Hello! I am very curious as to what algorithm Maple uses in Linear Solve. I have heard recently that some people do gaussian elimination (or maybe LU factorization) modulo some prime for exact arithmetic solvers and then reassmble the solution via Chinese Reminder theorem? I wonder if anyone has heard to this, or recommends this as a method for solving a system exactly?
I have a very special, very large and sparse matrix with only -1,0, and +1. I would love to solve this matrix exactly, but regretfully is too large for Maple (up in the millions by millions).
Would anyone have any references in literature for me in this area? Or perhaps maples LinearSolve uses a different exact-arithmetic algorithm?