AreSameSpace - Maple Help

AreSameSpace

check if a sequence of LHPDE objects live on the same space.

 Calling Sequence AreSameSpace( obj1,obj2, ...)

Parameters

 obj1, obj2, ... - a sequence of LHPDE objects

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{LieAlgebrasOfVectorFields}\right):$
 > $\mathrm{Typesetting}:-\mathrm{Settings}\left(\mathrm{userep}=\mathrm{true}\right):$
 > $\mathrm{Typesetting}:-\mathrm{Suppress}\left(\left\{\mathrm{\alpha },\mathrm{\beta },\mathrm{\eta },\mathrm{\xi }\right\}\left(x,y\right)\right)$
 > $\mathrm{E2}≔\mathrm{LHPDE}\left(\left[\mathrm{diff}\left(\mathrm{\xi }\left(x,y\right),y,y\right)=0,\mathrm{diff}\left(\mathrm{\eta }\left(x,y\right),x\right)=-\mathrm{diff}\left(\mathrm{\xi }\left(x,y\right),y\right),\mathrm{diff}\left(\mathrm{\eta }\left(x,y\right),y\right)=0,\mathrm{diff}\left(\mathrm{\xi }\left(x,y\right),x\right)=0\right],\mathrm{indep}=\left[x,y\right],\mathrm{dep}=\left[\mathrm{\xi },\mathrm{\eta }\right]\right)$
 ${\mathrm{E2}}{≔}\left[{{\mathrm{\xi }}}_{{y}{,}{y}}{=}{0}{,}{{\mathrm{\eta }}}_{{x}}{=}{-}{{\mathrm{\xi }}}_{{y}}{,}{{\mathrm{\eta }}}_{{y}}{=}{0}{,}{{\mathrm{\xi }}}_{{x}}{=}{0}\right]{,}{\mathrm{indep}}{=}\left[{x}{,}{y}\right]{,}{\mathrm{dep}}{=}\left[{\mathrm{\xi }}{,}{\mathrm{\eta }}\right]$ (1)
 > $\mathrm{Tx}≔\mathrm{LHPDE}\left(\left[\mathrm{diff}\left(\mathrm{\alpha }\left(x,y\right),x\right)=0,\mathrm{diff}\left(\mathrm{\beta }\left(x,y\right),y\right)=0,\mathrm{diff}\left(\mathrm{\alpha }\left(x,y\right),y\right)=0,\mathrm{diff}\left(\mathrm{\beta }\left(x,y\right),x\right)=0\right],\mathrm{indep}=\left[x,y\right],\mathrm{dep}=\left[\mathrm{\alpha },\mathrm{\beta }\right]\right)$
 ${\mathrm{Tx}}{≔}\left[{{\mathrm{\alpha }}}_{{x}}{=}{0}{,}{{\mathrm{\beta }}}_{{y}}{=}{0}{,}{{\mathrm{\alpha }}}_{{y}}{=}{0}{,}{{\mathrm{\beta }}}_{{x}}{=}{0}\right]{,}{\mathrm{indep}}{=}\left[{x}{,}{y}\right]{,}{\mathrm{dep}}{=}\left[{\mathrm{\alpha }}{,}{\mathrm{\beta }}\right]$ (2)
 > $\mathrm{AreSameSpace}\left(\mathrm{E2},\mathrm{Tx}\right)$
 ${\mathrm{true}}$ (3)
 > $\mathrm{Tx1}≔\mathrm{LHPDE}\left(\left[\mathrm{diff}\left(\mathrm{\alpha }\left(y,x\right),x\right)=0,\mathrm{diff}\left(\mathrm{\alpha }\left(y,x\right),y\right)=0,\mathrm{diff}\left(\mathrm{\beta }\left(y,x\right),x\right)=0,\mathrm{diff}\left(\mathrm{\beta }\left(y,x\right),y\right)=0\right],\mathrm{indep}=\left[y,x\right],\mathrm{dep}=\left[\mathrm{\alpha },\mathrm{\beta }\right]\right)$
 ${\mathrm{Tx1}}{≔}\left[\frac{{\partial }}{{\partial }{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{\alpha }}{}\left({y}{,}{x}\right){=}{0}{,}\frac{{\partial }}{{\partial }{y}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{\alpha }}{}\left({y}{,}{x}\right){=}{0}{,}\frac{{\partial }}{{\partial }{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{\beta }}{}\left({y}{,}{x}\right){=}{0}{,}\frac{{\partial }}{{\partial }{y}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{\beta }}{}\left({y}{,}{x}\right){=}{0}\right]{,}{\mathrm{indep}}{=}\left[{y}{,}{x}\right]{,}{\mathrm{dep}}{=}\left[{\mathrm{\alpha }}{}\left({y}{,}{x}\right){,}{\mathrm{\beta }}{}\left({y}{,}{x}\right)\right]$ (4)
 > $\mathrm{AreSameSpace}\left(\mathrm{E2},\mathrm{Tx1}\right)$
 ${\mathrm{false}}$ (5)
 > $\mathrm{AreSameSpace}\left(\mathrm{E2},\mathrm{Tx},\mathrm{Tx1}\right)$
 ${\mathrm{false}}$ (6)

Compatibility

 • The AreSameSpace command was introduced in Maple 2020.