Dchange - Maple Help

Dchange

change coordinates in a Distribution object

 Calling Sequence DChange( tr, dist, newvars, options ) dchange( tr, dist, 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 dist - a Distribution object newvars - list containing the new variables options - optional arguments that will be passed down to PDEtools[dchange] command

Description

 • 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.

Examples

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

Build vector fields associated with 3-d spatial rotations...

 > ${R}_{x}≔\mathrm{VectorField}\left(-z{\mathrm{D}}_{y}+y{\mathrm{D}}_{z},\mathrm{space}=\left[x,y,z\right]\right)$
 ${{R}}_{{x}}{≔}{-}{z}{}\left(\frac{{ⅆ}}{{ⅆ}{y}}\right){+}{y}{}\left(\frac{{ⅆ}}{{ⅆ}{z}}\right)$ (1)
 > ${R}_{y}≔\mathrm{VectorField}\left(-x{\mathrm{D}}_{z}+z{\mathrm{D}}_{x},\mathrm{space}=\left[x,y,z\right]\right)$
 ${{R}}_{{y}}{≔}{z}{}\left(\frac{{ⅆ}}{{ⅆ}{x}}\right){-}{x}{}\left(\frac{{ⅆ}}{{ⅆ}{z}}\right)$ (2)
 > ${R}_{z}≔\mathrm{VectorField}\left(-y{\mathrm{D}}_{x}+x{\mathrm{D}}_{y},\mathrm{space}=\left[x,y,z\right]\right)$
 ${{R}}_{{z}}{≔}{-}{y}{}\left(\frac{{ⅆ}}{{ⅆ}{x}}\right){+}{x}{}\left(\frac{{ⅆ}}{{ⅆ}{y}}\right)$ (3)

Construct the associated distribution...

 > $\mathrm{Σ}≔\mathrm{Distribution}\left({R}_{x},{R}_{y},{R}_{z}\right)$
 ${\mathrm{\Sigma }}{≔}\left\{{-}\frac{{y}{}\left(\frac{{ⅆ}}{{ⅆ}{x}}\right)}{{x}}{+}\frac{{ⅆ}}{{ⅆ}{y}}{,}{-}\frac{{z}{}\left(\frac{{ⅆ}}{{ⅆ}{x}}\right)}{{x}}{+}\frac{{ⅆ}}{{ⅆ}{z}}\right\}$ (4)

Set up change of coordinates to spherical polars...

 > $\mathrm{DChange}\left(\left\{x=r\mathrm{sin}\left(\mathrm{θ}\right)\mathrm{cos}\left(\mathrm{φ}\right),y=r\mathrm{sin}\left(\mathrm{θ}\right)\mathrm{sin}\left(\mathrm{φ}\right),z=r\mathrm{cos}\left(\mathrm{θ}\right)\right\},\mathrm{Σ},\left[r,\mathrm{θ},\mathrm{φ}\right]\right)$
 $\left\{\frac{{ⅆ}}{{ⅆ}{\mathrm{\theta }}}{,}\frac{{ⅆ}}{{ⅆ}{\mathrm{\phi }}}\right\}$ (5)

Compatibility

 • The Dchange command was introduced in Maple 2020.