The AreSameSpace command returns true if all objects live on the same space, false otherwise.

The obj1, obj2... can be a mixture of VectorField or OneForm and other objects.

This method is associated with the VectorField and OneForm objects. For more detail, see Overview of the VectorField object, Overview of the OneForm object.

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

$X≔\mathrm{VectorField}\left(\mathrm{components}=\left[x\,y\right]\,\mathrm{space}=\left[x\,y\right]\right)$

$X≔x\left(\frac{\ⅆ}{\ⅆx}\right)+y\left(\frac{\ⅆ}{\ⅆy}\right)$

$Y≔\mathrm{VectorField}\left(\mathrm{D}\left[x\right]\,\mathrm{space}=\left[x\,y\right]\right)$

$Y≔\frac{\ⅆ}{\ⅆx}$

$\mathrm{AreSameSpace}\left(X\,Y\right)$

$\mathrm{true}$

$\mathrm{Y1}≔\mathrm{VectorField}\left(\mathrm{D}\left[x\right]\,\mathrm{space}=\left[x\right]\right)$

$\mathrm{Y1}≔\frac{\ⅆ}{\ⅆx}$

$\mathrm{AreSameSpace}\left(Y\,\mathrm{Y1}\right)$

$\mathrm{false}$

$\mathrm{\omega }≔\mathrm{OneForm}\left(xd\left[x\right]+yd\left[y\right]\,\mathrm{space}=\left[x\,y\right]\right)$

$\mathrm{\omega }≔x\mathrm{dx}+y\mathrm{dy}$

$\mathrm{AreSameSpace}\left(X\,Y\,\mathrm{\omega }\right)$

$\mathrm{true}$

The AreSameSpace command was introduced in Maple 2020.

For more information on Maple 2020 changes, see Updates in Maple 2020.