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Yes, there is a more elegant way:

A = G(g(R1((1,))))
B = G(g(R1((0,))))

Explanations: R1((1,)) is the point of coordinate t=1 on the manifold R1, g(R1((1,))) is the image of this point by the map g; by the very definition of g, this is a point of R3 and finally, G(g(R1((1,)))) is the image by G of this last point.

Even better, if instead of declaring R1 as a manifold of dimension 1, you declare it as the real line manifold via RealLine (see this documentation), i.e. if you replace the two lines

R1 = Manifold(1, 'R1', start_index=1, latex_name=r'\mathbb{R}')
cartesian1d.<t> = R1.chart()

by the following single one:

R1.<t> = RealLine()

then you can use directly the notation g(1) instead of g(R1((1,))):

A = G(g(1))
B = G(g(0))