2024-05-19 23:30:13 +0200 received badge ● Famous Question (source) 2023-11-25 14:13:20 +0200 received badge ● Notable Question (source) 2023-11-25 14:13:20 +0200 received badge ● Popular Question (source) 2023-07-21 08:35:07 +0200 received badge ● Notable Question (source) 2023-07-21 08:35:07 +0200 received badge ● Popular Question (source) 2023-07-04 18:47:27 +0200 received badge ● Notable Question (source) 2023-07-04 18:47:27 +0200 received badge ● Popular Question (source) 2022-12-30 13:46:39 +0200 received badge ● Popular Question (source) 2022-03-05 22:34:58 +0200 marked best answer Incorrect result for complex integral Not sure if this is user error: I am trying to evaluate the following integral: var('t') f = sqrt((e^(i * t) - 1) * (e^(-i*t) - 1)) show(f.integrate(t, 0, 2 * pi))  Sagemath returns 0, but WolframAlpha returns 8. Have I mis-specified the problem, or is this a bug? 2022-03-05 22:34:03 +0200 marked best answer Assume a function is real-valued In the following expression: var('z') u = function('u')(z) v = function('v')(z) f = u + i * v show(f.diff(z).conjugate().expand().simplify_full()) # conjugate(diff(u(z), z)) - I*conjugate(diff(v(z), z))  I would like Sage to make the simplification conjugate(diff(u(z), z)) = diff(u(z), z) because $u, v$ are intended to be real-valued. But my first attempt: assume(u, 'real')  didn't work: TypeError: self (=u(z)) must be a relational expression What is the right way to write this assumption? 2022-02-28 17:45:13 +0200 received badge ● Nice Question (source) 2022-02-28 01:04:21 +0200 asked a question Incorrect result for complex integral Incorrect result for complex integral Not sure if this is user error: I am trying to evaluate the following integral: v 2022-02-27 20:45:00 +0200 asked a question Assume a function is real-valued Assume a function is real-valued In the following expression: var('z') u = function('u')(z) v = function('v')(z) f = 2022-02-27 20:44:21 +0200 asked a question Assume a function is real-valued Assume a function is real-valued In the following expression: var('z') u = function('u')(z) v = function('v')(z) f = 2022-02-27 20:44:20 +0200 asked a question Assume a function is real-valued Assume a function is real-valued In the following expression: var('z') u = function('u')(z) v = function('v')(z) f = 2021-06-21 15:44:23 +0200 commented answer Incorrect result for integral of (cos z) / z My About tab says: ┌────────────────────────────────────────────────────────────────────┐ │ SageMath version 9.1, Relea 2021-06-21 15:09:34 +0200 asked a question Incorrect result for integral of (cos z) / z Incorrect result for integral of (cos z) / z I am confused by the following result: I'd like to integrate cos(z) / z on 2021-05-02 22:13:02 +0200 marked best answer Integrating differential forms I'd like to integrate dx /\ dy over the unit square. Naively, I would expect the following to work: E. = EuclideanSpace(2) phi = E.diff_form(2) phi[1, 2] = 1 show(integrate(integrate(phi, x, 0, 1), y, 0, 1))  but it fails with: TypeError: unable to convert 2-form on the Euclidean plane E^2 to a symbolic expression  and I can't find anything about integration in the DiffFormFreeModule documentation. What is the right way to do this? 2021-05-02 21:42:57 +0200 asked a question Integrating differential forms Integrating differential forms I'd like to integrate dx /\ dy over the unit square. Naively, I would expect the followin 2021-05-02 21:42:54 +0200 asked a question Integrating differential forms Integrating differential forms I'd like to integrate dx /\ dy over the unit square. Naively, I would expect the followin 2021-05-01 22:01:42 +0200 marked best answer Differential forms on non-standard spherical coordinates I'd like to compute an exterior derivative in spherical coordinates. So far I have the following: E. = EuclideanSpace(3) Ec. = E.spherical_coordinates() EcM = Ec.manifold() EcM.set_default_frame(EcM.spherical_frame()) EcM.set_default_chart(EcM.spherical_coordinates()) F = function('F') show(F) F_1 = function('F_r')(r, theta, phi) F_2 = function('F_theta')(r, theta, phi) F_3 = function('F_phi')(r, theta, phi) psi = EcM.diff_form(2, 'psi') psi[2, 3] = F_1 psi[1, 3] = -F_2 psi[1, 2] = F_3 show(psi.display()) res = psi.exterior_derivative() show(res.display())  which works for the spherical coordinate transformation that is the default for Euclidean space. But, I see that Sagemath has a different spherical coordinate map than I do: > print(E.coord_change(E.spherical_coordinates(), E.cartesian_coordinates()).display()) x = r*cos(phi)*sin(theta) y = r*sin(phi)*sin(theta) z = r*cos(theta)  Instead, I'd like: x = r * cos(theta) * cos(phi) y = r * sin(theta) * cos(phi) z = r * sin(phi)  How can I supply a different change of coordinates function for this case? 2021-04-28 15:42:06 +0200 commented answer Differential forms on non-standard spherical coordinates How do I make sure the differential forms are on the right space? (Apologies if my vocabulary is not correct here). When 2021-04-28 15:41:50 +0200 commented answer Differential forms on non-standard spherical coordinates How do I make sure the differential forms are on the right space? (Apologies if my vocabulary is not correct here). When 2021-04-28 02:26:55 +0200 commented question Differential forms on non-standard spherical coordinates Yes, I do -- thanks! How do I get a Manifold that has the right coordinate system attached? 2021-04-28 02:25:01 +0200 edited question Differential forms on non-standard spherical coordinates Differential forms on non-standard spherical coordinates I'd like to compute an exterior derivative in spherical coordin 2021-04-28 02:16:17 +0200 asked a question Differential forms on non-standard spherical coordinates Differential forms on non-standard spherical coordinates I'd like to compute an exterior derivative in spherical coordin 2021-04-08 15:52:51 +0200 asked a question Plotting a 2d subspace of R^3 Plotting a 2d subspace of R^3 I'm trying to plot the 2d subspace of R^3 defined by a pair of vectors. Following some exa 2021-04-05 11:13:12 +0200 received badge ● Nice Question (source) 2021-04-04 15:55:47 +0200 edited question Evaluating a form field at a point on vectors Evaluating a form field at a point on vectors I am having trouble matching up terminology in my textbook (Hubbard's Vect 2021-04-04 15:51:03 +0200 received badge ● Editor (source) 2021-04-04 15:51:03 +0200 edited question Evaluating a form field at a point on vectors Evaluating a form field at a point on vectors I am having trouble matching up terminology in my textbook (Hubbard's Vect 2021-04-04 15:48:57 +0200 marked best answer Evaluating a form field at a point on vectors I am having trouble matching up terminology in my textbook (Hubbard's Vector Calculus) against SageMath operators. I'd like to understand how to solve the following example problem with Sage: Let phi = cos(x z) * dx /\ dy be a 2-form on R^3. Evaluate it at the point (1, 2, pi) on the vectors [1, 0, 1], [2, 2, 3]. The expected answer is:  cos (1 * pi) * Matrix([1, 2], [0, 2]).det() = -2  So far I have pieced together the following: E. = EuclideanSpace(3, 'E') f = E.diff_form(2, 'f') f[1, 2] = cos(x * z) point = E((1,2,pi), name='point') anchor = f.at(point) v1 = vector([1, 0, 1]) v2 = vector([2, 2, 3]) show(anchor(v1, v2))  which fails with the error: TypeError: the argument no. 1 must be a module element To construct a vector in E, I tried: p1 = E(v1.list()) p2 = E(v2.list()) show(anchor(p1, p2))  but that fails with the same error. What's the right way to construct two vectors in E? 2021-04-04 15:48:57 +0200 received badge ● Scholar (source) 2021-04-04 15:48:54 +0200 received badge ● Supporter (source) 2021-04-03 23:38:55 +0200 received badge ● Student (source) 2021-04-03 21:33:51 +0200 asked a question Evaluating a form field at a point on vectors Evaluating a form field at a point on vectors I am having trouble matching up terminology in my textbook (Hubbard's Vect 2021-04-03 20:35:23 +0200 received badge ● Organizer (source)