The empty matrix is NOT the Sylvester matrix of (0,0), (0,1) or (1,0). The degree of the zero polynomial is usually taken to be -infinity, though Sage uses -1 for some reason. In either case, the Sylvester matrix needs to have negative dimensions.
That is to say, return a ValueError in these cases. On Thu, Nov 11, 2010 at 9:32 AM, luisfe <lftab...@yahoo.es> wrote: > Hi, > > I am trying to write a procedure for univariate and multivariate > polynomial rings that computes the Sylvester matrix of two > polynomials. But I have a problem with corner cases. > > I am not sure what the method should resurn in the cases > > poly1, poly2 = 0, 1 > poly1, poly2 = 1, 0 > poly1, poly2 = 0, 0 > > For two constant polynomials, the method returns the empty matrix [ ], > whose determinant is 1. This equals the resultant of two constant > nonzero polynomials, so it is fine. > > If one (or both) of the constants is zero the resultant will be zero > which does not equal the determinant of the empty matrix. > > So, I see two posibilities: > > 1) In the three above cases, raise a ValueError indicating that in > this case the Sylvester matrix is not defined. > > 2) return the empty matrix and add in the documentation that in these > cases the determinant of the Sylvester matrix is NOT the resultant. > Maybe raise a warning in the code. > > I have not found a Sylvester matrix method in Maxima nor in Singular, > that might help to check what they do. I have checked maple and it > follows option 2. Return the empty matrix, even if in that case the > determinant is not the resultant. > > Any opinion about this case? > > -- > To post to this group, send an email to sage-devel@googlegroups.com > To unsubscribe from this group, send an email to > sage-devel+unsubscr...@googlegroups.com > For more options, visit this group at > http://groups.google.com/group/sage-devel > URL: http://www.sagemath.org > -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
