Hi!
Here are two independent Sage 4.1 sessions which demonstrate that the
construction of NumberField's is context dependent:
sage: K.<x> = CyclotomicField(5)[]
sage: W.<a> = NumberField(x^2 + 1)
sage: W
Number Field in a with defining polynomial x^2 + 1 over its base field
sage: W1 = NumberField(x^2+1,'a')
sage: K.<x> = CyclotomicField(5)[]
sage: W.<a> = NumberField(x^2 + 1)
sage: W
Number Field in a with defining polynomial x^2 + 1
In fact:
sage: W1 is W0
True
Related example, in a fresh Sage session:
sage: p = x^2 + 1
sage: K.<x> = CyclotomicField(5)[]
sage: q = x^2 + 1
sage: bool(p==q)
True
Personal analysis: p and q do not have the same ground field, but are
considered as equal, because p can be coerced into q. This confuses
the caching mechanism of NumberField.
Can anyone familiar with NumberField confirm?
Very personal interpretation: this is a strong argument for limiting
as much as possible the use of coercions in equality testing.
Cheers,
Nicolas
PS: This behavior appears with Sage 4.1, with or without the
Sage-Combinat patches applied. For some reason the tests for
number_field_rel trigger it in the first case, but not the second
one. William: what should I do about this? I don't want to wait for a
fix to release sagecombinat 4.1. Should I just ignore this? comment
out the tests?
--
Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/
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