The DChange method performs changes of variables in a VectorField or OneForm object.

This method returns a new VectorField or OneForm object living on the space specified by newVars.

The name dchange is provided as an alias.

This DChange method is based on the existing Maple function PDEtools[dchange].

These methods are associated with the VectorField and OneForm objects. For more detail see Overview of the VectorField object, Overview of the OneForm object.

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

$R≔\mathrm{VectorField}\left(\left[\left[-y\,x\right]\,\left[x\,y\right]\right]\right)$

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

$P≔\mathrm{DChange}\left(\left\{x=r\cos \left(\mathrm{\theta }\right)\,y=r\sin \left(\mathrm{\theta }\right)\right\}\,R\,\left[r\,\mathrm{\theta }\right]\right)$

$P≔\left({\cos \left(\mathrm{\theta }\right)}^2+{\sin \left(\mathrm{\theta }\right)}^2\right)\left(\frac{\ⅆ}{\ⅆ\mathrm{\theta }}\right)$

$\mathrm{simplify}\left(P\right)$

$\frac{\ⅆ}{\ⅆ\mathrm{\theta }}$

$\mathrm{GetSpace}\left(R\right)$

$\left[x\,y\right]$

$\mathrm{GetSpace}\left(P\right)$

$\left[r\,\mathrm{\theta }\right]$

The DChange command was introduced in Maple 2020.

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