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...

 > $T≔\mathrm{VectorField}\left({\mathrm{D}}_{z},\mathrm{space}=\left[x,y,z\right]\right)$
 ${T}{≔}\frac{{ⅆ}}{{ⅆ}{z}}$ (1)
 > $R≔\mathrm{VectorField}\left(-y{\mathrm{D}}_{x}+x{\mathrm{D}}_{y},\mathrm{space}=\left[x,y,z\right]\right)$
 ${R}{≔}{-}{y}{}\left(\frac{{ⅆ}}{{ⅆ}{x}}\right){+}{x}{}\left(\frac{{ⅆ}}{{ⅆ}{y}}\right)$ (2)

Construct the associated distribution...

 > $\mathrm{Σ}≔\mathrm{Distribution}\left(T,R\right)$
 ${\mathrm{\Sigma }}{≔}\left\{{-}\frac{{y}{}\left(\frac{{ⅆ}}{{ⅆ}{x}}\right)}{{x}}{+}\frac{{ⅆ}}{{ⅆ}{y}}{,}\frac{{ⅆ}}{{ⅆ}{z}}\right\}$ (3)
 > $\mathrm{Gamma}≔\mathrm{Distribution}\left(T+R\right)$
 ${\mathrm{Γ}}{≔}\left\{{-}{y}{}\left(\frac{{ⅆ}}{{ⅆ}{x}}\right){+}{x}{}\left(\frac{{ⅆ}}{{ⅆ}{y}}\right){+}\frac{{ⅆ}}{{ⅆ}{z}}\right\}$ (4)

Test containment...

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

Compatibility

 • The IsSubspace command was introduced in Maple 2020.