Let B be an IDBasis object associated with a LHPDE object S of finite type. The GetChangeBasis method returns the change-of-basis for initial data of S, as recorded in B.

By default, the method returns a list of expressions which are linear combinations of the standard initial data basis (i.e. of the parametric derivatives from the associated LHPDE object S).

The method can return the change-of-basis as a matrix by specifying the optional argument output = "matrix".

In the second calling sequence, the call GetChangeBasis(B, "newToOld") returns the inverse of this change-of-basis matrix.

This method is associated with the IDBasis object. For more detail, see Overview of the IDBasis object.

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

$\mathrm{Typesetting}:-\mathrm{Settings}\left(\mathrm{userep}=\mathrm{true}\right)\:$

$\mathrm{Typesetting}:-\mathrm{Suppress}\left(\left[\mathrm{\xi }\left(x\,y\right)\,\mathrm{\eta }\left(x\,y\right)\right]\right)\:$

$\mathrm{E2}≔\mathrm{LHPDE}\left(\left[\mathrm{diff}\left(\mathrm{\xi }\left(x\,y\right)\,y\,y\right)=0\,\mathrm{diff}\left(\mathrm{\eta }\left(x\,y\right)\,x\right)=-\mathrm{diff}\left(\mathrm{\xi }\left(x\,y\right)\,y\right)\,\mathrm{diff}\left(\mathrm{\eta }\left(x\,y\right)\,y\right)=0\,\mathrm{diff}\left(\mathrm{\xi }\left(x\,y\right)\,x\right)=0\right]\,\mathrm{indep}=\left[x\,y\right]\,\mathrm{dep}=\left[\mathrm{\xi }\,\mathrm{\eta }\right]\right)$

$\mathrm{E2}≔\left[{\mathrm{\xi }}_{y,y}=0\,{\mathrm{\eta }}_x=-{\mathrm{\xi }}_y\,{\mathrm{\eta }}_y=0\,{\mathrm{\xi }}_x=0\right],\mathrm{indep}=\left[x\,y\right],\mathrm{dep}=\left[\mathrm{\xi }\,\mathrm{\eta }\right]$

$\mathrm{ParametricDerivatives}\left(\mathrm{E2}\right)$

$\left[\mathrm{\xi }\,{\mathrm{\xi }}_y\,\mathrm{\eta }\right]$

$B≔\mathrm{IDBasis}\left(\mathrm{E2}\,\left[\mathrm{\xi }\left(x\,y\right)-y\mathrm{diff}\left(\mathrm{\xi }\left(x\,y\right)\,y\right)\,\mathrm{\eta }\left(x\,y\right)-x\mathrm{diff}\left(\mathrm{\xi }\left(x\,y\right)\,y\right)\,-\mathrm{diff}\left(\mathrm{\xi }\left(x\,y\right)\,y\right)\right]\right)$

$B≔\left[\mathrm{\xi }-y\left({\mathrm{\xi }}_y\right)\,\mathrm{\eta }-x\left({\mathrm{\xi }}_y\right)\,-{\mathrm{\xi }}_y\right]$

$\mathrm{GetChangeBasis}\left(B\right)$

$\left[\mathrm{\xi }-y\left({\mathrm{\xi }}_y\right)\,\mathrm{\eta }-x\left({\mathrm{\xi }}_y\right)\,-{\mathrm{\xi }}_y\right]$

$\mathrm{GetChangeBasis}\left(B\,'\mathrm{output}'=''matrix''\right)$

$\left[\begin{array}{ccc}1& -y& 0\\ 0& -x& 1\\ 0& \mathrm{-1}& 0\end{array}\right]$

$\mathrm{GetParametricDerivatives}\left(B\right)$

$\left[\mathrm{\xi }\,{\mathrm{\xi }}_y\,\mathrm{\eta }\right]$

$\mathrm{GetChangeBasis}\left(B\,''newToOld''\right)$

$\left[\begin{array}{ccc}1& 0& -y\\ 0& 0& \mathrm{-1}\\ 0& 1& -x\end{array}\right]$

The GetChangeBasis command was introduced in Maple 2020.

For more information on Maple 2020 changes, see Updates in Maple 2020.