With the DifferentialGeometry package, the user can create many manifolds (coordinate systems) and Lie algebras within a single Maple session.  The structure equations and other attributes of these manifolds and Lie algebras are all stored in memory and are accessible at any time.  However, at any given moment one manifold or Lie algebra has the preferred status of the current frame.  The default value of the current frame is the frame in which the most recent calculation was performed or the most recent object displayed.

The DifferentialGeometry:-DGinfo("CurrentFrame") returns the value of the current frame.

The command ChangeLieAlgebraTo(AlgName) simply changes the current frame to the frame for the Lie algebra AlgName. It returns the name of the previous frame.

The command ChangeLieAlgebraTo is part of the DifferentialGeometry:-LieAlgebras package.  It can be used in the form ChangeLieAlgebraTo(...) only after executing the commands with(DifferentialGeometry) and with(LieAlgebras), but can always be used by executing DifferentialGeometry:-LieAlgebras:-ChangeLieAlgebraTo(...).

$\mathrm{with}\left(\mathrm{DifferentialGeometry}\right)\:$$\mathrm{with}\left(\mathrm{LieAlgebras}\right)\:$

$\mathrm{L1}≔\mathrm{\_DG}\left(\left[\left[''LieAlgebra''\,\mathrm{Alg1}\,\left[3\right]\right]\,\left[\left[\left[2\,3\,1\right]\,1\right]\right]\right]\right)$

$\mathrm{\_DG}\left(\left[\left[''LieAlgebra''\,\mathrm{Alg1}\,\left[3\right]\right]\,\left[\left[\left[2\,3\,1\right]\,1\right]\right]\right]\right)$

$\mathrm{DGsetup}\left(\mathrm{L1}\right)\:$

$\mathrm{L2}≔\mathrm{\_DG}\left(\left[\left[''LieAlgebra''\,\mathrm{Alg2}\,\left[2\right]\right]\,\left[\right]\right]\right)$

$\mathrm{DGsetup}\left(\mathrm{L2}\right)\:$

$\mathrm{\_DG}\left(\left[\left[''LieAlgebra''\,\mathrm{Alg2}\,\left[2\right]\right]\,\left[\right]\right]\right)$

$\mathrm{Tools}:-\mathrm{DGinfo}\left(''CurrentFrame''\right)$

$\mathrm{Alg2}$

$\mathrm{ChangeLieAlgebraTo}\left(\mathrm{Alg1}\right)$

$\mathrm{Alg2}$

$\mathrm{Tools}:-\mathrm{DGinfo}\left(''CurrentFrame''\right)$

$\mathrm{Alg1}$

$\mathrm{Tools}:-\mathrm{DGinfo}\left(''CurrentFrame''\right)$

$\mathrm{Alg1}$

$\mathrm{lprint}\left(\mathrm{e1}\right)$

_DG([["vector", Alg1, []], [[[1], 1]]])

$\mathrm{Tools}:-\mathrm{DGinfo}\left(\mathrm{e1}\,''ObjectFrame''\right)$

$\mathrm{Alg1}$

$\mathrm{ChangeLieAlgebraTo}\left(\mathrm{Alg2}\right)$

$\mathrm{Alg1}$

$\mathrm{lprint}\left(\mathrm{e1}\right)$

_DG([["vector", Alg2, []], [[[1], 1]]])

$\mathrm{Tools}:-\mathrm{DGinfo}\left(\mathrm{e1}\,''ObjectFrame''\right)$

$\mathrm{Alg2}$