#9645: Bugs in the computation of Groebner bases over the integers
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Reporter: SimonKing | Owner: duleorlovic
Type: defect | Status: new
Priority: critical | Milestone: sage-5.0
Component: commutative algebra | Keywords: Groebner basis integer
Author: | Upstream: Reported upstream. Little or
no feedback.
Reviewer: | Merged:
Work_issues: |
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Comment(by SimonKing):
Replying to [comment:4 duleorlovic]:
> Replying to [comment:1 SimonKing]:
>
> > There is a new singular spkg at #8059. However, this does not solve
the problem. The only difference is that now one has ` sage:
I.groebner_basis(algorithm='toy:buchberger2') [2*x^2 + x*y, 3*x*y, 2*y^2]
` Hence, the result is reduced (the first bug is gone), but still wrong.
>
> Result is '''right '''because reduce is different in field and in ring
(please read
[http://books.google.com/books?id=Caoxi78WaIAC&pg=PA201&dq=adams+loustaunau+introduction+to+grobner+bases+chapter+4&hl=sr&ei=CwdYTJzPHcGe4AaZsKmhBw&sa=X&oi=book_result&ct=result&resnum=1&ved=0CCkQ6AEwAA#v=onepage&q=adams%20loustaunau%20introduction%20to%20grobner%20bases%20chapter%204&f=false
this book chapter 4]).
>
> x*y!^2 is reduced to zero on [2*x!^2 + x*y, 3*x*y, 2*y!^2] because
x*y!^2 - (y*3*x*y-x*2*y!^2)=0.
I don't buy this and repeat that this is not a reduction. Martin, do you
agree?
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9645#comment:5>
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