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Slug #1737

Homogenization of an ideal with ZZ^1-grading

Added by John Abbott 12 months ago. Updated 3 months ago.

Status:
In Progress
Priority:
Normal
Assignee:
Anna Maria Bigatti
Category:
Improving
Target version:
CoCoALib-0.99880
Start date:
29 Apr 2023
Due date:
% Done:

20%

Estimated time:
Spent time:
0.60 h

Description

(1) With a ZZ^1-grading I think it is enough to compute a "wdeg-rev" ReducedGBasis then "saturate" each element independently (cannot currently find the relevant lemma in K+R).
I think that CoCoALib does not handle this case cleverly: check what the code actually does.

(2) Moreover, do we want allow homogenization by an indet whose degree is not 1?
Sometimes this is possible:
e.g. deg(x) = 3, deg(h) = 2 then we can homogenize x^3+2*x to get x^3 + 2*x*h^3; but we cannot homogenize x^2+2*x.
My current inclination is to allow homogenization by an indet whose degree is not 1. Opinions? Comments?

Related issues

Related to CoCoALib - Feature #1778: HomogenizerIn Progress2024-02-02

History

#1 Updated by John Abbott 3 months ago

  • Status changed from New to In Progress
  • Target version changed from CoCoALib-0.99850 to CoCoALib-0.99880
  • % Done changed from 0 to 10

Yes, it would be possible to implement this, and perhaps not even too hard. But why?
When would it be useful? Is there any point in "cluttering up" CoCoALib with code which probably no one will use?

#2 Updated by Anna Maria Bigatti 3 months ago

  • Subject changed from Homogenization with ZZ^1-grading to Homogenization of an ideal with ZZ^1-grading
  • Description updated (diff)

#3 Updated by Anna Maria Bigatti 3 months ago

  • Description updated (diff)

#4 Updated by Anna Maria Bigatti 3 months ago

  • Description updated (diff)

#5 Updated by Anna Maria Bigatti 3 months ago

  • Assignee set to Anna Maria Bigatti

By Kreuzer-Robbiano: Corollary 4.3.20. It requires that P is positively graded.

#6 Updated by Anna Maria Bigatti 3 months ago

  • Description updated (diff)

(2) I think we should not provide homogenization by an indet whose degree is not 1, because this is not entirely trivial to do, so it would take time from more important things, and I doubt it is useful to anyone.

Of course, if someone asks for it, we can reconsider.

#7 Updated by Anna Maria Bigatti 3 months ago

By Robbiano: No need to allow homogenization by an indet whose degree is not 1.

#8 Updated by John Abbott 3 months ago

  • % Done changed from 10 to 20

Anna, are you willing to investigate point (1): the implementation behaving cleverly if the term order is wdeg-compatible, and the grading is strictly positive?

#9 Updated by John Abbott 3 months ago

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