#1951: [with patch, needs review] reducation map modulo a number field prime
ideal
still not 100% done
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Reporter: was | Owner: was
Type: defect | Status: new
Priority: major | Milestone: sage-3.1.3
Component: number theory | Resolution:
Keywords: number field residue field reduction |
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Changes (by cremona):
* keywords: => number field residue field reduction
* summary: reducation map modulo a number field prime ideal still not
100% done => [with patch, needs review]
reducation map modulo a number field prime
ideal still not 100% done
Comment:
The patch fixes this, so that any element which is P-integral can be
reduced modulo P (non-P-integral elements will raise a ZeroDivisionError
with an explanation).
It took a long time to find out where to put the new code, since the
structure of the residue fields and reduction maps code is so byzantine!
In the end the solution was not hard, though I used a different method
from what was suggested (see comments in the patch).
The new code is in sage.rings.residue_field.pyx; I also put a doctest
into number_field.number_field_ideal.py.
By the way, it is not really necessary to use recursion since when the
function calls itself it always bottoms out right away. So it would be
easy to rewrite it without any; I just found it easier to write
{{{self(nx)}}} than {{{self.__F(self.__to_vs(nx) * self.__PBinv)}}} and
similar.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/1951#comment:1>
SAGE <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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