The DChange method changes coordinates in a Distribution object, and returns a new Distribution object on space with coordinates as specified by the newvars parameter.

The DChange method is closely modeled on the PDEtools:-dchange command, the calling sequence is identical.

The newvars argument is required.  Other options are as for PDEtools:-dchange , and are ultimately passed through to it.

The name dchange is provided as an alias.

If the PDEtools package is loaded, a name conflict may arise.  In this case the calling sequence should be modified to dist:-DChange(tr, dist, newvars, options).

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

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

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

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

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

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

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

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

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

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

$\mathrm{DChange}\left(\left\{x=r\sin \left(\mathrm{\theta }\right)\cos \left(\mathrm{\phi }\right)\,y=r\sin \left(\mathrm{\theta }\right)\sin \left(\mathrm{\phi }\right)\,z=r\cos \left(\mathrm{\theta }\right)\right\}\,\mathrm{\Sigma }\,\left[r\,\mathrm{\theta }\,\mathrm{\phi }\right]\right)$

$\left\{\frac{\ⅆ}{\ⅆ\mathrm{\phi }}\,\frac{\ⅆ}{\ⅆ\mathrm{\theta }}\right\}$

The Dchange command was introduced in Maple 2020.

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