2021-04-11 15:07:07 +0200 received badge ● Notable Question (source) 2020-05-05 03:39:41 +0200 received badge ● Popular Question (source) 2020-01-08 21:05:47 +0200 asked a question SageMath-9.0.app fails to start on macOS 10.14.6 Happy New Year Hi, SageMath-9.0.app fails to start on macOS 10.14.6 : the file:///Applications/SageMath-9.0.app/Contents/Resources/loading-page.html appears on Firefox the log file says : /Applications/SageMath-9.0.app/Contents/Resources/sage/src/bin/sage: line 617: exec: python3: not found However, everything works fine in a term window /Applications/SageMath-9.0.app/Contents/Resources/sage/sage --notebook=jupyter copy and paste one of these URLs: http://localhost:8888/?token=688ebf86... Can anyone help ? Thank you 2019-04-12 21:26:19 +0200 commented answer multiprocessing.Pool does not work Thank you ! 2019-04-12 20:13:39 +0200 received badge ● Associate Editor (source) 2019-04-12 19:50:35 +0200 asked a question multiprocessing.Pool does not work Hi, when trying to run SM_black_hole_rendering.ipynb with sagemanifols https://nbviewer.jupyter.org/github/s... the cell 28 does not execute well Process PoolWorker-1: Traceback (most recent call last): File "/Applications/SageMath-8.7.app/Contents/Resources/sage/local/lib/python2.7/multiprocessing/process.py", line 267, in _bootstrap self.run() ... Can anyone help ? Thank you Epi 2019-02-27 14:56:51 +0200 received badge ● Notable Question (source) 2019-02-27 14:56:51 +0200 received badge ● Popular Question (source) 2019-02-27 14:56:51 +0200 received badge ● Famous Question (source) 2018-08-22 22:10:44 +0200 received badge ● Nice Question (source) 2018-08-22 20:47:48 +0200 received badge ● Student (source) 2018-08-22 17:30:44 +0200 commented answer su2 matrix exponentiation Thank you for your answer. I have added these sage commands ((G_exp.expand().simplify_full() - cos(t)*matrix.diagonal([1,1]))/sin(t)).expand().simplify_trig() ((G_exp[1,0].real_part().simplify_trig() + i* G_exp[1,0].imag_part().simplify_trig()).factor())/sin(t) (-i*sigma_x*u[0]-i*sigma_y*u[1]-i*sigma_z*u[2]).factor()  for checking the expected result (exp(tX)=cos(t)Id+sin(t)X, X in su(2) and det(X)=1). It is surprising that the sage exp cannot perform it. 2018-08-22 17:29:20 +0200 answered a question su2 matrix exponentiation Thank you for your answer. I have added these sage commands ((G_exp.expand().simplify_full() - cos(t)*matrix.diagonal([1,1]))/sin(t)).expand().simplify_trig() ((G_exp[1,0].real_part().simplify_trig() + i* G_exp[1,0].imag_part().simplify_trig()).factor())/sin(t) (-i*sigma_x*u[0]-i*sigma_y*u[1]-i*sigma_z*u[2]).factor()  for checking the expected result (exp(tX)=cos(t)Id+sin(t)X). 2018-08-22 13:57:53 +0200 asked a question su2 matrix exponentiation Hi, does anyone know if sage math is able to successfully calculate exp(G) where G belongs to su(2) ? The sagemath commands are given below : var('phi theta', domain='real') u = vector([cos(phi)*sin(theta),sin(phi)*sin(theta),cos(theta)]) u.norm().simplify_trig() sigma_x = matrix([[0,1],[1,0]]) sigma_y = matrix([[0,-i],[i,0]]) sigma_z = matrix([[1,0],[0,-1]]) sigma_x, sigma_y, sigma_z var('t',domain='real') G = -i*t*(sigma_x*u[0]+sigma_y*u[1]+sigma_z*u[2]) G.trace(), (G.det()/t**2).simplify_full(), G.is_hermitian() exp(G)  exp(G) returns the following error code : TypeError: ECL says: Error executing code in Maxima: Unable to find the spectral representation Thank you for helping. Epi 2018-01-26 20:06:35 +0200 commented question integral(rho*sqrt(1/(-m*sin(u)^2 + 1)),(u,0,x)) gives a wrong answer rho is a constant integral(sqrt(1/(-m*sin(u)^2 + 1)),(u,0,x))  returns 2*x/m  2018-01-25 22:16:50 +0200 asked a question integral(rho*sqrt(1/(-m*sin(u)^2 + 1)),(u,0,x)) gives a wrong answer HI