#12839: reduced Groebner basis not unique
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Reporter: mariah | Owner: malb
Type: defect | Status: new
Priority: major | Milestone: sage-5.1
Component: commutative algebra | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers:
Authors: | Merged in:
Dependencies: | Stopgaps:
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Comment (by john_perry):
I think I see a way to get this to work.
The first thing that can be tried is whether the groebner bases are equal,
which is what we are doing now. If that succeeds, then great.
Otherwise, we can compare by reducing the elements of one groebner basis
over the other's groebner basis. If all reductions give us 0, then we
return true. Otherwise, we return false.
I think this is related to #12802, and this trick should fix both of them:
`__lt__` can test if the first is contained in the second, `__gt__` can
check if the second is contained in the first, and `__eq__` checks if both
are satisfied.
This would be easy to implement, but is the algorithm I'm outlining
correct?
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12839#comment:3>
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