Following the sagemanifolds tutorial I can make $\mathbb{R}^2$ with rectangular and polar coordinates:
R2 = Manifold(2, 'R2', r'\mathbb{R}^2', start_index=1)
Rect.<x,y> = R2.chart()
U = R2.open_subset('U', coord_def={Rect : (y != 0, x < 0)})
RectU = Rect.restrict(U)
Polar.<r,th> = U.chart(r'r:(0,+oo) th:(0,2*pi):\theta')
This uses the range $(0,2\pi)$ for $\theta$, excluding the positive $x$-axis. But if I try to use instead the range $(-\pi,\pi)$ for $\theta$, excluding the negative $x$-axis:
R2 = Manifold(2, 'R2', r'\mathbb{R}^2', start_index=1)
Rect.<x,y> = R2.chart()
U = R2.open_subset('U', coord_def={Rect : (y != 0, x > 0)})
RectU = Rect.restrict(U)
Polar.<r,th> = U.chart(r'r:(0,+oo) th:(-pi,pi):\theta')
SageMathCloud gives me "ValueError: Assumption is redundant". But strangely, SageMathCell doesn't complain at all. What is the problem?
