I was exploring some quotient ring operations and came across the following:
{{{
R.<y>=QQ[]
K.<w>=NumberField(y^3 + 2*y - 2401)
k.<v>=K.quo(K.prime_factors(7)[1])
R.<x,y>=PolynomialRing(k)
R.monomial_divides(y,x^3*y)
Error
}}}
{{{
R.<y>=QQ[]
K.<w>=NumberField(y^3 + 2*y - 2401)
k.<v>=K.residue_field(K.prime_factors(7)[1])
R.<x,y>=PolynomialRing(k)
R.monomial_divides(y,x^3*y)
True
}}}
The second works, the first does not. I came across this since
.monomial_divides is used is a groebner basis computation. So played around
a little more and the following seems weirder
{{{
A.<x,y,z> = PolynomialRing(Zmod(42))
A.monomial_divides(y,x^2*y)
True
}}}
{{{
A.<x,y,z> = PolynomialRing(Zmod(2521515232)) #but one less digit works
A.monomial_divides(y,x^2*y)
Error
}}
The first works, but the 2nd does not, even though neither is prime. It
seems to have to do with what type of polynomial ring they are initialized
as, but I had a hard time tracking down where that code lived and how it
decided. Is there someone familiar with polynomial rings in Sage who could
shed some light on whether this is expected behavior?
Thanks,
Ben
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