Let R be a fixed point of the plane, g and co denote the sensed angle. By the rotation $R\left(\mathrm{O}\,g\,\mathrm{co}\right)$ we mean the transformation of the plane S onto itself which carries each point P of the plane into the point P1 of the plane such that OP1 = OP and the angle $\mathrm{POP1}=g$ in the direction specified by co.

Point O is called the center of the rotation, and g is called the angle of the rotation.

If the fifth argument is omitted, then the origin is the center of rotation.

For a detailed description of the object created Q, use the routine detail (i.e., detail(Q))

The command with(geometry,rotation) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{geometry}\right)\:$

$\mathrm{point}\left(P\,2\,0\right),\mathrm{point}\left(Q\,1\,0\right)$

$P,Q$

$\mathrm{rotation}\left(\mathrm{P1}\,P\,\mathrm{\pi }\,'\mathrm{counterclockwise}'\right)$

$\mathrm{P1}$

$\mathrm{coordinates}\left(\mathrm{P1}\right)$

$\left[\mathrm{-2}\,0\right]$

$\mathrm{rotation}\left(\mathrm{P2}\,P\,\frac{\mathrm{\pi }}{2}\,'\mathrm{clockwise}'\,Q\right)$

$\mathrm{P2}$

$\mathrm{coordinates}\left(\mathrm{P2}\right)$

$\left[1\,\mathrm{-1}\right]$

$f≔y^2=x\:$$\mathrm{parabola}\left(p\,f\,\left[x\,y\right]\right)\:$

$\mathrm{point}\left(\mathrm{OO}\,0\,0\right)\:$

$\mathrm{rotation}\left(\mathrm{p1}\,p\,\frac{\mathrm{\pi }}{2}\,'\mathrm{counterclockwise}'\,\mathrm{OO}\right)\:$

$\mathrm{detail}\left(\left\{p\,\mathrm{p1}\right\}\right)$

$\left\{\begin{array}{ll}\text{name of the object}& p\\ \text{form of the object}& \mathrm{parabola2d}\\ \text{vertex}& \left[0\,0\right]\\ \text{focus}& \left[\frac{1}{4}\,0\right]\\ \text{directrix}& x+\frac{1}{4}=0\\ \text{equation of the parabola}& y^2-x=0\end{array}\,\begin{array}{ll}\text{name of the object}& \mathrm{p1}\\ \text{form of the object}& \mathrm{parabola2d}\\ \text{vertex}& \left[0\,0\right]\\ \text{focus}& \left[0\,\frac{1}{4}\right]\\ \text{directrix}& y+\frac{1}{4}=0\\ \text{equation of the parabola}& x^2-y=0\end{array}\right\}$

$\mathrm{rotation}\left(\mathrm{p2}\,p\,\mathrm{\pi }\,'\mathrm{counterclockwise}'\,\mathrm{OO}\right)\:$

$\mathrm{rotation}\left(\mathrm{p3}\,p\,\frac{\mathrm{\pi }}{2}\,'\mathrm{clockwise}'\,\mathrm{OO}\right)\:$

$\mathrm{draw}\left(\left[p\left(\mathrm{style}=\mathrm{LINE}\,\mathrm{thickness}=2\right)\,\mathrm{p1}\,\mathrm{p2}\,\mathrm{p3}\right]\,\mathrm{style}=\mathrm{POINT}\,\mathrm{symbol}=\mathrm{DIAMOND}\,\mathrm{color}=\mathrm{green}\,\mathrm{title}=\mathrm{`rotation\; of\; a\; parabola`}\right)$