Hi Juan, On 13 Okt., 07:08, juaninf <juan...@gmail.com> wrote: > I want implement a efficient linear solve system over GF(2) (and too > parallel if this is posible), i reading this article, but i dont > understand > > http://ask.sagemath.org/question/467/solve-large-system-of-linear-equ...
It very much depends on what you mean by "solve". From the small bits that you tell, I deduce that you are *not* dealing with (linear) differential equations, right? Am I right in guessing that your problem is as follows: You have a matrix A, and you look for vectors v such that A*v is the zero vector. If this is the case, then I really don't see why one should use boolean polynomial rings. They would be the right tool if you look for solutions in GF(2) of POLYNOMIAL (not linear) equations. Sage is actually quite good at linear algebra over GF(2), thanks to the underlying implementation in M4RI. I am doing some random 10x10 matrix. One way to get all solutions for A*v==0 is this: sage: MS = MatrixSpace(GF(2),10,10) sage: A = MS.random_element() sage: K = A.right_kernel_matrix() sage: K [0 0 0 1 0 1 1 1 1 1] I am afraid it is not a vector but a matrix. But in general, the rows of K will span the space of solutions. For verifying it, we multiply with the transpose of K: sage: A*K.transpose() [0] [0] [0] [0] [0] [0] [0] [0] [0] [0] Of course, there is a different method that returns solutions of v*A==0. Best regards, Simon -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
