1714.sagews

x = PolynomialRing(QQ, 'x').gen()
K.<a>=NumberField(x^4+x^3+x^2+x+1)
K

Number Field in a with defining polynomial x^4 + x^3 + x^2 + x + 1

K.factor(9931)

(Fractional ideal (11*a^3 + 5*a^2 + 5)) * (Fractional ideal (5*a^3 + 11*a^2 + 5)) * (Fractional ideal (-5*a^3 - 5*a^2 + 6*a)) * (Fractional ideal (-11*a^3 - 11*a^2 - 6*a - 6))

L.<b>=NumberField(x^2+x-1)
L.factor(9931)

(Fractional ideal (-91*b - 66)) * (Fractional ideal (-91*b - 25))

c=(11*a^3 + 5*a^2 + 5)*(-5*a^3 - 5*a^2 + 6*a)

(Fractional ideal (11*a^3 + 5*a^2 + 5)) * (Fractional ideal (5*a^3 + 11*a^2 + 5))

c=36*a^3 + 66*a^2 + 66*a + 121

d=36*a^2 + 66*a^3 + 66*a^4 + 121

f=36*a^1 + 66*a^4 + 66*a^2 + 121

g=36*a^4 + 66*a^1 + 66*a^3 + 121

((c-d)*(c-f)*(c-g)*(d-f)*(d-g)*(f-g))^2

45110609483479183872000

((a*c-a^4*d)*(a*c-a^2*f)*(a*c-a^3*g)*(a^4*d-a^2*f)*(a^4*d-a^3*g)*(a^2*f-a^3*g))^2

251380574447052001953125

factor(251380574447052001953125)

5^15 * 17^4 * 9931^2

factor(45110609483479183872000)

2^12 * 3^12 * 5^3 * 41^2 * 9931^2

((c-f)*(d-g)*(c-g)*(d-f))

64352880

factor(64352880)

2^4 * 3^4 * 5 * 9931

((c-1)*(d-1)*(f-1)*(g-1))

95529456

factor(95529456)

2^4 * 3^4 * 11 * 6701