Dear Sage folks, For a number field K whose defining polynomial has a non-integral rational coefficient, factoring a polynomial with coefficients in K sometimes results in the following UserWarning:
SageMath version 8.8.beta1, Release Date: 2019-04-07 sage: K.<a> = NumberField(x^2 - 1/2) sage: R.<y> = PolynomialRing(K) sage: p = 11*a*y + 7 sage: p.factor() /sage/local/lib/python3.7/site-packages/sage/rings/number_field/number_field.py:1682: UserWarning: interpreting PARI polynomial 11 relative to the defining polynomial x^2 - 2 of the PARI number field % (x, self.pari_polynomial())) (11*a) * (y + 14/11*a) Oddly, I'm only seeing this error for linear polynomials in y, not things of higher degree: sage: q = p**2*y + p/3 + (a/5)*y^3 sage: prod(q.factor()) == q True The only reference in trac to this error message I could find is: https://trac.sagemath.org/ticket/22202 Indeed the doctest added in #22202 to show that this ticket is fixed fails if the defining polynomial of the number field is made non-integral: sage: y = QQ['y'].gen() sage: R = QQ.extension(y^2-1/2,'a')['x'] # was y^2 - 2 sage: R("a*x").factor() /sage/local/lib/python3.7/site-packages/sage/rings/number_field/number_field.py:1682: UserWarning: interpreting PARI polynomial 0 relative to the defining polynomial x^2 - 2 of the PARI number field % (x, self.pari_polynomial())) /sage/local/lib/python3.7/site-packages/sage/rings/number_field/number_field.py:1682: UserWarning: interpreting PARI polynomial 1 relative to the defining polynomial x^2 - 2 of the PARI number field % (x, self.pari_polynomial())) In all the instances I've seen, the polynomial being interpreted in the warning is a constant, meaning that the warning is harmless. I assume the issues is related to the fact that K.pari_polynomial() is not just K.absolute_polynomial(): sage: K.pari_polynomial() x^2 - 2 sage: K.absolute_polynomial() x^2 - 1/2 Best, Nathan -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
