The GetIDBasis method returns the initial data basis as an IDBasis object for a LHPDE object.

The SetIDBasis method sets the IDBasis object in a LHPDE object.

To set an initial data basis in a LHPDE object, constructing an IDBasis object is required. See LieAlgebrasOfVectorFields[IDBasis] for more detail.

For an IDBasis object to be eligible to be set in a LHPDE object, their parametric derivatives must be the same. See example below.

These methods are associated with the LHPDE and IDBasis objects. For more detail, see Overview of the LHPDE object and Overview of the IDBasis object.

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

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

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

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

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

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

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

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

$\mathrm{FAIL}$

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

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

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

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

$\mathrm{SetIDBasis}\left(\mathrm{E2}\,B\right)$

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

$\mathrm{B1}≔\mathrm{GetIDBasis}\left(\mathrm{E2}\right)$

$\mathrm{B1}≔\left[\mathrm{\xi }-y\left({\mathrm{\xi }}_y\right)\,\mathrm{\eta }-x\left({\mathrm{\xi }}_y\right)\,-{\mathrm{\xi }}_y\right]$

$\mathrm{type}\left(\mathrm{B1}\,'\mathrm{IDBasis}'\right)$

$\mathrm{true}$

The GetIDBasis and SetIDBasis commands were introduced in Maple 2020.

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