hi there,

this is going to be even worse than my recent bug report in terms of
reproducing the error. I guess i'll start with describing what
happens, and then if someone tells me that it's a bug and not a
feature, then i'll try to get a minimal example.

So I've got a polynomial ring with a few dozens variables, over a
cyclotomic field, and i've got an ideal J with hundreds of generators.
J contains at least y9 + y12. Then i got something like:

sage: J.reduce(y9 - y12)
2*y9   #which is fine

sage: J.reduce(y13*y15)
y13*y15 #why not

sage: J.reduce(y13*y15 + y9 - y12)
y13*y15 + y9 - y12

Now what's up with that ? shouldn't it be y13*y15 + 2*y9 ? that's what
i expect from the term 'reduction' anyway. Is this normal or is it a
bug ? if it's a bug, could it influence the equivalence x in J iff
J.reduce(x) == 0 ?

So if this is a bug i'll give you more details.

thanks!
Pierre




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