#5566: [with patch, needs review] Symmetric Groebner bases and Infinitely
Generated Polynomial Rings
---------------------------------+------------------------------------------
Reporter: SimonKing | Owner: SimonKing
Type: enhancement | Status: new
Priority: major | Milestone: sage-4.0
Component: commutative algebra | Keywords: Symmetric Ideal
---------------------------------+------------------------------------------
Comment(by SimonKing):
Dear Martin,
I am very sorry, but I found one bug. Since the ticket is not yet closed,
I allowed myself to add yet another patch.
The bug was:
{{{
sage: X.<x,y>=InfinitePolynomialRing(QQ)
sage: p=x[2]-x[1]
sage: q=x[1]-x[2]
sage: p.reduce([q])
0
sage: q.reduce([p])
-x2 + x1
}}}
Reason: In {{{SymmetricReductionStrategy.[tail]reduce()}}}, I compared
polynomials rather than leading monomials: I was not aware that
{{{-x<x}}}. This is now fixed
At this occasion, there also is an enhancement: It is now possible to use
fraction fields as base ring. In the previous version, this was
impossible, since the duck typing in {{{_coerce_map_from_}}} was not
appropriate, and since in {{{_div_}}} I have to work around the bug that I
reported at #5917.
Now, one can do:
{{{
sage: F = FractionField(PolynomialRing(QQ,['a','b']))
sage: X.<x,y>=InfinitePolynomialRing(F)
sage: I=(F('a')*x[1]*y[2]+F('b')*x[2])*X
sage: G=I.groebner_basis()
sage: G
[y1*x2 + b/a*x1, y2*x1 + b/a*x2]
sage: for p in Permutations(4):
....: print [(x^p).reduce(G) for x in G]
....:
[0, 0]
[0, 0]
[0, 0]
[0, 0]
[0, 0]
[0, 0]
[0, 0]
[0, 0]
[0, 0]
[0, 0]
[0, 0]
[0, 0]
[0, 0]
[0, 0]
[0, 0]
[0, 0]
[0, 0]
[0, 0]
[0, 0]
[0, 0]
[0, 0]
[0, 0]
[0, 0]
[0, 0]
}}}
'''__How to apply the patches__'''
1. {{{SymmetricIdealsFinal}}}
2. {{{SymmetricIdealsForgotten}}}
3. {{{SymmetricIdealsBugfix}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5566#comment:42>
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
-~----------~----~----~----~------~----~------~--~---
