#1951: [with patch, needs review] reducation map modulo a number field prime
ideal
still not 100% done
--------------------------------------------------+-------------------------
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 |
--------------------------------------------------+-------------------------
Comment (by cremona):
It's a small thing but I just noticed that the number field function
residue_field() has this definition:
{{{
def residue_field(self, prime, names = None, check = False):
}}}
where the "check" parameter claims to control whether "prime" really is
prime, but this is ignored. It should be passed down through the call to
{{{sage.rings.residue_field.ResidueField(prime, names = names)}}}
which does honour the check parameter.
Example:
{{{
sage: K.<i> = NumberField(x^2 + 1)
sage: Q = K.ideal(5)
sage: Q.is_prime()
False
sage: K.residue_field(Q, check=False)
---------------------------------------------------------------------------
ValueError Traceback (most recent call
last)
/home/john/sage-3.1.2.rc1/devel/<ipython console> in <module>()
/home/john/sage-3.1.2.rc1/local/lib/python2.5/site-
packages/sage/rings/number_field/number_field.py in residue_field(self,
prime, names, check)
3000 raise ValueError, "prime must be a prime ideal of
self"
3001 import sage.rings.residue_field
-> 3002 return sage.rings.residue_field.ResidueField(prime, names
= names)
3003
3004 def signature(self):
/home/john/sage-3.1.2.rc1/devel/residue_field.pyx in
sage.rings.residue_field.ResidueField (sage/rings/residue_field.c:2778)()
ValueError: p must be prime
}}}
The second patch fixes this. Note that the default was "check=False",
while the called function ResidueField() has its default as "check=True".
I thought it safer to change the deafult to "check=True" since this makes
the new default behaviour like the old behaviour. (If you use check=False
and the ideal is not prime, the first error which arises is a bit obscure:
{{{
AttributeError: 'NumberFieldFractionalIdeal' object has no attribute
'_NumberFieldIdeal__smallest_integer'
}}}
since smallest_integer() is defined only for prime ideals. But something
has to go wrong at some point in this situation, and at least now it will
only happen when the user has deliberately turned off checking.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/1951#comment:2>
SAGE <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
--~--~---------~--~----~------------~-------~--~----~
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To post to this group, send email to [email protected]
To unsubscribe from this group, send email to [EMAIL PROTECTED]
For more options, visit this group at
http://groups.google.com/group/sage-trac?hl=en
-~----------~----~----~----~------~----~------~--~---
