresult}
    \pgfmathparse{\iB/\iC}\xdef\myy{\pgfmathresult}
    \pscircle*(\myx,\myy){0.02}
    }
  }
}
\end{pspicture}
\end{document}

Just for curiosity, could you please also add your TikZ example? I am a bit surprised about the error you get.

UPDATE: I do not get any problems when doing this with TikZ, where the code is shorter, no packages are required and the compilation is more convenient (even though I really like PSTricks).

\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[scale=10]
\foreach \iC in {1,...,15}{%
  \foreach \iA in {0,...,\iC}{%
   \foreach \iB in {0, ...,\iC}{%
      \draw[fill=black] ({\iA/\iC},{\iB/\iC}) circle (0.002);
    }
  }
}
\end{tikzpicture}
\end{document}

Answer 3

Also available in Metapost, here wrapped up in luamplib so compile with lualatex or work out how to adapt it for GMP, or plain MP.

I've added a bit of color too.

\documentclass[border=5mm]{standalone}
\usepackage{luatex85, luamplib}
\begin{document}
\mplibtextextlabel{enable}
\begin{mplibcode}
beginfig(1);
    n = 25;
    for i = 1 upto n:
        for j = 0 upto i:
            for k = 0 upto i:
                fill fullcircle 
                     scaled 3 
                     shifted ((j/i, k/i) scaled (n*cm)) 
                     withcolor 3/4(j/i, k/i, i/n);
            endfor
        endfor
    endfor
endfig;
\end{mplibcode}
\end{document}