sage: alpha=sqrt(-17/2 + sqrt(17^2-4(17))/2)
sage: f=alpha.minpoly()
sage: K.<a>=NumberField(x^4+17*x^2+17)
sage: R<y>=PolynomialRing(K)
sage: R(f).factor()
(y-a)(y+a)(y^2+a^2+17)
sage: g=y^2+a^2+17
sage: L.<b>=K.extension(g)
sage: L.relative_discriminant()
Fractional ideal (1)
Revision history [back]
 | 1 | initial version |
Hi, What does it mean that the relative discriminant is generated by a unit?, Does it mean that there is no relative integral basis?
Hi, What does it mean that the relative discriminant is generated by a unit?, Does it mean that there is no relative integral basis?
sage: alpha=sqrt(-17/2 + sqrt(17^2-4(17))/2)
sage: f=alpha.minpoly()
sage: K.<a>=NumberField(x^4+17*x^2+17)
sage: R<y>=PolynomialRing(K)
sage: R(f).factor()
(y-a)(y+a)(y^2+a^2+17)
sage: g=y^2+a^2+17
sage: L.<b>=K.extension(g)
sage: L.relative_discriminant()
Fractional ideal (1)
Hi, What does it mean that the relative discriminant is generated by a unit?, unit?
Does it mean that there is no relative integral basis?
sage: alpha=sqrt(-17/2 + sqrt(17^2-4(17))/2)
sage: f=alpha.minpoly()
sage: K.<a>=NumberField(x^4+17*x^2+17)
sage: R<y>=PolynomialRing(K)
sage: R(f).factor()
(y-a)(y+a)(y^2+a^2+17)
sage: g=y^2+a^2+17
sage: L.<b>=K.extension(g)
sage: L.relative_discriminant()
Fractional ideal (1)
Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.