Hi Daniel, On 10 Dez., 00:17, Daniel Starin <dsta...@gmail.com> wrote: > Hi all, > > How can I use sage to generate a random rxr matrix over F_q (q is a > prime power) with determinant 1?
First, create the group of all matrices with determinant 1 (in the example, q is 9 and r is 5) sage: G = SL(5, GF(9,'z')) Then, you can create random elements in the same way as for any other object with elements (if it's implemented): sage: G.random_element() [ 0 1 z + 1 2 2] [2*z + 1 2*z + 2 z 2*z + 2 2] [2*z + 1 z + 1 2 z + 2 2*z + 2] [ z z z + 2 0 2*z + 1] [ 1 2*z + 2 2 z 2*z + 1] sage: G.random_element() [2*z + 2 2*z + 1 0 z + 2 z + 2] [ 2*z 0 2*z + 2 z + 2 2] [ 0 2*z + 1 2*z 1 z] [ z + 1 2*z z + 2 z + 1 z] [ z + 2 2*z + 2 2*z + 1 2*z + 2 z + 2] Note that the return value is not a matrix, but an element of the group G. It is easy to obtain the matrix, though: sage: type(G.random_element()) <class 'sage.groups.matrix_gps.matrix_group_element.SpecialLinearGroup_finite_field_with_category.element_class'> sage: type(G.random_element().matrix()) <type 'sage.matrix.matrix_generic_dense.Matrix_generic_dense'> Just to be on the safe side, verify that the determinant of the matrices is 1: sage: G.random_element().matrix().determinant() 1 sage: G.random_element().matrix().determinant() 1 Cheers, 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
