#11770: Add ability to detect CM number fields and take complex conjugate of
their
elements
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Reporter: robharron | Owner: tba
Type: enhancement | Status: needs_review
Priority: minor | Milestone: sage-5.3
Component: number fields | Resolution:
Keywords: CM field | Work issues:
Report Upstream: N/A | Reviewers: Francis Clarke
Authors: Robert Harron | Merged in:
Dependencies: | Stopgaps:
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Changes (by robharron):
* status: needs_work => needs_review
Old description:
> This ticket adds a function to the NumberField class that checks if self
> is a CM field, and adds a function to the NumberFieldElement class giving
> the ability to compute the complex conjugate of an element in a totally
> real or CM field.
New description:
This ticket adds 3 functions to the NumberField class, 1 function to the
RelativeNumberField class, and modifies 1 function of the
NumberFieldElement class. For number fields, there's now a function that
checks if self is a CM field, a function that returns the complex
conjugation map of self (if self is contained in a CM field), and a
function that finds the maximal totally real subfield of self. In the
relative case, there's a function that checks if self is a CM extension.
Finally, the conjugate function of NumberFieldElement is enhanced giving
it the ability to compute the complex conjugate of any element in any
totally real or CM field.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11770#comment:3>
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