Thank you so much for the prompt and helpful reply Dmitrii! Much appreciated.
Best, Boyan On Saturday, October 19, 2019 at 4:53:32 AM UTC-4, [email protected] wrote: > > On Fri, Oct 18, 2019 at 09:09:01PM -0700, Boyan Kostadinov wrote: > > I want to get the transformation matrix from the echelon form reduction > > over finite fields but I found in the SageMath documentation the > following > > statement: > > > > *The matrix library used for Z/pZ/p-matrices does not return the > > transformation matrix, so the transformation option is ignored* > > > > Link: > > > http://doc.sagemath.org/html/en/reference/matrices/sage/matrix/matrix2.html#sage.matrix.matrix2.Matrix.echelon_form > > > > > > > More specifically, the call: *M.echelon_form(transformation=True**) > *does > > not return the transformation matrix T when M is over a finite field, > only > > the echelon matrix E; T is such that we have T*M=E, so T is just the > > product of the elementary matrices, which perform the reducing row > > operations. > > > > Is there any workaround to get the transformation matrix T over a finite > > field? Can I get the transformation matrix T over ZZ and then reduce it > > over the finite field? > > Yes, this should work (with a loss in efficiency, which can be > substantial on large matrices). Anyway, this is how to do this. > > sage: MS = MatrixSpace(GF(19),2,3) > ....: C = MS.matrix([1,2,3,4,5,6]) > ....: E,T = map(lambda t: matrix(GF(19),t), > matrix(ZZ,C).echelon_form(transformation=True)) > ....: T*C == E > ....: E in MS > ....: > True > True > > --------------------------------------------------------------- > > HTH > Dmitrii > > > > Any advice would be much appreciated. > > > > -- > > You received this message because you are subscribed to the Google > Groups "sage-support" group. > > To unsubscribe from this group and stop receiving emails from it, send > an email to [email protected] <javascript:>. > > To view this discussion on the web visit > https://groups.google.com/d/msgid/sage-support/2e5a18f6-d022-4d67-ae09-c7825e5abb4c%40googlegroups.com. > > > > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-support/78c8fb51-6495-4920-ba0a-97f4052eb093%40googlegroups.com.
