Feature #1249
principal ideal has a Gbasis
Description
If and ideal has a single (non-zero) generator then that generator is automatically a Gbasis.
CoCoALib does not currently recognize this.
Discuss/fix.
Related issues
History
#1 Updated by John Abbott over 5 years ago
- Related to Support #1240: John's visit Feb 2019 added
#2 Updated by John Abbott over 5 years ago
- Status changed from New to In Progress
- % Done changed from 0 to 10
Also if the gens happen to have coprime LTs wrt to current ordering then they are a GBasis. Might be useful to have a function which checks if the gens are "obviously" a GBasis (without computing anything)?
Also it could be worth computing a GBasis with a low timeout...
---> moved to #1255
#3 Updated by John Abbott over 5 years ago
- Anna was concerned about potential cost if there are many gens;
- if there are more (non-zero) gens than indets then the LTs cannot be coprime;
- when scanning through the list of LTs, if the number of unseen indets is less than the number of remaining (non-zero) gens then they cannot all be pairwise coprime.
---> moved to #1255
#4 Updated by Anna Maria Bigatti over 5 years ago
- Related to Design #1255: Ideals with trivial GBasis added
#5 Updated by Anna Maria Bigatti over 5 years ago
- % Done changed from 10 to 80
Done and partly tested.
#6 Updated by John Abbott over 5 years ago
- Related to Bug #1256: RingID: different values in test-output on different platforms added
#7 Updated by John Abbott over 5 years ago
Having seen in the code that computing a GBasis over QQ
implies creating a new ring (with coeffs in ZZ
), encourages me to push for avoiding computing a GBasis if the gens are already "obviously" a GBasis (e.g. LPPs are coprime).
One could also use a heuristic: reduce the gens mod p (for several primes), and then check that all S-pairs reduce to 0 mod p (probably with a time limit). Maybe this is too complicated while also being uncertain...
#8 Updated by John Abbott almost 5 years ago
- Assignee set to Anna Maria Bigatti
Has this already been done?
I think what Anna showed me in Genova, indicated that it has been done. If so, we can close!
#9 Updated by Anna Maria Bigatti almost 5 years ago
- Status changed from In Progress to Closed
- % Done changed from 80 to 100
#10 Updated by Anna Maria Bigatti over 4 years ago
- Estimated time set to 3.01 h