Feature #143
Buchberger-Moeller (parent task)
38%
Description
Robbiano wants to have Buchberger-Moeller in C5. It makes most sense to implement it in CoCoALib and then make it visible in C5.
There are several versions to implement: these are in the subtasks.
Subtasks
Related issues
History
#1 Updated by Anna Maria Bigatti over 11 years ago
- Category set to New Function
#2 Updated by John Abbott over 11 years ago
- Status changed from New to In Progress
- Assignee set to John Abbott
- Target version set to CoCoALib-0.9953
#3 Updated by John Abbott about 11 years ago
- generators of the ideal (list of polynomials)
- separators (list of polynomials)
- quotient basis (list of PPs, or perhaps list of polynomials)
The definition of separator in the case of projective points is not unique. In C4 we opted for polynomials which evaluate to 1 on the given representatives; should we continue to use this definition in CoCoA-5? Or perhaps there should no way to compute the separators in this case?
Opinions? Comments?
#4 Updated by John Abbott about 11 years ago
JAA proposes offering two functions IdealOfPoints
(for the affine case) and IdealOfProjectivePoints
(for the projective case) which produce ideals.
In CoCoALib (and perhaps also in CoCoA-5) we could offer further functions for computing a complete result (presumably represented as a RECORD
). In C4 these had cumbersome names such as IdealAndSeparatorsOfProjectivePoints
. JAA proposes simpler names such as BuchbergerMoeller
and ProjectiveBuchbergerMoeller
. In the result JAA prefers a list of generators rather than an ideal -- it is quite easy for a user to produce an ideal from a list of generators (or vice versa).
Opinions?
#5 Updated by John Abbott about 11 years ago
My old impls in CoCoA-4 returned a matrix as the result: the entries in the matrix are the coeffs of the basis elements and of the separators.
The result also contained a list of PPs so that the appropriate polys could be reconstructed easily.
JAA now thinks that this is probably the most sensible type of value to return (for the internal BM fns that actually do the work).
The conversion from matrix to list of polys is straightforward, and can be effected by some auxiliary fns.
#6 Updated by John Abbott about 11 years ago
- Target version changed from CoCoALib-0.9953 to CoCoALib-0.99534 Seoul14
The stopgap impls will have to suffice for 0.9953/CoCoA School as there's no chance of completing a proper impl in time.
#7 Updated by Anna Maria Bigatti over 10 years ago
- Target version changed from CoCoALib-0.99534 Seoul14 to CoCoALib-0.99532
#8 Updated by John Abbott about 10 years ago
- Target version changed from CoCoALib-0.99532 to CoCoALib-0.99533 Easter14
#9 Updated by John Abbott about 10 years ago
- Target version changed from CoCoALib-0.99533 Easter14 to CoCoALib-0.99534 Seoul14
#10 Updated by John Abbott almost 10 years ago
- Target version changed from CoCoALib-0.99534 Seoul14 to CoCoALib-1.0