On Wednesday 01 October 2008, Stephen Hartke wrote: > Hi! I have some questions about matrices and solving linear systems of > equations. These issues arose out of my using Sage for examples in my > Linear Optimization class (it's great for demonstrating how the simplex > algorithm works!) and for research I'm doing involving finite fields. > > If I have a matrix A defined over some finite field, and a vector b over > the same finite field, what's the easiest way to solve the equation Ax=b?
You can either use the "\" operator or the functions solve_left and solve_right: sage: A = random_matrix(GF(127),200,200) sage: x = random_matrix(GF(127),200,1) sage: A\x 200 x 1 dense matrix over Finite Field of size 127 sage: b = _ sage: A*b == x True sage: A.solve_left(transpose(x)) 1 x 200 dense matrix over Finite Field of size 127 sage: b = _ sage: b*A == transpose(x) True > Is there any easy way to augment A with b as an extra column? Is there an > easy way to insert a row or column? sage: A = random_matrix(GF(127),3,3) sage: A [76 36 72] [30 5 51] [29 58 49] sage: A.augment(random_matrix(GF(127),3,1)) [76 36 72 49] [30 5 51 45] [29 58 49 27] > Is there an easy way to delete a row or column? The same questions apply for > matrices over the rationals. sage: A.matrix_from_rows([0,2]) [76 36 72] [29 58 49] This API should be uniform across base rings. > The functions stack() and insert_row() are pretty useful, but they seem to > be only defined for matrices over the integers. AFAIK stack is available for all matrices: sage: A = random_matrix(GF(127),20,20) sage: A.stack(A) 40 x 20 dense matrix over Finite Field of size 127 sage: A = random_matrix(GF(2^4,'a'),20,20) sage: A.stack(A) 40 x 20 dense matrix over Finite Field in a of size 2^4 but insert_row is not. This could be an oversight. Cheers, Martin -- name: Martin Albrecht _pgp: http://pgp.mit.edu:11371/pks/lookup?op=get&search=0x8EF0DC99 _www: http://www.informatik.uni-bremen.de/~malb _jab: [EMAIL PROTECTED] --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
