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.

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

$T≔\mathrm{VectorField}\left(\mathrm{D}\left[z\right]\,\mathrm{space}=\left[x\,y\,z\right]\right)$

$T≔\frac{\ⅆ}{\ⅆz}$

$R≔\mathrm{VectorField}\left(-y\mathrm{D}\left[x\right]+x\mathrm{D}\left[y\right]\,\mathrm{space}=\left[x\,y\,z\right]\right)$

$R≔-y\left(\frac{\ⅆ}{\ⅆx}\right)+x\left(\frac{\ⅆ}{\ⅆy}\right)$

$\mathrm{\Sigma }≔\mathrm{Distribution}\left(T\,R\right)$

$\mathrm{\Sigma }≔\left\{-\frac{y\left(\frac{\ⅆ}{\ⅆx}\right)}{x}+\frac{\ⅆ}{\ⅆy}\,\frac{\ⅆ}{\ⅆz}\right\}$

$\mathrm{Gamma}≔\mathrm{Distribution}\left(T+R\right)$

$\mathrm{\Γ}≔\left\{-y\left(\frac{\ⅆ}{\ⅆx}\right)+x\left(\frac{\ⅆ}{\ⅆy}\right)+\frac{\ⅆ}{\ⅆz}\right\}$

$\mathrm{IsSubspace}\left(\mathrm{Gamma}\,\mathrm{\Sigma }\right)$

$\mathrm{true}$

$\mathrm{IsSubspace}\left(\mathrm{\Sigma }\,\mathrm{Gamma}\right)$

$\mathrm{false}$

The IsSubspace command was introduced in Maple 2020.

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