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

Let S be a LHPDE object. Then IsFiniteType(S) returns true if and only if SolutionDimension(S) $\ne \mathrm{\infty }$.

Let S be a LHPDE object. Then IsTrivial(S) returns true if and only if SolutionDimension(S) $\=0$.

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

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

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

$S≔\left[\frac{{\partial }^2}{\partial y^2}\mathrm{\xi }\left(x\,y\right)=0\,\frac{\partial }{\partial x}\mathrm{\eta }\left(x\,y\right)=-\frac{\partial }{\partial y}\mathrm{\xi }\left(x\,y\right)\,\frac{\partial }{\partial y}\mathrm{\eta }\left(x\,y\right)=0\,\frac{\partial }{\partial x}\mathrm{\xi }\left(x\,y\right)=0\right],\mathrm{indep}=\left[x\,y\right],\mathrm{dep}=\left[\mathrm{\xi }\left(x\,y\right)\,\mathrm{\eta }\left(x\,y\right)\right]$

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

$3$

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

$\mathrm{true}$

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

$\mathrm{false}$

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

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