[pstricks] Thomae's Function

[Jean-Côme Charpentier]

Herbert Voss a écrit :
> sebastian perez schrieb:
> 
>> I'd like to know if it is possible to use pstricks to make the graph of Thomae's function
>>
>>
>> http://en.wikipedia.org/wiki/Thomae's_function
> 
> 
> not yet possible

... with a direct way. Otherwise, we can cheat :-)

\documentclass{article}
\usepackage{pstricks-add}
\usepackage{multido}

\makeatletter
\newcommand\IfRelPrime[4]{%
  \def\reserved at a{#1}%
  \def\reserved at b{#2}%
  \loop\ifnum\reserved at b>0
    \pst at mod\reserved at a\reserved at b\reserved at c
    \let\reserved at a\reserved at b
    \let\reserved at b\reserved at c
  \repeat
  \ifnum\reserved at a=1
    \def\reserved at c{#3}%
  \else
    \def\reserved at c{#4}%
  \fi
  \reserved at c\ignorespaces
}
\makeatother

\begin{document}
\begin{center}
  \psset{unit=4cm,dotsize=1pt 0}
  \begin{pspicture}(2.5,1.5)
    \psaxes{->}(0,0)(2.5,1.5)
    \multido{\ip=1+1}{50}{%
      \multido{\iq=1+1}{100}{%
        \unless\ifnum\ip>\numexpr2*\iq % for x \in [0,2]
          \IfRelPrime{\ip}{\iq}{%
            \psdots(!\ip\space \iq\space div 1 \iq\space div)
          }{\relax}
       \fi
      }%
    }%
  \end{pspicture}
\end{center}
\end{document}

Attention! The two loops can't be extended. For instance, with

  \multido{\ip=1+1}{80}{%
    \multido{\iq=1+1}{160}{%

I obtain a beautiful

Runaway text?
" tx at Dict begin STP newpath 0.8 SLW 0  setgray  [ 41 147 div 1 147 di\ETC.
! TeX capacity exceeded, sorry [main memory size=1500000].
\pst at code ...r .5 add exch itransform Dot } repeat

l.36     }
          %
No pages of output.

I suppose (I'm not sure) that it's working with recursive macro rather
multido but I'm too lasy to test it :-)

  Jean-Côme Charpentier