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
