2021-11-26 04:09:44 +0100 received badge ● Popular Question (source) 2021-02-15 01:48:38 +0100 received badge ● Famous Question (source) 2020-08-05 13:56:27 +0100 received badge ● Popular Question (source) 2019-06-26 12:21:03 +0100 asked a question Compute the square root of a complex matrix Hello, I can't find how to compute the square root of a complex matrix... I tried m.sqrt(), sqrt(m) (display only symbolic sqrt), sqrt(m).n()... None of them work. What is the regular way to compute the root of a complex matrix? (you can assume the matrix is self-adjoint if needed). Thanks! def test(): phi = matrix(CC, [[1/sqrt(2)],[i]]) m = phi * phi.C.T print("Matrix: {}".format(m)) s = sqrt(m).n() # Does not work: AttributeError: 'ComplexField_class_with_category' object has no attribute 'complex_field' #s = m^(1/2) # Does not work either, NotImplementedError: non-integral exponents not supported # s = m.sqrt() # Does not work either, no attribute sqrt print("Sqrt: {}".format(s)) print("s*s: {}".format(s*s)) if s*s == m: print("Ok") else: print("Nope :(")  EDIT: For now I'm using the numpy backend with manual diagonalisation, but I'd like to know if there is a better way to proceed...  phi = matrix(CDF, [[1/sqrt(2)],[i]]) D, P = m.eigenmatrix_right() s = P*diagonal_matrix([sqrt(x) for x in D.diagonal()])*P^-1  2018-05-22 04:11:21 +0100 received badge ● Notable Question (source) 2018-04-16 09:57:45 +0100 asked a question Square root of polynomial modulo another irreducible polynomial Hello, If I'm not wrong, it is always possible to compute the square root of a polynomial $P$ modulo an irreducible polynomial $g$ when the base field is in $GF(2^m)$, i.e. find $Q \in GF(2^m)$ such that $Q^2 \equiv P \mod g$. Indeed, the operation $Q \rightarrow Q^2 \pmod g$ should be linear (because we are in $GF(2^m)$) so an idea would be to compute the matrix $T$ that perform this operation, and then invert it, but I'd like to find an embedded operation in sage. I tried the sagemath $P.sqrt()$ method, but the problem is that because it does not take into account the modulo, it fails most of the time when the polynomial has some terms with odd power of $X$. Any idea? Thanks! 2018-04-16 09:46:43 +0100 received badge ● Scholar (source) 2018-04-16 09:46:40 +0100 received badge ● Supporter (source) 2018-04-16 09:46:37 +0100 commented answer Map a matrix to a block matrix Ok, thank you for your help ! 2018-04-11 00:15:48 +0100 asked a question Map a matrix to a block matrix Hello, I have a function that maps an element $x$ into a $1\times n$ matrix, say for example $[x,x,x]$. I would like to map this function to a matrix and consider the resulting matrix as a "block matrix". E.g: change matrix([[1,2],[3,4]]) into matrix([[1,1,1,2,2,2],[3,3,3,4,4,4]]). For now, I use a trick that basically converts back the matrix to a a list using something like: block_matrix([[f(elt) for elt in row] for row in M.rows()])  but it looks quite dirty so I would like to know if there are some better way to proceed. Thank you! 2016-07-26 21:14:24 +0100 received badge ● Popular Question (source) 2013-06-11 09:15:52 +0100 received badge ● Student (source) 2013-06-10 17:19:31 +0100 received badge ● Editor (source) 2013-06-10 17:02:53 +0100 asked a question Choose the viewpoint in plot3d Hello, I would like to display lots of spheres (about 6000) in jmol but when I've to many points it crashs. If I try to run the interactive mode (even If don't have any picture) I've this error : "Jmol Applet #2 is having trouble loading. Will retry once." How could I do to get a picture of my work ? --- EDIT --- I found the function save('filename') and now I've a display, but I'd like to change the point of view. Is it possible ? Thanks, Tobias.