The Intersection method returns a Distribution object representing the intersection of the input Distribution objects.  More precisely, the result is a distribution such that at each point, the subspace of tangent space is the intersection of the subspaces spanned by the input distributions.

Similarly, the VectorSpaceSum command returns a Distribution object representing the vector space sum of the input Distribution objects.  More precisely, the result is a distribution such that at each point, the subspace of tangent space is the vector space sum of the subspaces spanned by the input distributions.

These methods are associated with the Distribution object. For more detail see Overview of the Distribution object.

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

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

$T_x≔\frac{\ⅆ}{\ⅆx}$

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

$T_y≔\frac{\ⅆ}{\ⅆy}$

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

$T_z≔\frac{\ⅆ}{\ⅆz}$

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

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

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

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

$\mathrm{Gamma}≔\mathrm{Distribution}\left(T\left[x\right]\,T\left[y\right]\right)$

$\mathrm{\Γ}≔\left\{\frac{\ⅆ}{\ⅆy}\,\frac{\ⅆ}{\ⅆx}\right\}$

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

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

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

$\left\{\frac{\ⅆ}{\ⅆx}\,\frac{\ⅆ}{\ⅆy}\,\frac{\ⅆ}{\ⅆz}\right\}$

The Intersection and VectorSpaceSum commands were introduced in Maple 2020.

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