The IsSubspace method returns true if solution space of obj1 is a subspace of solution space of obj2. False otherwise.

More precisely, the method returns true if at each point $x_0$, the local solution space of obj1  at $x_0$ is a subspace of the local solution space of obj2 at $x_0$.

The input arguments obj1 and obj2 need not have the same dependent variable names or dependencies.

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

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

$\mathrm{C2}≔\mathrm{LHPDE}\left(\left[\mathrm{diff}\left(\mathrm{\xi }\left(x\,y\right)\,x\,x\right)=0\,\mathrm{diff}\left(\mathrm{\xi }\left(x\,y\right)\,x\,y\right)=0\,\mathrm{diff}\left(\mathrm{\xi }\left(x\,y\right)\,y\,y\right)=0\,\mathrm{diff}\left(\mathrm{\eta }\left(x\,y\right)\,x\right)=-\mathrm{diff}\left(\mathrm{\xi }\left(x\,y\right)\,y\right)\,\mathrm{diff}\left(\mathrm{\eta }\left(x\,y\right)\,y\right)=\mathrm{diff}\left(\mathrm{\xi }\left(x\,y\right)\,x\right)\right]\,\mathrm{indep}=\left[x\,y\right]\,\mathrm{dep}=\left[\mathrm{\xi }\,\mathrm{\eta }\right]\,\mathrm{inRifReducedForm}=\mathrm{true}\right)$

$\mathrm{C2}≔\left[\frac{{\partial }^2}{\partial x^2}\mathrm{\xi }\left(x\,y\right)=0\,\frac{{\partial }^2}{\partial x\partial y}\mathrm{\xi }\left(x\,y\right)=0\,\frac{{\partial }^2}{\partial y^2}\mathrm{\xi }\left(x\,y\right)=0\,\frac{\partial }{\partial x}\mathrm{\eta }\left(x\,y\right)=-\frac{\partial }{\partial y}\mathrm{\xi }\left(x\,y\right)\,\frac{\partial }{\partial y}\mathrm{\eta }\left(x\,y\right)=\frac{\partial }{\partial x}\mathrm{\xi }\left(x\,y\right)\right],\mathrm{indep}=\left[x\,y\right],\mathrm{dep}=\left[\mathrm{\xi }\left(x\,y\right)\,\mathrm{\eta }\left(x\,y\right)\right]$

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

$\mathrm{E2}≔\left[\frac{{\partial }^2}{\partial y^2}\mathrm{\xi }\left(x\,y\right)=0\,\frac{\partial }{\partial x}\mathrm{\eta }\left(x\,y\right)=-\frac{\partial }{\partial y}\mathrm{\xi }\left(x\,y\right)\,\frac{\partial }{\partial y}\mathrm{\eta }\left(x\,y\right)=0\,\frac{\partial }{\partial x}\mathrm{\xi }\left(x\,y\right)=0\right],\mathrm{indep}=\left[x\,y\right],\mathrm{dep}=\left[\mathrm{\xi }\left(x\,y\right)\,\mathrm{\eta }\left(x\,y\right)\right]$

$\mathrm{IsSubspace}\left(\mathrm{E2}\,\mathrm{C2}\right)$

$\mathrm{true}$

$\mathrm{E2p}≔\mathrm{LHPDE}\left(\left[\mathrm{diff}\left(\mathrm{\alpha }\left(y\right)\,y\,y\right)=0\,\mathrm{diff}\left(\mathrm{\beta }\left(x\right)\,x\right)=-\mathrm{diff}\left(\mathrm{\alpha }\left(y\right)\,y\right)\right]\,\mathrm{indep}=\left[x\,y\right]\,\mathrm{dep}=\left[\mathrm{\alpha }\,\mathrm{\beta }\right]\,\mathrm{inRifReducedForm}=\mathrm{true}\right)$

$\mathrm{E2p}≔\left[\frac{{\ⅆ}^2}{\ⅆy^2}\mathrm{\alpha }\left(y\right)=0\,\frac{\ⅆ}{\ⅆx}\mathrm{\beta }\left(x\right)=-\frac{\ⅆ}{\ⅆy}\mathrm{\alpha }\left(y\right)\right],\mathrm{indep}=\left[x\,y\right],\mathrm{dep}=\left[\mathrm{\alpha }\left(y\right)\,\mathrm{\beta }\left(x\right)\right]$

$\mathrm{IsSubspace}\left(\mathrm{E2p}\,\mathrm{C2}\right)$

$\mathrm{true}$

The IsSubspace command was introduced in Maple 2020.

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