#2420: Extending the gap interface to uni- and multivariate polynomial rings
over
number fields
---------------------------+------------------------------------------------
Reporter: SimonKing | Owner: SimonKing
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.7.1
Component: interfaces | Keywords: gap interface, polynomial rings,
number fields, interface cache
Work_issues: | Upstream: N/A
Reviewer: | Author: Simon King
Merged: | Dependencies:
---------------------------+------------------------------------------------
Changes (by SimonKing):
* dependencies: #8909, #9423 =>
Old description:
> Up to now, the gap interface did not work on polynomial rings over number
> fields. This patch extends the interface accordingly, so that now the
> following works.
> Univariate:
> {{{
> sage: F=CyclotomicField(8)
> sage: R=PolynomialRing(F,'x')
> sage: gap(R)
> PolynomialRing( <algebraic extension over the Rationals of degree 4>,
> ["x"] )
> sage: p=R('zeta8^2*x+zeta8')
> sage: gap(p)^3
> ((-1*zeta8^2))*x^3+((-3*zeta8))*x^2+(!-3)*x+(zeta8^3)
> sage: p^3
> (-zeta8^2)*x^3 + (-3*zeta8)*x^2 + (-3)*x + zeta8^3
> }}}
>
> Multivariate:
> {{{
> sage: R=PolynomialRing(F,'x,y')
> sage: gap(R)
> PolynomialRing( <algebraic extension over the Rationals of degree
> 4>, ["x", "y"] )
> sage: p=R('zeta8*x+zeta8^2*y')^2
> sage: gap(p)
> (zeta8^2)*x^2+(2*zeta8^3)*x*y-y^2
> sage: p
> zeta8^2*x^2 + 2*zeta8^3*x*y + (-1)*y^2
> }}}
>
> The patches also provide doc tests.
>
> However, there is one problem: On my machine, the doc tests of
> sage.rings.polynomial.polynomial_element.pyx trigger the bug reported in
> #2419.
> That bug seems to occur only on few machines (up to now, only one other
> person can reproduce #2419).
>
> So, there should be discussion how to deal with that issue.
New description:
Up to now, the gap interface did not work on polynomial rings over number
fields. This patch extends the interface accordingly, so that now the
following works.
Univariate:
{{{
sage: F=CyclotomicField(8)
sage: R=PolynomialRing(F,'x')
sage: gap(R)
PolynomialRing( <algebraic extension over the Rationals of degree 4>,
["x"] )
sage: p=R('zeta8^2*x+zeta8')
sage: gap(p)^3
((-1*zeta8^2))*x^3+((-3*zeta8))*x^2+(!-3)*x+(zeta8^3)
sage: p^3
(-zeta8^2)*x^3 + (-3*zeta8)*x^2 + (-3)*x + zeta8^3
}}}
Multivariate:
{{{
sage: R=PolynomialRing(F,'x,y')
sage: gap(R)
PolynomialRing( <algebraic extension over the Rationals of degree
4>, ["x", "y"] )
sage: p=R('zeta8*x+zeta8^2*y')^2
sage: gap(p)
(zeta8^2)*x^2+(2*zeta8^3)*x*y-y^2
sage: p
zeta8^2*x^2 + 2*zeta8^3*x*y + (-1)*y^2
}}}
The patches also provide doc tests.
However, there is one problem: On my machine, the doc tests of
sage.rings.polynomial.polynomial_element.pyx trigger the bug reported in
#2419.
That bug seems to occur only on few machines (up to now, only one other
person can reproduce #2419).
So, there should be discussion how to deal with that issue.
Apply [attachment:trac2420_gap_interface_polynomials.patch]
--
Comment:
I have rebased the patch, so that it should work on top of sage-4.7.rc2. I
haven't run tests, though.
For the patchbot:
Apply trac2420_gap_interface_polynomials.patch
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/2420#comment:14>
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