Hi Pierre,

> perhaps i should have posted to sage-devel instead ? i don't even know
> how to "properly" report a bug.
>

No, this was the right place to report the bug. Probably no one has
responded just because no one has had a chance to look at the bug. I
just went ahead and took a look, and it turns out this is actually a
bug in Singular! Here's a simpler bit of code that is creating the
underlying error (or, at least, the first underlying error):

sage: K.<I> = CyclotomicField(4) ; R.<x0,x1,x2,x3,x4> = K[]
sage: x = (7+I)*x1^2*x2*x3*x4 + x1*x2^2*x3*x4 + x1*x2*x3^2*x4 + x1*x2*x3*x4^2
sage: y = x1*x2*x3*x4
sage: x.gcd(y)
(I - 7)*x1^2*x2*x3*x4

We just call singular for this; in fact, here's the same bug in
singular (thanks to Martin Albrecht for translating this for me):

> ring r = (0,I),(x0,x1,x2,x3,x4),dp;
> minpoly = I^2 + 1;
> poly x = (7+I)*x1^2*x2*x3*x4 + x1*x2^2*x3*x4 + x1*x2*x3^2*x4 + x1*x2*x3*x4^2;
> poly y = x1*x2*x3*x4;
> gcd(x,y);
(I-7)*x1^2*x2*x3*x4

I'm going to go ahead and report this upstream; I'll reply to this
thread again when I find out what they say.

For the record, though, people on this list definitely respond faster
if you try to whittle down your examples to the smallest case you can
find that creates the error.

Sorry I don't have a workaround, but I hear the Singular people are
usually quite quick to respond.

-cc

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