UserWarning when factoring polys over NumberFields

[NathanDunfield]

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)

This is related to #22202 and see https://groups.google.com/forum/#!topic/sage-devel/-4B4322qI9M for further discussion.

CC: @videlec @jdemeyer @unhyperbolic @culler

Component: number fields

Author: Nathan Dunfield

Branch/Commit: 5b89a97

Reviewer: Matthias Goerner

Issue created by migration from https://trac.sagemath.org/ticket/27765

[NathanDunfield]

comment:1

I think I have a reasonable solution to this: _element_constructor_ shouldn't raise the warning if the polynomial it's given is constant since that case is unambiguous. Writing patch now...

[NathanDunfield]

New commits:

d064855

NumberField._element_constructor_: when given a constant PARI t_POL, there's no ambiguity and hence no need to warn the user

[NathanDunfield]

Commit: d064855

[NathanDunfield]

Branch: u/dunfield/nf_warning

[NathanDunfield]

comment:3

Ok, I think that does it.

[unhyperbolic]

comment:4

Thanks!

[unhyperbolic]

comment:5

I am so sorry for re-opening this. But I was just playing around some more with pari and discovered the following:

>>> (pari('y^4')+pari('x^2')-pari('x^2')).poldegree()
0
>>> (pari('y^4')+pari('x^2')-pari('x^2'))[0]
y^4

I am not sure how much of a corner case this is and that there is actually additional work necessary. But I definitively want to think this over before giving it a positive review.

[embray]

comment:6

Tickets still needing working or clarification should be moved to the next release milestone at the soonest (please feel free to revert if you think the ticket is close to being resolved).

[NathanDunfield]

comment:7

Replying to @unhyperbolic:

I am so sorry for re-opening this. But I was just playing around some more with pari and discovered the following:

Hmm, Pari's handling of multivariable polynomials is pretty idiosyncratic:

sage: p = pari('x^2 + y^4')
sage: q = pari('x^2')
sage: p.variables(), q.variables()
([x, y], [x])
sage: a = p - p + 1
sage: a, a.poldegree(), a.variables()
(1, 0, [x])
sage: b = q - q
sage: b, b.poldegree(), b.variables()
(0, -9223372036854775807, [x])
sage: c = p - q
sage: c, c.poldegree(), c.variables()
(y^4, 0, [x, y])
sage: pari('z - z').variables()
[z]
sage: pari('z + x - z - x').variables()
[x]

I think the following is a better test for being constant:

sage: def degrees(poly): return [poly.poldegree(v) for v in poly.variables()]
sage: degrees(a)
[0]
sage: degrees(b)
[-9223372036854775807]
sage: degrees(c)
[0, 4]
sage: def is_const(poly): 
          return all(poly.poldegree(v) <= 0 for v in poly.variables())
sage: [is_const(x) for x in [a, b, c, p, q]]
[True, True, False, False, False]

I will update my branch along these lines.

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

f63c289	Merge branch 'master' into t/27765/nf_warning
5b89a97	Improved test for constant polynomial.

[sagetrac-git]

Changed commit from d064855 to 5b89a97

[unhyperbolic]

comment:10

Thanks!

[NathanDunfield]

Reviewer: Matthias Goerner

[vbraun]

Changed branch from u/dunfield/nf_warning to 5b89a97