Thanks for the quick response.
But we will analyze a concrete example, because of which the question arose. This is exercise 4, lesson 2, DifferentialGeometry Lessons in Help (Maple16).
TwoFormBasis2 := proc(M)
local n ,i, j, alpha, beta, Basis;
n := DifferentialGeometry:-Tools:-DGinfo(M, "FrameBaseDimension");
Basis := Array(1 .. n*(n - 1)/2):
k := 0;
for i to n do
alpha := DifferentialGeometry:-Tools:-DGform(i);
for j from i + 1 to n do
k := k + 1;
beta := DifferentialGeometry:-Tools:-DGform(j);
Basis[k] := alpha &wedge beta;
[dx1 ^ dx2, dx1 ^ dx3, dx1 ^ dx4, dx2 ^ dx3, dx2 ^ dx4, dx3 ^ dx4]
In the first line, the procedure is defined in frame M, and the second line is already in frame E4. If, after the first line, you issue a command to change the frame, then, naturally, an error is produced: it is impossible to interpret.
Further, in other lines, there are switching between M and E4; However, no real a command to change the frame are being introduced by the authors. How they do it ?... it's unclear.