#2789: [with patch, needs review] multivariate polynomials over residue fields
of
number fields are broken
-------------------------------------------------------------+--------------
Reporter: dmharvey | Owner:
malb
Type: defect | Status:
new
Priority: critical | Milestone:
sage-3.4.1
Component: commutative algebra | Resolution:
Keywords: residue field multivariate prime groebner basis |
-------------------------------------------------------------+--------------
Changes (by ncalexan):
* keywords: => residue field multivariate prime groebner basis
* owner: somebody => malb
* summary: multivariate polynomials over residue fields of number fields
are broken => [with patch, needs review]
multivariate polynomials over residue fields of
number fields are broken
* component: basic arithmetic => commutative algebra
* priority: major => critical
Comment:
This now works without major changes... but I found a show stopper bug.
It had to do with hashing "large" residue fields, meaning large
characteristic residue fields. The hash method tried to hash an ideal of
the residue field itself, which tried to hash its parent, leading to an
infinite loop.
This means that at no time has a residue field with cardinality a very
large prime been created in Sage!
I've added the obvious .ideal() method, tested the hashing and
construction for larger examples, and added doctests showing Groebner
basis computations.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/2789#comment:2>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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