sage.rings.number_field.number_field_ideal

Module number_field_ideal_rel

Relative Number Field Ideals AUTHOR: -- Steven Sivek (2005-05-16) -- Willia Stein (2007-09-06)

Functions

[hide private]

is_NumberFieldFractionalIdeal_rel(x)
Return True if x is a fractional ideal of a relative number field.

source code

Variables

[hide private]

QQ = Rational Field

Function Details

[hide private]

is_NumberFieldFractionalIdeal_rel(x)

source code


Return True if x is a fractional ideal of a relative number field.

EXAMPLES:
    sage: is_NumberFieldFractionalIdeal_rel(2/3)
    False
    sage: is_NumberFieldFractionalIdeal_rel(ideal(5))
    False
    sage: k.<a> = NumberField(x^2 + 2)
    sage: I = k.ideal([a + 1]); I
    Fractional ideal (a + 1)
    sage: is_NumberFieldFractionalIdeal_rel(I)
    False
    sage: R.<x> = QQ[]
    sage: K.<a> = NumberField(x^2+6)
    sage: L.<b> = K.extension(K['x'].gen()^4 + a)
    sage: I = L.ideal(b); I
    Fractional ideal (b)
    sage: is_NumberFieldFractionalIdeal_rel(I)
    True
    sage: N = I.norm(); N
    Fractional ideal (-a)
    sage: is_NumberFieldFractionalIdeal_rel(N)
    False
    sage: is_NumberFieldFractionalIdeal(N)
    True