#7596: QQ.number_field() does not behave like any other NumberField
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Reporter: rlm | Owner: davidloeffler
Type: defect | Status: new
Priority: major | Milestone: sage-4.6.2
Component: number fields | Keywords:
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Description changed by jdemeyer:
Old description:
> Here's an example:
>
> {{{
> sage: K.<a> = NumberField(x)
> sage: K.ideal(5)
> Fractional ideal (5)
> sage: QQ.ideal(5)
> Principal ideal (1) of Rational Field
> sage: QQ.number_field().ideal(5)
> Principal ideal (1) of Rational Field
> }}}
New description:
Several examples:
{{{
sage: K.<a> = NumberField(x)
sage: K.ideal(5)
Fractional ideal (5)
sage: QQ.ideal(5)
Principal ideal (1) of Rational Field
sage: QQ.number_field().ideal(5)
Principal ideal (1) of Rational Field
}}}
{{{
K = QQ
I = K.ideal(7)
}}}
This creates ideal that does not have the functions I.denominator,
I.numerator, I.prime_ideals() ... which a fractional ideal in a number
field should have
{{{
K.<a> = NumberField(x^2+2)
I = K.ideal(7)
}}}
Similarly, QQ.places() is not implemented; it should return the one
infinite place for Q. Although there seems to be QQ.embeddings().
{{{
QQ.places()
}}}
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7596#comment:4>
Sage <http://www.sagemath.org>
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