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Several of the coordinate systems provided with the VectorCalculus package include up to 3 parameters in their definitions. In the documentation for this package, these parameters are given the names a, b and c, as needed.

The default values for these parameters are $a=1$, $b=\frac{1}{2}$, and $c=\frac{1}{3}$.

These parameters can be queried and set by using the GetCoordinateParameters and SetCoordinateParameters commands.

The GetCoordinateParameters command returns an expression sequence containing the current values of a, b, and c.

The SetCoordinateParameters command takes 1, 2, or 3 arguments, and sets the values of a, a and b, or a, b, and c respectively.

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

$\mathrm{SetCoordinateParameters}\left(\mathrm{\alpha }\,\mathrm{\beta }\right)$

$\mathrm{SetCoordinates}\left(\mathrm{conical}\left[u,v,w\right]\right)$

${\mathrm{conical}}_{u,v,w}$

$V≔⟨1\,2\,3⟩$

$V≔\left(1\right)e_u\+\left(2\right)e_v\+\left(3\right)e_w$

$\mathrm{MapToBasis}\left(V\,\mathrm{cartesian}\right)$

$\left(\frac{6}{\mathrm{\alpha }\mathrm{\beta }}\right)e_x\+\left(\frac{\sqrt{\frac{\left(-{\mathrm{\beta }}^2+4\right)\left({\mathrm{\beta }}^2-9\right)}{{\mathrm{\alpha }}^2-{\mathrm{\beta }}^2}}}{\mathrm{\beta }}\right)e_y\+\left(\frac{\sqrt{\frac{\left({\mathrm{\alpha }}^2-4\right)\left({\mathrm{\alpha }}^2-9\right)}{{\mathrm{\alpha }}^2-{\mathrm{\beta }}^2}}}{\mathrm{\alpha }}\right)e_z$

$\mathrm{GetCoordinateParameters}\left(\right)$

$\mathrm{\alpha },\mathrm{\beta },\frac{1}{3}$