Dear all,
In some circumstance polynomial ring quotients returns wrong results: the
following quotient by a single polynomial works correctly:
sage: R.<x> = PolynomialRing(ZZ)
sage:
sage: S.<xbar> = R.quotient(x^2+x+1)
sage: xbar^2
-xbar - 1
sage: xbar^2 + x + 1 == 0
True
whereas quotient by several polynomial is wrong:
sage: S.<xbar> = R.quotient((x^2+x+1, x^2))
sage: xbar^2
xbar^2
sage: xbar^2 + x + 1 == 0
False
The reason is that the default implementation of reduce in ideal.py is
def reduce(self, f):
return f # default
and is *not* overloaded for those kinds of polynomials. I'd rather replace
that with
raise NotImplementedError
leading
sage: R.<x> = PolynomialRing(ZZ)
sage: S.<xbar> = R.quotient((x^2+x+1, x^2))
to raise a NotImplementedError. Do you all agree with this behavior ? Is there
a simple way to fix that, knowing that "multivariate" polynomials in one
variable correctly implement the feature:
sage: R.<x> = PolynomialRing(ZZ, 1)
sage: S.<xbar> = R.quotient((x^2+x+1, x^2))
sage: xbar^2 + x + 1 == 0
True
Thanks for any advice.
Cheers,
Florent
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