Let obj1, obj2, ... be a sequence of LHPDE objects living on the same space (see AreSameSpace). The VectorSpaceSum method finds a LHPDEs system whose solution space is the vector space sum of solution spaces of obj1,obj2,....

The method returns a rif-reduced LHPDE object.

By default, the dependent variable names of the returned object are taken from obj1. The dependent variable names will be vars if the optional argument depname = vars is specified.

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

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

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

$\mathrm{Typesetting}:-\mathrm{Suppress}\left(\left\{\mathrm{\ξ}\,\mathrm{\η}\,\mathrm{\α}\,\mathrm{\β}\,\mathrm{\φ}\,\mathrm{\ψ}\right\}\left(x\,y\right)\right)\:$

$S≔\mathrm{LHPDE}\left(\left[\frac{\partial }{\partial x}\mathrm{\ξ}\left(x\,y\right)\=0\,\frac{\partial }{\partial y}\mathrm{\η}\left(x\,y\right)\=0\,\frac{\partial }{\partial y}\mathrm{\ξ}\left(x\,y\right)\+\frac{\partial }{\partial x}\mathrm{\η}\left(x\,y\right)\=0\,\frac{{\partial }^2}{\partial y^2}\mathrm{\ξ}\left(x\,y\right)\=0\,\frac{{\partial }^2}{\partial x^2}\mathrm{\η}\left(x\,y\right)\=0\right]\right)$

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

$\mathrm{S1}≔\mathrm{LHPDE}\left(\left[\frac{{\partial }^2}{\partial x^2}\mathrm{\α}\left(x\,y\right)\=0\,\frac{\partial }{\partial y}\mathrm{\α}\left(x\,y\right)\=0\,\frac{\partial }{\partial x}\mathrm{\β}\left(x\,y\right)\=0\,\frac{{\partial }^2}{\partial y^2}\mathrm{\β}\left(x\,y\right)\=0\,\frac{\partial }{\partial x}\mathrm{\α}\left(x\,y\right)-\left(\frac{\partial }{\partial y}\mathrm{\β}\left(x\,y\right)\right)\=0\right]\,\mathrm{indep}\=\left[x\,y\right]\,\mathrm{dep}\=\left[\mathrm{\α}\,\mathrm{\β}\right]\right)$

$\mathrm{S1}≔\left[{\mathrm{\alpha }}_{x,x}=0\,{\mathrm{\alpha }}_y=0\,{\mathrm{\beta }}_x=0\,{\mathrm{\beta }}_{y,y}=0\,{\mathrm{\alpha }}_x-{\mathrm{\beta }}_y=0\right],\mathrm{indep}=\left[x\,y\right],\mathrm{dep}=\left[\mathrm{\alpha }\,\mathrm{\beta }\right]$

$\mathrm{VectorSpaceSum}\left(S\,\mathrm{S1}\right)$

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

$\mathrm{VectorSpaceSum}\left(S\,\mathrm{S1}\,\mathrm{depname}\=\left[\mathrm{\φ}\,\mathrm{\ψ}\right]\right)$

$\left[{\mathrm{\phi }}_{x,x}=0\,{\mathrm{\phi }}_y=0\,{\mathrm{\psi }}_{y,y}=0\,{\mathrm{\psi }}_x=0\right],\mathrm{indep}=\left[x\,y\right],\mathrm{dep}=\left[\mathrm{\phi }\,\mathrm{\psi }\right]$

The VectorSpaceSum command was introduced in Maple 2020.

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