On Monday, January 14, 2013 2:31:46 PM UTC-8, Michael Beeson wrote:
>
> sage: K.<p,d,e,N> = FractionField(PolynomialRing(QQ,4,'pdeN'))
>
Why not just
sage: K.<p,d,e,N> = PolynomialRing(QQ,4,'pdeN')
>
With this change, sage doesn't hang (for me). Oh, I see, later you need
field coefficients.
sage: R.<x> = K[]
> sage: a = x^3-x^-3
> sage: b = x^5-x^-5
> sage: c = x^8-x^-8
> sage: X = p*a + d*b + e*c
> sage: f = x^16 *(X^2- N*b*c)
>
> and Sage does not answer. It just hangs and I have to kill the session.
> If it would answer I would like to continue with
>
> F = R(f)
>
When I do this, I get
TypeError: denominator must be a unit
sage: f.denominator()
x^45
Starting over:
sage: P.<p,d,e,N> = (PolynomialRing(QQ,4,'pdeN')
sage: R.<x> = P[]
sage: a = x^3-x^-3
sage: b = x^5-x^-5
sage: c = x^8-x^-8
sage: X = p*a + d*b + e*c
sage: f = x^16 *(X^2- N*b*c)
sage: K = FractionField(P)
sage: S.<x> = K[]
sage: F = S(f.numerator()) # not sure if this is what you want
sage: psi = cyclotomic_polynomial(30)
sage: g = F.quo_rem(psi)[1]
sage: g
(p^2 + 6*p*d + 2*p*e)*x^7 + (4*p*d + 2*d*e - N)*x^6 + (-p^2 - 2*p*d - 2*p*e
+ 2*d*e - N)*x^5 + (-4*p*d - 2*d*e + N)*x^4 + (-8*p*d - 4*d*e + 2*N)*x^3 +
(-4*p*d - 2*p*e - 2*d*e - e^2 + N)*x^2 + (-2*p^2 + 2*p*d - 3*d^2 - 2*p*e -
2*d*e - 2*e^2 + N)*x + p^2 + 6*p*d - e^2
--
John
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