How to draw a point if the angle value and radial function are both given in algebraic (infix) form?

Question

\documentclass[preview,border=12pt]{standalone}
\usepackage{pst-plot}
\psset{polarplot}
\def\RPN#1{2 #1 10 div exp}
\def\Infix#1{2^(#1/10)}

\begin{document}
\begin{pspicture}[showgrid=true](-3,-3)(3,3)
    \psplot{2 Pi mul neg RadtoDeg}{2 Pi mul RadtoDeg}{\RPN{x DegtoRad}}
    \qdisk(!\RPN{Pi 3 mul 2 div} Pi 3 mul 2 div RadtoDeg PtoC){3pt}
\end{pspicture}\qquad
\begin{pspicture}[showgrid=true](-3,-3)(10,3)
    \psplot[algebraic]{2 Pi mul neg}{2 Pi mul}{\Infix{x}}
    %\qdisk(<your expression using \Infix goes here>){3pt} 
\end{pspicture}
\end{document}

How to draw a point if the angle value and radial function are both given in algebraic (infix) form?

Notes: Both angle and radius must accommodate infix expression such as 3*Pi/2 for the angle and 2^(3*Pi/2/10) for the radius.

Answer 1

\documentclass[border=12pt]{standalone}
\usepackage{pst-plot}
\def\ItoP{ AlgParser cvx }
\def\AtoP{ \ItoP exec x RadtoDeg PtoC}
\def\psDot(#1,#2){\psdot[dotscale=2](! #1 \ItoP /x ED #2 \AtoP)}

\def\Y#1{(2^(#1/10))}
\def\X#1{(#1)}

\begin{document}
\begin{pspicture}[showgrid](-3,-3)(3,3)
  \psplot[algebraic,polarplot]{2 Pi mul neg}{2 Pi mul}{\Y{x}} 
%  \psDot(\X{Pi}, \Y{x})
  \psDot(\X{3*Pi/10}, \Y{x})
\end{pspicture}

\end{document}

Answer 2

Just another simpler way but it is totally bad as we have to determine the quadrant manually (the sign of ordinate must be determined manually whether or not it is below or above the x-axis).

\qdisk(+{\Infix{(3*Pi/2)}*cos(3*Pi/2)},{-sqrt((\Infix{(3*Pi/2)})^2-x^2)}){3pt} 

The MWE:

\documentclass[preview,border=12pt]{standalone}
\usepackage{pst-plot}
\psset{polarplot}

\def\Infix#1{2^(#1/10)}

\begin{document}
\begin{pspicture}[showgrid=true](-3,-3)(3,3)
    \psplot[algebraic]{2 Pi mul neg}{2 Pi mul}{\Infix{x}}
    \qdisk(+{\Infix{(3*Pi/2)}*cos(3*Pi/2)},{-sqrt((\Infix{(3*Pi/2)})^2-x^2)}){3pt} 
\end{pspicture}
\end{document}