#5618: Cyclotomic field elements are not converted to Gap correctly
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Reporter: saliola | Owner: tbd
Type: defect | Status: needs_review
Priority: major | Milestone: sage-4.5
Component: algebra | Keywords: gap interface cyclotomic field
Author: Simon King | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Changes (by newvalueoldvalue):
* keywords: => gap interface cyclotomic field
* status: new => needs_review
* author: => Simon King
Comment:
I created the patch after the patches from #8909 and #9423 -- so, it is
possible that the new patch actually depends on the two other tickets (but
one of them already has a positive review).
With the patch, a cyclotomic field in Sage is represented as a cyclotomic
field (and not as a number field) in GAP:
{{{
sage: Z = CyclotomicField(8)
sage: gap(Z)
CF(8)
sage: Z(gap(Z.0^2))
zeta8^2
}}}
The advantage is that the motivating example from the ticket description
now works (and is used as a doctest):
{{{
sage: H = AlternatingGroup(4)
sage: g = H.list()[1]
sage: K = H.subgroup([g])
sage: z = CyclotomicField(3).an_element(); z
sage: c = K.character([1,z,z**2]); c
Character of Subgroup of AlternatingGroup(4) generated by [(2,3,4)]
sage: c(g^2); z^2
-zeta3 - 1
-zeta3 - 1
}}}
The disadvantage: While it is still possible to chose the name of a number
field generator in GAP as in Sage
{{{
sage: K.<tau> = NumberField(x^2+x+1)
sage: gap(K)
<algebraic extension over the Rationals of degree 3>
sage: K.0
tau
sage: gap(K.0)
tau
}}}
it is now impossible to do the same for cyclotomic fields:
{{{
sage: L.<zeta> = CyclotomicField(3)
sage: L.0
zeta
sage: gap(L.0)
E(3)
}}}
By consequence, I had to fix a couple of doctests. All doctests pass, but
I can not vouch for external code.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5618#comment:3>
Sage <http://www.sagemath.org>
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