GetSpace - Maple Help

GetSpace

get space coordinates of a VectorField or OneForm object

 Calling Sequence GetSpace( obj )

Parameters

 obj - a VectorField or a OneForm object

Description

 • The GetSpace method returns a list of space coordinate variables for a VectorField or OneForm object.
 • This method is associated with the VectorField and OneForm objects. For more detail, see Overview of the VectorField object, Overview of the OneForm object.

Examples

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

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

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

The method returns the space where X, R live. Although these two vector fields have identical appearance, they live on difference spaces: (x,y) versus (x,y,z)

 > $\mathrm{GetSpace}\left(X\right)$
 $\left[{x}{,}{y}\right]$ (3)
 > $\mathrm{GetSpace}\left(R\right)$
 $\left[{x}{,}{y}{,}{z}\right]$ (4)

 > $\mathrm{\omega }≔\mathrm{OneForm}\left(\mathrm{components}=\left[1,{x}^{2},{y}^{2}\right],\mathrm{space}=\left[x,y,z\right]\right)$
 ${\mathrm{\omega }}{≔}{{x}}^{{2}}{}{\mathrm{dy}}{+}{{y}}^{{2}}{}{\mathrm{dz}}{+}{\mathrm{dx}}$ (5)

 > $\mathrm{GetSpace}\left(\mathrm{\omega }\right)$
 $\left[{x}{,}{y}{,}{z}\right]$ (6)

Compatibility

 • The GetSpace command was introduced in Maple 2020.