The Dimension method returns the dimension of the subspace of tangent space spanned by a distribution.

The Codimension method returns the codimension of this subspace. If a distribution of dimension r lives on a space of dimension n, the codimension is n-r.

The IsTrivial method returns true if dist is of dimension 0 and false otherwise.

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

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

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

$R_x≔-z\left(\frac{\ⅆ}{\ⅆy}\right)+y\left(\frac{\ⅆ}{\ⅆz}\right)$

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

$R_y≔z\left(\frac{\ⅆ}{\ⅆx}\right)-x\left(\frac{\ⅆ}{\ⅆz}\right)$

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

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

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

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

$\mathrm{Dimension}\left(\mathrm{\Sigma }\right)$

$2$

$\mathrm{Codimension}\left(\mathrm{\Sigma }\right)$

$1$

$\mathrm{IsTrivial}\left(\mathrm{\Sigma }\right)$

$\mathrm{false}$

The Dimension, Codimension and IsTrivial commands were introduced in Maple 2020.

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