The AreSameSpace method returns true if all objects live on the same space, false otherwise.

For LHPDE objects to live on the same space, they must have the same independent variables $x_1\,x_2\,\dots \,x_n$ and the same number of dependent variables.

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

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

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

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

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

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

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

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

$\mathrm{AreSameSpace}\left(\mathrm{E2}\,\mathrm{Tx}\right)$

$\mathrm{true}$

$\mathrm{Tx1}≔\mathrm{LHPDE}\left(\left[\mathrm{diff}\left(\mathrm{\alpha }\left(y\,x\right)\,x\right)=0\,\mathrm{diff}\left(\mathrm{\alpha }\left(y\,x\right)\,y\right)=0\,\mathrm{diff}\left(\mathrm{\beta }\left(y\,x\right)\,x\right)=0\,\mathrm{diff}\left(\mathrm{\beta }\left(y\,x\right)\,y\right)=0\right]\,\mathrm{indep}=\left[y\,x\right]\,\mathrm{dep}=\left[\mathrm{\alpha }\,\mathrm{\beta }\right]\right)$

$\mathrm{Tx1}≔\left[\frac{\partial }{\partial x}\mathrm{\alpha }\left(y\,x\right)=0\,\frac{\partial }{\partial y}\mathrm{\alpha }\left(y\,x\right)=0\,\frac{\partial }{\partial x}\mathrm{\beta }\left(y\,x\right)=0\,\frac{\partial }{\partial y}\mathrm{\beta }\left(y\,x\right)=0\right],\mathrm{indep}=\left[y\,x\right],\mathrm{dep}=\left[\mathrm{\alpha }\left(y\,x\right)\,\mathrm{\beta }\left(y\,x\right)\right]$

$\mathrm{AreSameSpace}\left(\mathrm{E2}\,\mathrm{Tx1}\right)$

$\mathrm{false}$

$\mathrm{AreSameSpace}\left(\mathrm{E2}\,\mathrm{Tx}\,\mathrm{Tx1}\right)$

$\mathrm{false}$

The AreSameSpace command was introduced in Maple 2020.

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