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...

 > $R\left[x\right]≔\mathrm{VectorField}\left(-z\mathrm{D}\left[y\right]+y\mathrm{D}\left[z\right],\mathrm{space}=\left[x,y,z\right]\right)$
 ${{R}}_{{x}}{≔}{-}{z}{}\frac{{\partial }}{{\partial }{y}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{+}{y}{}\frac{{\partial }}{{\partial }{z}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}$ (1)
 > $R\left[y\right]≔\mathrm{VectorField}\left(-x\mathrm{D}\left[z\right]+z\mathrm{D}\left[x\right],\mathrm{space}=\left[x,y,z\right]\right)$
 ${{R}}_{{y}}{≔}{z}{}\frac{{\partial }}{{\partial }{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{-}{x}{}\frac{{\partial }}{{\partial }{z}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}$ (2)
 > $R\left[z\right]≔\mathrm{VectorField}\left(-y\mathrm{D}\left[x\right]+x\mathrm{D}\left[y\right],\mathrm{space}=\left[x,y,z\right]\right)$
 ${{R}}_{{z}}{≔}{-}{y}{}\frac{{\partial }}{{\partial }{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{+}{x}{}\frac{{\partial }}{{\partial }{y}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}$ (3)

Construct the associated distribution...

 > $\mathrm{\Sigma }≔\mathrm{Distribution}\left(R\left[x\right],R\left[y\right],R\left[z\right]\right)$
 ${\mathrm{\Sigma }}{≔}\left\{{-}\frac{{y}{}\frac{{\partial }}{{\partial }{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}}{{x}}{+}\frac{{\partial }}{{\partial }{y}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{,}{-}\frac{{z}{}\frac{{\partial }}{{\partial }{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}}{{x}}{+}\frac{{\partial }}{{\partial }{z}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}\right\}$ (4)

Set up change of coordinates to spherical polars...

 > $\mathrm{DChange}\left(\left\{x=r\mathrm{sin}\left(\mathrm{\theta }\right)\mathrm{cos}\left(\mathrm{\phi }\right),y=r\mathrm{sin}\left(\mathrm{\theta }\right)\mathrm{sin}\left(\mathrm{\phi }\right),z=r\mathrm{cos}\left(\mathrm{\theta }\right)\right\},\mathrm{\Sigma },\left[r,\mathrm{\theta },\mathrm{\phi }\right]\right)$
 $\left\{\frac{{\partial }}{{\partial }{\mathrm{\theta }}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{,}\frac{{\partial }}{{\partial }{\mathrm{\phi }}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}\right\}$ (5)

Compatibility

 • The Dchange command was introduced in Maple 2020.
 • For more information on Maple 2020 changes, see Updates in Maple 2020.