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VectorCalculus

 GetCoordinateParameters
 get coordinate system parameters
 SetCoordinateParameters
 set coordinate system parameters

 Calling Sequence GetCoordinateParameters() SetCoordinateParameters(a, b, c)

Parameters

 a - algebraic; specify the first coordinate system parameter (default=1) b - (optional) algebraic; specify the second coordinate system parameter (default=1/2) c - (optional) algebraic; specify the third coordinate system parameter (default=1/3)

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{VectorCalculus}\right):$
 > $\mathrm{SetCoordinateParameters}\left(\mathrm{α},\mathrm{β}\right)$
 > $\mathrm{SetCoordinates}\left({\mathrm{conical}}_{u,v,w}\right)$
 ${{\mathrm{conical}}}_{{u}{,}{v}{,}{w}}$ (1)
 > $V≔⟨1,2,3⟩$
 ${V}{:=}{{e}}_{{u}}{+}{2}{{e}}_{{v}}{+}{3}{{e}}_{{w}}$ (2)
 > $\mathrm{MapToBasis}\left(V,\mathrm{cartesian}\right)$
 $\frac{{6}}{{\mathrm{α}}{}{\mathrm{β}}}{{e}}_{{x}}{+}\left(\frac{\sqrt{\frac{\left({-}{{\mathrm{β}}}^{{2}}{+}{4}\right){}\left({{\mathrm{β}}}^{{2}}{-}{9}\right)}{{{\mathrm{α}}}^{{2}}{-}{{\mathrm{β}}}^{{2}}}}}{{\mathrm{β}}}\right){{e}}_{{y}}{+}\left(\frac{\sqrt{\frac{\left({{\mathrm{α}}}^{{2}}{-}{4}\right){}\left({{\mathrm{α}}}^{{2}}{-}{9}\right)}{{{\mathrm{α}}}^{{2}}{-}{{\mathrm{β}}}^{{2}}}}}{{\mathrm{α}}}\right){{e}}_{{z}}$ (3)
 > $\mathrm{GetCoordinateParameters}\left(\right)$
 ${\mathrm{α}}{,}{\mathrm{β}}{,}\frac{{1}}{{3}}$ (4)