#8327: Implement the universal cyclotomic field, using Zumbroich basis
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Reporter: nthiery | Owner:
Type: enhancement | Status:
needs_work
Priority: major | Milestone: sage-5.0
Component: number fields | Resolution:
Keywords: Cyclotomic field, Zumbroich basis | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Christian Stump, Simon King | Merged in:
Dependencies: #4539 #10771 #7980 | Stopgaps:
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Comment (by stumpc5):
Replying to [comment:99 davidloeffler]:
> See [http://www.sagemath.org/doc/reference/coercion.html#methods-to-
implement]. The magic routines here are
{{{ _coerce_map_from_ }}}
Thanks, I now see how I can do the coercion here - except that I do not
know how to handle non-standard embeddings. I do not know how to test if a
non-standard embedding is used, and if so, I also do not know how to
coerce then into the {{{UCF}}}.
{{{ _element_constructor_}}}
I want that an element of {{{UCF}}} is never constructed using the
{{{__call__}}} method but only using the function {{{E}}}. In the 4 steps
in http://www.sagemath.org/doc/reference/coercion.html#provided-methods
{{{__call__}}}, I want the first 3 to proceed, and if no coercion is
found, that an error is raised. The idea here is that {{{UCF}}} has an
infinite number of generators, and the easiest to play with them seems to
be the same way this is done in {{{GAP}}}; simply doing things like
{{{
sage: E(3)
E(3)
sage: E(3)+E(4)
E(12)^4 - E(12)^7 - E(12)^11
}}}
Also, I want to see
{{{
sage: UCF(5)
5
sage: UCF(5).parent()
Universal Cyclotomic Field endowed with the Zumbroich basis
sage: X = CyclotomicField(6)
sage: UCF(X.gen())
-E(3)^2
}}}
Is this generally wrong, or is the way I proposed to define
{{{_element_constructor_}}} in my last comment just not the way to do
that?
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8327#comment:100>
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