Let’s recall what is spaces of matrices of constant rank, that is, in spaces of matrices in which every nonzero matrix has the same rank. The case is, i’m reading journal by NIGEL BOSTON titled “SPACES OF CONSTANT RANK MATRICES OVER GF(2)”, the same with this question’s title. In the journal’s abstract, it said that, “for each n, we cconsider there exist an (n+1)- dimensional space of n by n matrices GF(2) in which nonzero matrix has rank n-1. Examples are given for n=3,4, and 5, together with evidence for the conjecture that none exist for n>8". The problem is, NIGEL BOSTON used MAGMA to show that there are exactly 1176 such spaces for n=3. And under conjugation by GL(3,2), these fall into 12 orbits. A basis for a representative of each orbit is given by:
I got task from my lecture to make simulation for it (using MAGMA), but we know that there is no trial/free version of MAGMA, so i remember about SAGE, is SAGE be able to do such thing? And if yes, how i do that (the code for SAGE), otherwise if not, is there another program similar to MAGMA (open source or free) and possible to do the simulation? Hope you help me, thanks you so much!
Note: this is link for the journal