The SolutionDimension method calculates the solution dimension of the determining system for a LAVF object. It returns $\mathrm{\infty }$ if the solution dimension is not finite.

Let L be a LAVF object. Then IsFiniteType(L) returns true if and only if SolutionDimension(L) < $\mathrm{\infty }$.

Let L be a LAVF object. Then IsTrivial(L) returns true if and only if SolutionDimension(L) = 0.

These methods are front-end to the corresponding methods of a LHPDE object. That is, let L be a LAVF object and S be its determining system (i.e.  S = GetDeterminingSystem(L)), then SolutionDimension(L) equals SolutionDimension(S), IsFiniteType(L) equals IsFiniteType(S) and IsTrivial(L) equals IsTrivial(S). For more detail, see the corresponding methods: SolutionDimension, IsFiniteType, IsTrivial of a LHPDE object.

These methods are associated with the LAVF object. For more detail, see Overview of the LAVF object.

$\mathrm{with}\left(\mathrm{LieAlgebrasOfVectorFields}\right)\&colon;$

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

$\mathrm{Typesetting}:-\mathrm{Suppress}\left(\left[\mathrm{\xi }\left(x\&comma;y\right)\&comma;\mathrm{\eta }\left(x\&comma;y\right)\right]\right)\&colon;$

$V≔\mathrm{VectorField}\left(\mathrm{\xi }\left(x\&comma;y\right)\mathrm{D}\left[x\right]+\mathrm{\eta }\left(x\&comma;y\right)\mathrm{D}\left[y\right]\&comma;\mathrm{space}=\left[x\&comma;y\right]\right)$

$V≔\mathrm{\xi }\left(\frac{\&DifferentialD;}{\&DifferentialD;x}\right)+\mathrm{\eta }\left(\frac{\&DifferentialD;}{\&DifferentialD;y}\right)$

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

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

$L≔\mathrm{LAVF}\left(V\&comma;\mathrm{E2}\right)$

$L≔\left[\mathrm{\xi }\left(\frac{\&DifferentialD;}{\&DifferentialD;x}\right)+\mathrm{\eta }\left(\frac{\&DifferentialD;}{\&DifferentialD;y}\right)\right]\&where\left\{\left[{\mathrm{\xi }}_{y,y}=0\&comma;{\mathrm{\xi }}_x=0\&comma;{\mathrm{\eta }}_x=-{\mathrm{\xi }}_y\&comma;{\mathrm{\eta }}_y=0\right]\right\}$

$\mathrm{SolutionDimension}\left(L\right)$

$3$

$\mathrm{IsFiniteType}\left(L\right)$

$\mathrm{true}$

$\mathrm{IsTrivial}\left(L\right)$

$\mathrm{false}$

The SolutionDimension, IsFiniteType and IsTrivial commands were introduced in Maple 2020.

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