It should not be difficult to convert the power series over GF(p) to pari. If you do
sage: R.<x>=PowerSeriesRing(GF(5),"x") sage: f = x^2+1 and then sage: f._pari_?? you will see the comment that converson of power series from Sage to pari is currently only implemented over QQ and ZZ. And that implementation is rather crude, as it goes via the string representation. It would be better to be able to convert power series over any ring which itself can be converted. John Cremona 2008/10/28 salmanhb <[EMAIL PROTECTED]>: > > > Hi, > > I've got a (truncated) matrix over a power series ring over a finite > field that I want to convert to a GP matrix so that I can take its > kernel. Since the matrix is truncated, it can be viewed as just being > over a univariate polynomial ring. I want to take its kernel, but the > echelon form over a univariate polynomial ring over a finite field is > not yet implemented. I knew GP can do this, so I was going to send the > matrix to GP and have GP compute the kernel. But if I send the matrix > as a matrix over the power series ring, the coefficients are not sent > as being over a finite field. On the other hand, if I redefine the > matrix over the polynomial ring, the coefficients are treated as being > over a finite field. I could reconstruct all of my matrices as being > over the polynomial ring once I truncate my series, but that seems > like a silly hack -- GP understands power series rings over a finite > field, so the conversion shouldn't be a problem. I'm running SAGE > v3.0.2. > > Thanks, > Salman > > Here is the code and output: > > sage: R.<x>=PowerSeriesRing(GF(5),"x") > sage: m=matrix(R,2,[2+x, 1+x, 2+3*x,1+2*x]) > sage: m.kernel() > --------------------------------------------------------------------------- > NotImplementedError Traceback (most recent call > last) > > /Users/salmanhb/Documents/work/research/computations/sage/<ipython > console> in <module>() > > /Users/salmanhb/Documents/work/research/computations/sage/matrix2.pyx > in sage.matrix.matrix2.Matrix.left_kernel (sage/matrix/matrix2.c:7985) > () > > /Users/salmanhb/Documents/work/research/computations/sage/matrix2.pyx > in sage.matrix.matrix2.Matrix.echelon_form (sage/matrix/matrix2.c: > 15292)() > > /Users/salmanhb/Documents/work/research/computations/sage/matrix2.pyx > in sage.matrix.matrix2.Matrix.echelonize (sage/matrix/matrix2.c:15092) > () > > /Users/salmanhb/Documents/work/research/computations/sage/matrix2.pyx > in sage.matrix.matrix2.Matrix._echelonize_ring (sage/matrix/matrix2.c: > 14807)() > > NotImplementedError: echelon form over Power Series Ring in x over > Finite Field of size 5 not yet implemented > sage: gp(m) > [x + 2, x + 1; 3*x + 2, 2*x + 1] > sage: R.<x>=PolynomialRing(GF(5),"x") > sage: m=matrix(R,2,[2+x, 1+x, 2+3*x,1+2*x]) > sage: m.kernel() > --------------------------------------------------------------------------- > NotImplementedError Traceback (most recent call > last) > > /Users/salmanhb/Documents/work/research/computations/sage/<ipython > console> in <module>() > > /Users/salmanhb/Documents/work/research/computations/sage/matrix2.pyx > in sage.matrix.matrix2.Matrix.left_kernel (sage/matrix/matrix2.c:7985) > () > > /Users/salmanhb/Documents/work/research/computations/sage/matrix2.pyx > in sage.matrix.matrix2.Matrix.echelon_form (sage/matrix/matrix2.c: > 15292)() > > /Users/salmanhb/Documents/work/research/computations/sage/matrix2.pyx > in sage.matrix.matrix2.Matrix.echelonize (sage/matrix/matrix2.c:15092) > () > > /Users/salmanhb/Documents/work/research/computations/sage/matrix2.pyx > in sage.matrix.matrix2.Matrix._echelonize_ring (sage/matrix/matrix2.c: > 14807)() > > NotImplementedError: echelon form over Univariate Polynomial Ring in x > over Finite Field of size 5 not yet implemented > sage: gp(m) > [Mod(1, 5)*x + Mod(2, 5), Mod(1, 5)*x + Mod(1, 5); Mod(3, 5)*x + > Mod(2, 5), Mod(2, 5)*x + Mod(1, 5)] > > > --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
