DChange - Maple Help

DChange

perform change of variables in a vector field or a one-form.

 Calling Sequence DChange (tr, obj, newVars, options) dchange (tr, obj, newVars, options)

Parameters

 tr - set of equations corresponding to the transformation from the old variables on the left-hand side of the equations to the new variables on the right-hand side. obj - a VectorField or OneForm object newVars - a list of new variable names options - optional arguments that will be passed down to PDEtools[dchange] command

Description

 • 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.

Examples

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

 > $R≔\mathrm{VectorField}\left(\left[\left[-y,x\right],\left[x,y\right]\right]\right)$
 ${R}{≔}{-}{y}{}\frac{{\partial }}{{\partial }{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{+}{x}{}\frac{{\partial }}{{\partial }{y}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}$ (1)

Change variables to use polar coordinates (r,theta):

 > $P≔\mathrm{DChange}\left(\left\{x=r\mathrm{cos}\left(\mathrm{\theta }\right),y=r\mathrm{sin}\left(\mathrm{\theta }\right)\right\},R,\left[r,\mathrm{\theta }\right]\right)$
 ${P}{≔}\left({{\mathrm{cos}}{}\left({\mathrm{\theta }}\right)}^{{2}}{+}{{\mathrm{sin}}{}\left({\mathrm{\theta }}\right)}^{{2}}\right){}\frac{{\partial }}{{\partial }{\mathrm{\theta }}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}$ (2)

We can further simplify this VectorField object, using the overloaded builtin simplify:

 > $\mathrm{simplify}\left(P\right)$
 $\frac{{\partial }}{{\partial }{\mathrm{\theta }}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}$ (3)

These two vector fields are on different spaces.

 > $\mathrm{GetSpace}\left(R\right)$
 $\left[{x}{,}{y}\right]$ (4)
 > $\mathrm{GetSpace}\left(P\right)$
 $\left[{r}{,}{\mathrm{\theta }}\right]$ (5)

Compatibility

 • The DChange command was introduced in Maple 2020.