Ticket #419 (closed enhancement: fixed)
row reduction for matrices over multivariate polynomial rings
|Reported by:||malb||Owned by:||malb|
sage: P.<x,y> = PolynomialRing(GF(2),2) sage: A = Matrix(P,2,2,[1,x,x,x+1]); A [ 1 x] [ x x + 1]
A.echelon_form() returns the identity matrix because it computes the reduced echelon form over a fraction field and not over the polynomial ring. However, SINGULAR has a (educational == slow) rowred command to perform row reduction as far as this is possible over the polynomial ring. This behaviour is desired in several applications and thus it should be ported to SAGE.
In fact, I've got an implementation/port of this already (c.f. https://sage.math.washington.edu:8102/home/pub/35/) it just needs to be named and included with SAGE.