GetComponents - Maple Help

GetComponents

get components of a VectorField or OneForm object

 Calling Sequence GetComponents( obj) GetComponents( obj, output = opt)

Parameters

 obj - a VectorField or a OneForm object opt - a string : either "expression" or "table"

Description

 • The GetComponents method returns a list of components of a VectorField or OneForm object.
 • The components can also be returned as a table, by specifying output = "table". See example below.
 • 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

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

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

 > $\mathrm{GetComponents}\left(X\right)$
 $\left[{\mathrm{\xi }}{,}{\mathrm{\eta }}\right]$ (2)

 > $\mathrm{\omega }≔\mathrm{OneForm}\left(\mathrm{components}=\left[1,{x}^{2},{y}^{2}\right],\mathrm{space}=\left[x,y,z\right]\right)$
 ${\mathrm{\omega }}{≔}{{x}}^{{2}}{}{\mathrm{dy}}{+}{{y}}^{{2}}{}{\mathrm{dz}}{+}{\mathrm{dx}}$ (3)

 > $T≔\mathrm{GetComponents}\left(\mathrm{\omega },\mathrm{output}="table"\right)$
 ${T}{≔}{table}{}\left(\left[{y}{=}{{x}}^{{2}}{,}{z}{=}{{y}}^{{2}}{,}{x}{=}{1}\right]\right)$ (4)

The entries of this table T are the components of the OneForm object, the indices are the corresponding space variables.

 > $T\left[x\right],T\left[y\right],T\left[z\right]$
 ${1}{,}{{x}}^{{2}}{,}{{y}}^{{2}}$ (5)

Compatibility

 • The GetComponents command was introduced in Maple 2020.