2019-09-14 01:21:58 -0500 received badge ● Popular Question (source) 2019-07-22 09:15:08 -0500 received badge ● Taxonomist 2018-09-11 15:50:10 -0500 received badge ● Popular Question (source) 2014-06-29 04:57:50 -0500 received badge ● Popular Question (source) 2014-06-29 04:57:50 -0500 received badge ● Notable Question (source) 2012-11-06 07:59:59 -0500 received badge ● Good Question (source) 2012-11-06 07:26:15 -0500 received badge ● Nice Question (source) 2012-03-25 02:00:29 -0500 received badge ● Nice Question (source) 2012-01-26 01:32:53 -0500 marked best answer Finding short vectors kernel Just write M.LLL() instead of M.lll() 2012-01-18 23:20:02 -0500 received badge ● Scholar (source) 2012-01-18 23:20:02 -0500 marked best answer Explicit representation of element of ideal I think you want the .lift() method: sage: P.=PolynomialRing(QQ,4) sage: C1= 17*x^2 + 7*y^2 - 26*y*z + 7*z^2 sage: C2= 13*y^2 - 7*y*z + 13*z^2 - 51*t^2 sage: f = x^4+y^4+z^4-18*t^4 sage: sage: f in ideal(C1,C2) True sage: sage: CI = ideal(C1, C2) sage: coords = f.lift(CI) sage: coords [1/17*x^2 + 1/13*y*z - 21/221*t^2, -7/221*x^2 + 1/13*y^2 + 1/13*z^2 + 6/17*t^2] sage: rebuilt = sum(coord*base for coord, base in zip(coords, [C1, C2])) sage: rebuilt x^4 + y^4 + z^4 - 18*t^4 sage: f == rebuilt True  2012-01-17 14:42:40 -0500 received badge ● Student (source) 2012-01-17 12:40:59 -0500 asked a question Explicit representation of element of ideal P.=PolynomialRing(QQ,4) C1= 17*x^2 + 7*y^2 - 26*y*z + 7*z^2 C2= 13*y^2 - 7*y*z + 13*z^2 - 51*t^2 x^4+y^4+z^4-18*t^4 in ideal(C1,C2)  So there exist \alpha, \beta in P with \alpha C1 + \beta C2 = x^4+y^4+z^4-18*t^4 What's the command to find \alpha and \beta explicitly ? 2012-01-17 00:03:41 -0500 commented answer Finding short vectors kernel Ah yes, thanks! 2012-01-17 00:01:29 -0500 received badge ● Supporter (source) 2012-01-16 23:59:06 -0500 asked a question memory leak when doing lots of ideal tests I'm trying to find elliptic curves lying on a quartic surface; there are probably clever ways to do this, but at the moment I am finding lots of quadrics through an integer point on the surface, then iterating over pairs of them and checking x^4+y^4+z^4-67*t^4 in ideal(f1,f2) This leaks about 2MB memory per second, presumably because the Groebner bases for the ideals are being cached; is there a way to tell sage not to cache them? 2012-01-13 10:39:28 -0500 asked a question Finding short vectors kernel I am looking for quadratic forms with a given point - so I want short integer vectors which are perpendicular to v=[X*X,X*Y,X*Z,X*T,Y*Y,Y*Z,Y*T,Z*Z,Z*T,T*T]  for (in this case) [X,Y,Z,T]=[4423,7583,8765,3459] This sounds like a problem with LLL written all over it, so I do  L=[[Y,-X,0,0,0,0,0,0,0,0],[0,Z,-Y,0,0,0,0,0,0,0],[0,0,T,-Z,0,0,0,0,0,0],[0,0,0,Y*Y,-X*T,0,0,0,0,0],[0,0,0,0,Z,-Y,0,0,0,0], [0,0,0,0,0,T,-Z,0,0,0],[0,0,0,0,0,0,Z*Z,-Y*T,0,0],[0,0,0,0,0,0,0,T,-Z,0],[0,0,0,0,0,0,0,0,T,-Z]] M=matrix(L) M.lll()  but this gives an error message AttributeError: 'sage.matrix.matrix_integer_dense.Matrix_integer_dense' object has no attribute 'lll'