#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):
Correct me if I am wrong, but you cannot have a reduced Groebner basis
over a field that is not a ring. Besides, the ideals are ''not'' the same,
even if their varieties are.
Singular seems to feel this way:
* Singular is computing the basis.
* According to Remark 1.6.14 in ''A '''Singular''' Introduction to
Commutative Algebra'', if you want to compute a ''standard basis over a
ring'' which is merely Noetherian (not necessarily a field, as in
Definition 1.6.1), you need to have agreement of leading ''terms'' (which
includes coefficients), not leading ''monomials''.
* See this answer in [http://www.singular.uni-
kl.de/forum/viewtopic.php?f=10&t=1750&p=2349&hilit=std+integer#p2349 the
Singular forums].
Macaulay also feels this way:
* I installed Macaulay2, computed groebner bases for both I and J, and
got the same thing singular computes.
* Macaulay2's
[http://www.math.uiuc.edu/Macaulay2/doc/Macaulay2-1.4/share/doc/Macaulay2/Macaulay2Doc/html/_simple_sp__Groebner_spbasis_spcomputations_spover_spvarious_springs.html
webpage] implies the same.
Unless I'm wrong, this is not a bug.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12839#comment:1>
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