#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: closed
Priority: minor | Milestone: sage-5.4
Component: number fields | Resolution: fixed
Keywords: CM field | Work issues:
Report Upstream: N/A | Reviewers: Francis Clarke
Authors: Robert Harron | Merged in: sage-5.4.beta0
Dependencies: | Stopgaps:
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Description changed by jdemeyer:
Old 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.
>
> Apply [trac_11770_CM_field_functionality_v2.3.patch] and
> [attachment:11770_long_time.patch]
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.
Apply [attachment:trac_11770_CM_field_functionality_v2.3.patch] and
[attachment:11770_long_time.patch]
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11770#comment:21>
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