IsSubSpace - Maple Help

IsSubspace

check if one distribution is contained in another

 Calling Sequence IsSubspace(dist1, dist2)

Parameters

 dist1, dist2 - Distribution objects

Description

 • The IsSubspace method decides whether Distribution object dist1 specifies a subspace of tangent space which is contained in the subspace specified by Distribution dist2 at each point in space. It returns the values true or false.
 • This method is associated with the Distribution object. For more detail see Overview of the Distribution object.

Examples

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

Build vector fields...

 > $T≔\mathrm{VectorField}\left(\mathrm{D}\left[z\right],\mathrm{space}=\left[x,y,z\right]\right)$
 ${T}{≔}\frac{{\partial }}{{\partial }{z}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}$ (1)
 > $R≔\mathrm{VectorField}\left(-y\mathrm{D}\left[x\right]+x\mathrm{D}\left[y\right],\mathrm{space}=\left[x,y,z\right]\right)$
 ${R}{≔}{-}{y}{}\frac{{\partial }}{{\partial }{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{+}{x}{}\frac{{\partial }}{{\partial }{y}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}$ (2)

Construct the associated distribution...

 > $\mathrm{\Sigma }≔\mathrm{Distribution}\left(T,R\right)$
 ${\mathrm{\Sigma }}{≔}\left\{{-}\frac{{y}{}\frac{{\partial }}{{\partial }{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}}{{x}}{+}\frac{{\partial }}{{\partial }{y}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{,}\frac{{\partial }}{{\partial }{z}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}\right\}$ (3)
 > $\mathrm{Gamma}≔\mathrm{Distribution}\left(T+R\right)$
 ${\mathrm{Γ}}{≔}\left\{{-}{y}{}\frac{{\partial }}{{\partial }{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{+}{x}{}\frac{{\partial }}{{\partial }{y}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{+}\frac{{\partial }}{{\partial }{z}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}\right\}$ (4)

Test containment...

 > $\mathrm{IsSubspace}\left(\mathrm{Gamma},\mathrm{\Sigma }\right)$
 ${\mathrm{true}}$ (5)
 > $\mathrm{IsSubspace}\left(\mathrm{\Sigma },\mathrm{Gamma}\right)$
 ${\mathrm{false}}$ (6)

Compatibility

 • The IsSubspace command was introduced in Maple 2020.