The DerivedDistribution method returns a Distribution object spanned by all the commutators of vector fields in dist.

This method is of little interest if the input Distribution dist is involutive, since in that case DerivedDistribution(dist) will simply return dist itself.

This method is associated with the Distribution object. For more detail see Overview of the Distribution object.

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

$\mathrm{V1}≔\mathrm{VectorField}\left(\mathrm{D}\left[x\right]\,\mathrm{space}=\left[x\,y\,z\,w\right]\right)$

$\mathrm{V1}≔\frac{\ⅆ}{\ⅆx}$

$\mathrm{V2}≔\mathrm{VectorField}\left(\mathrm{D}\left[y\right]+x\mathrm{D}\left[z\right]+z\mathrm{D}\left[w\right]\,\mathrm{space}=\left[x\,y\,z\,w\right]\right)$

$\mathrm{V2}≔\frac{\ⅆ}{\ⅆy}+x\left(\frac{\ⅆ}{\ⅆz}\right)+z\left(\frac{\ⅆ}{\ⅆw}\right)$

$\mathrm{\Sigma }≔\mathrm{Distribution}\left(\mathrm{V1}\,\mathrm{V2}\right)$

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

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

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

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

$\mathrm{false}$

The DerivedDistribution command was introduced in Maple 2020.

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