The class is for number field.
polynomial must be a monic irreducible polynomial defining the number field.
Ex.
>>> K = algfield.NumberField([-2, 0, 1]) >>> F = algfield.NumberField([-3, 0, 0, 1]) >>> print K NumberField([-2, 0, 1]) >>> print F NumberField([-3, 0, 0, 1])
defining polynomial of the number field.
degree of number field.
Compute the discriminant of the number field. However the output is not disc of the number field itself but disc of defining polynomial.
Using Strum's algorithm, compute the signature of the number field.
Given a polynomial f i.e. a field defined by f, output some polynomials defining subfield of the given number field.
Determine whether standard basis of the number field is integral basis of the field.
Determine whether self/other is Galois field.
Return characteristic of the number field (it is always zero).
operator | explanation |
K * F | composite field K and F |