malb's profile - activity

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2011-11-10 12:36:58 +0200	answered a question	Row echelon form of a matrix containing symbolic expresssions `sage: P.<b1,b2,b3> = QQ[] sage: A = Matrix(P, 3, 4, [[1,1,2,b1], [1,0,1,b2], [2,1,3,b3]]) sage: A [ 1 1 2 b1] [ 1 0 1 b2] [ 2 1 3 b3] sage: A.echelon_form('row_reduction') [ 1 0 1 b2] [ 0 1 1 b1 - b2] [ 0 0 0 -b1 - b2 + b3]`
2011-10-13 14:35:59 +0200	answered a question	Solve large system of linear equations over GF(2) Hi, 20,000 x 20,000 is not large and you should be able to do it in a few seconds on a modern CPU: `http://m4ri.sagemath.org/performance.html` However, Sage doesn't expose the fast code we have for this in M4RI:, cf. `http://m4ri.sagemath.org/doxygen/solve_8h.html` That's why it's not as fast as it should be. Sorry, we should fix this.
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2011-01-13 11:27:31 +0200	answered a question	Quotient decomposition by Groebner basis Do you mean this? `sage: R.<x,y,z> = GF(127)[] sage: p = R.random_element(degree=3) sage: Q = [R.random_element() for _ in range(R.ngens())] sage: r = p.reduce(Ideal(Q)) sage: M = (p - r).lift(Q) sage: p -r == sum([M[i]*Q[i] for i in range(len(M))]) True`