2020-05-03 02:48:48 -0600 received badge ● Famous Question (source) 2016-08-15 00:17:52 -0600 received badge ● Scholar (source) 2016-08-14 23:20:00 -0600 commented answer Polar coordinates with negative angle Ohh... is that true even if I evaluate the first example and then edit it to change it into the second? (Not a very helpful error message, in that case...) 2016-08-12 13:55:19 -0600 received badge ● Editor (source) 2016-08-12 13:54:29 -0600 asked a question Polar coordinates with negative angle 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. = R2.chart() U = R2.open_subset('U', coord_def={Rect : (y != 0, x < 0)}) RectU = Rect.restrict(U) Polar. = 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. = R2.chart() U = R2.open_subset('U', coord_def={Rect : (y != 0, x > 0)}) RectU = Rect.restrict(U) Polar. = 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? 2016-08-12 13:41:22 -0600 received badge ● Notable Question (source) 2015-08-04 03:05:05 -0600 received badge ● Popular Question (source) 2013-12-05 06:29:59 -0600 commented answer Symbolic functions without named variables Okay, I guess I see what the developers were thinking, even if I don't agree with it. (Wouldn't "coproduct" be a more appropriate term?) 2013-12-02 16:50:22 -0600 received badge ● Supporter (source) 2013-12-02 16:49:58 -0600 commented answer Symbolic functions without named variables I'm trying to understand this. Is the expression tree really necessary? It seems like a wrapper around a callable symbolic expression that knows how to reset the variables as needed might be sufficient for what I want. For instance, could you also overload function application, addition, etc.? 2013-12-02 16:34:28 -0600 commented answer Symbolic functions without named variables Hmm... if it were really consistent about behaving this way, then I would expect f+h to be a type error, since you can't add elements of different rings. 2013-12-02 16:31:29 -0600 commented answer Symbolic functions without named variables Thanks! Why do you refer to defining mathematical functions as "adding more semantics"? 2013-11-29 02:27:53 -0600 received badge ● Student (source) 2013-11-27 08:33:17 -0600 asked a question Symbolic functions without named variables Is there a way to define a symbolic function that can (e.g.) be differentiated, but doesn't remember the name of its input variable(s)? For instance, consider: sage: f(x) = x^2 sage: g(x) = x^2 sage: h(t) = t^2  Mathematically, f, g, and h, should all be the same function. However, Sage doesn't think so: sage: f+g x |--> 2*x^2 sage: f+h (t, x) |--> t^2 + x^2  I guess that this is happening because a "function" defined with f(x)=x^2 is actually just a symbolic expression equipped with an ordering on its variables, rather than what a mathematician would call a "function". Is there a way to define an actual mathematical function?