everybody, var('x u m') assume(x>0) assume(m>0) assume(m<1) integral(rho*sqrt(1/(-m*sin(u)^2 +1)),(u,0,x))  returns 2*rho*x/m  Expected answer is elliptic_f(x,m)  Does anyone know how to fix this ? Thank you. 2017-06-09 20:34:05 +0200 received badge ● Self-Learner (source) 2017-06-09 20:34:05 +0200 received badge ● Teacher (source) 2017-06-08 21:49:42 +0200 answered a question integrate x^3/(exp(x)-1) between 0 and infinity Before proceeding, I have installed the giac package 1.2.3.25 integral(x^3/(exp(x)-1),x,0,infinity, algorithm='giac') returns ValueError: Unknown algorithm: giac even after restarting SageMath What would you advice ? Thank you. 2017-06-08 19:56:33 +0200 asked a question integrate x^3/(exp(x)-1) between 0 and infinity If I type integrate(x^3/(exp(x)-1),x,0,infinity) I get -1/15pi^4 + limit(-1/4x^4 + x^3log(-e^x + 1) + 3x^2dilog(e^x) - 6xpolylog(3, e^x) + 6polylog(4, e^x), x, +Infinity, minus) The command numerical_integral(x^3/(exp(x)-1),0,infinity) gives 6.4939394075 I have two questions : How do I evaluate the limit ? The correct answer is pi^4/15(=6.49393940226683) : why SageMath does not give it with symbolic integration ? Thanks 2017-05-03 00:22:29 +0200 received badge ● Popular Question (source) 2017-02-27 16:16:59 +0200 received badge ● Popular Question (source) 2016-11-27 17:41:11 +0200 asked a question simplifying ( x^beta )^( (mu - Lambda) / ( mu -2)) * x ^ ( alpha - beta + 4) is not satisfactory The SageMath commands var('x alpha beta Lambda mu') f(x) = ( x^beta )^( (mu - Lambda) / ( mu -2)) * x ^ ( alpha - beta + 4) f(x).simplify()  donot give the correct answer which I would expect that is g(x) alpha_x = ((x*f.diff(x)/f).simplify_full()).factor() g(x) = x^alpha_x  Does anyone know why ? Here is what I would expect x^(-(Lambda*beta - alpha*mu + 2*alpha - 2*beta - 4*mu + 8)/(mu - 2))  Here is what SageMath answers :  x^(alpha - beta + 4)/(x^beta)^((Lambda - mu)/(mu - 2))  It does not mix the exponants of x in the numerator with those of x in the denominator. Thank you Philippe 2016-11-27 17:33:16 +0200 commented question simplifying ( x^beta )^( (mu - Lambda) / ( mu -2)) * x ^ ( alpha - beta + 4) This is what I would expect : x^(-(Lambda*beta - alpha*mu + 2*alpha - 2*beta - 4*mu + 8)/(mu - 2))  instead of x^(alpha - beta + 4)/(x^beta)^((Lambda - mu)/(mu - 2))  Thank you Philippe 2016-11-27 17:32:16 +0200 answered a question simplifying ( x^beta )^( (mu - Lambda) / ( mu -2)) * x ^ ( alpha - beta + 4) This is what I would expect : x^(-(Lambda*beta - alpha*mu + 2*alpha - 2*beta - 4*mu + 8)/(mu - 2))  instead of x^(alpha - beta + 4)/(x^beta)^((Lambda - mu)/(mu - 2))  Thank you Philippe 2016-11-27 14:30:06 +0200 asked a question simplifying ( x^beta )^( (mu - Lambda) / ( mu -2)) * x ^ ( alpha - beta + 4) the sage command var('x alpha beta Lambda mu') f(x) = ( x^beta )^( (mu - Lambda) / ( mu -2)) * x ^ ( alpha - beta + 4) f(x).simplify()  does not give the correct answer g(x) alpha_x = ((x*f.diff(x)/f).simplify_full()).factor() g(x) = x^alpha_x  does anyone know why ? thank you Philippe 2015-05-08 16:46:39 +0200 edited question unable to solve([x^2+y^2==4, (y-y0)^2+z^2==4], [x, y, z]) here is the script: x, y, z = var('x, y, z'); y0 = var('y0'); solve([x^2+y^2==4, (y-y0)^2+z^2==4], [x, y, z]); [x^2 + y^2 == 4, (y - y0)^2 + z^2 == 4]  but if: y0 = 0 solve([x^2+y^2==4, (y-y0)^2+z^2==4], [x, y, z]);  gives the expected answer: [[x == r1, y == -sqrt(-r1^2 + 4), z == r13, [x == r2, y == sqrt(-r2^2 + 4), z == r2, [x == r3, y == -sqrt(-r3^2 + 4), z == -r3], [x == r4, y == sqrt(-r4^2 + 4), z == -r4]]  With parameter y0, I would expect: [x = +- sqrt(4-u^2), y = u, z = +- sqrt(4-(u-y0)^2)]  Thank you for helping me. 2015-05-08 16:45:48 +0200 received badge ● Editor (source)