AreSameSpace - Maple Help

AreSameSpace

check if a sequence of LAVF, VFPDO, and/or Distribution objects live on the same space.

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

Parameters

 obj1,obj2, ... - a sequence of LAVF, VFPDO, and/or Distribution objects

Description

 • The AreSameSpace method returns true if all objects live on the same space, false otherwise.
 • For these objects to live on the same space, their corresponding vector fields must live on same space. See the GetSpace method for LAVF, Distribution and VFPDO objects for more detail.
 • This method is associated with the LAVF, Distribution, and VFPDO objects. For more detail, see Overview of the LAVF object, Overview of the Distribution object, and Overview of the VFPDO object.

Examples

 > $\mathrm{with}\left(\mathrm{LieAlgebrasOfVectorFields}\right):$
 > $\mathrm{Typesetting}:-\mathrm{Settings}\left(\mathrm{userep}=\mathrm{true}\right):$
 > $\mathrm{Typesetting}:-\mathrm{Suppress}\left(\left[\mathrm{\xi }\left(x,y\right),\mathrm{\eta }\left(x,y\right)\right]\right):$
 > $V≔\mathrm{VectorField}\left(\mathrm{\xi }\left(x,y\right)\mathrm{D}\left[x\right]+\mathrm{\eta }\left(x,y\right)\mathrm{D}\left[y\right],\mathrm{space}=\left[x,y\right]\right)$
 ${V}{≔}{\mathrm{\xi }}{}\frac{{\partial }}{{\partial }{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{+}{\mathrm{\eta }}{}\frac{{\partial }}{{\partial }{y}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}$ (1)
 > $\mathrm{E2}≔\mathrm{LHPDE}\left(\left[\mathrm{diff}\left(\mathrm{\xi }\left(x,y\right),y,y\right)=0,\mathrm{diff}\left(\mathrm{\eta }\left(x,y\right),x\right)=-\mathrm{diff}\left(\mathrm{\xi }\left(x,y\right),y\right),\mathrm{diff}\left(\mathrm{\eta }\left(x,y\right),y\right)=0,\mathrm{diff}\left(\mathrm{\xi }\left(x,y\right),x\right)=0\right],\mathrm{indep}=\left[x,y\right],\mathrm{dep}=\left[\mathrm{\xi },\mathrm{\eta }\right]\right)$
 ${\mathrm{E2}}{≔}\left[{{\mathrm{\xi }}}_{{y}{,}{y}}{=}{0}{,}{{\mathrm{\eta }}}_{{x}}{=}{-}{{\mathrm{\xi }}}_{{y}}{,}{{\mathrm{\eta }}}_{{y}}{=}{0}{,}{{\mathrm{\xi }}}_{{x}}{=}{0}\right]{,}{\mathrm{indep}}{=}\left[{x}{,}{y}\right]{,}{\mathrm{dep}}{=}\left[{\mathrm{\xi }}{,}{\mathrm{\eta }}\right]$ (2)
 > $L≔\mathrm{LAVF}\left(V,\mathrm{E2}\right)$
 ${L}{≔}\left[{\mathrm{\xi }}{}\frac{{\partial }}{{\partial }{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{+}{\mathrm{\eta }}{}\frac{{\partial }}{{\partial }{y}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}\right]\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{&where}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\left\{\left[{{\mathrm{\xi }}}_{{y}{,}{y}}{=}{0}{,}{{\mathrm{\xi }}}_{{x}}{=}{0}{,}{{\mathrm{\eta }}}_{{x}}{=}{-}{{\mathrm{\xi }}}_{{y}}{,}{{\mathrm{\eta }}}_{{y}}{=}{0}\right]\right\}$ (3)
 > $\mathrm{OD}≔\mathrm{OrbitDistribution}\left(L\right)$
 ${\mathrm{OD}}{≔}\left\{\frac{{\partial }}{{\partial }{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{,}\frac{{\partial }}{{\partial }{y}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}\right\}$ (4)
 > $\mathrm{\Delta }≔\mathrm{VFPDO}\left(L\right)$
 ${\mathrm{\Delta }}{≔}{X}{→}\left[\frac{{\partial }}{{\partial }{y}}{}\left(\frac{{\partial }}{{\partial }{y}}{}{X}{}\left({x}\right)\right){,}\frac{{ⅆ}}{{ⅆ}{x}}{}{X}{}\left({x}\right){,}\frac{{\partial }}{{\partial }{x}}{}{X}{}\left({y}\right){+}\frac{{\partial }}{{\partial }{y}}{}{X}{}\left({x}\right){,}\frac{{ⅆ}}{{ⅆ}{y}}{}{X}{}\left({y}\right)\right]$ (5)
 > $\mathrm{AreSameSpace}\left(L,\mathrm{OD},\mathrm{\Delta }\right)$
 ${\mathrm{true}}$ (6)

Compatibility

 • The AreSameSpace command was introduced in Maple 2020.