CoCoA » CoCoALib

the GBasis is not reduced if the ring is not commutative
(ideal(x,dx) is homogeneous, so the algorithm does not expect degree drops)

For the moment I fixed this in CoCoA-5, but I should set the right flag inside cocoalib.

• the name ReducedGBasis gives a guarantee for the future... the caller knows that it should return a result with known properties
• the name GBasis gives the caller a potentially weaker guarantee, and would allow us (as developers) the freedom to return non reduced bases (e.g. with integer coeffs rather than made monic)

Also I think someone reading code which uses ReducedGBasis knows that the result should be "nice".

John Abbott wrote:

I prefer to have two distinct functions GBasis and ReducedGBasis because:

done.
Should pass it to cocoa-5.

Subtle.... I think there were two problems: I fixed one (now repeating the cycle if a new LPP is found during interreduction), but the bug is still there.
Now I think the problem is a dangling iterator (aaaargh!).

I checked the example in https://cocoa.dima.unige.it/redmine/issues/418.
I convinced myself that this cannot happen in the final interreduction of a GB computation, i.e. no new LPP can appear at this stage (its a GB!!).
So my earlier suspicion was wrong.

Also the suspiction of a dangly iterator was wrong: it just happened that, in the unlikely event that the first poly in the GB has to be removed, the second is skipped by the ++it in the for loop. I put the increment in the right place of the cycle, and it works.