#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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Changes (by duleorlovic):
* owner: malb => duleorlovic
Comment:
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.
So libsingular:slimgb and toy:buchberger2 are right, and singular:std and
libsingular:std has bug.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9645#comment:4>
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