#11770: Add ability to detect CM number fields and take complex conjugate of
their
elements
---------------------------------+------------------------------------------
Reporter: robharron | Owner: tba
Type: enhancement | Status: positive_review
Priority: minor | Milestone: sage-5.4
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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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'''
> 1. [attachment: trac_11770_CM_field_functionality_v2.2.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]
--
Comment (by fwclarke):
Replying to [comment:9 robharron]:
> Oops! There was another use of zeta.multiplicative_order() in the
complex_conjugation() function. I have now changed that in version 2.3. I
don't know how to change this back to needs_review...
Yes, I should have spotted this. The positive review can, of course, stay
(I think the way to "needs review" is via "needs work"). But I've altered
the description to refer to version 2.3.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11770#comment:10>
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