#8327: Implement the universal cyclotomic field, using Zumbroich basis
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Reporter: nthiery | Owner:
Type: enhancement | Status:
needs_review
Priority: major | Milestone: sage-5.6
Component: number fields | Resolution:
Keywords: Cyclotomic field, Zumbroich basis | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Christian Stump, Simon King | Merged in:
Dependencies: #13727, #13728 | Stopgaps:
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Comment (by chapoton):
A few more comments
* this import is apparently not used :
from sage.rings.complex_field import ComplexField
* the sort of elements is backwards compared to the order for cyclotomic
fields
{{{
sage: v=UCF.random_element(7);v
-5*E(7) - 4*E(7)^3 + 4*E(7)^4 + E(7)^5
sage: v.to_cyclotomic_field()
zeta7^5 + 4*zeta7^4 - 4*zeta7^3 - 5*zeta7
}}}
maybe it would be better to go the same way ? but maybe this is the same
as gap ?
* Is the is_subring method necessary ? it is almost empty !
* in the element constructor, maybe one could answer by something like
"no coercion found for elements of XXX"
with XXX the parent of the argument ? It would be more informative, no ?
* maybe zumbroich_basis should be called zumbroich_basis_indices ? I would
expect that something called zumbroich_basis would return elements of the
field, which is not really the case. Well, this is not that important..
* why is the hash function test tagged with random ? does it depend on the
computer or something like that ?
* in _invert_, one should rather raise a ZeroDivisionError when trying to
invert 0 ?
* more generally, maybe one could try to avoid using assert, and better
raise precise Exceptions ?
* I have not read seriously the cython part, but found a typo :
inverse for the univeral
That's all for today
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8327#comment:121>
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