poly, [variable=True], [check=a]) |
class_group,
composite_fields,
disc,
discriminant,
factor_integer,
integral_basis,
pari_bnf,
pari_nf,
pari_polynomial,
trace_pairing,
variable
These methods are defined as follows:
) |
WARNING: Assume GRH, etc. !! TODO: Change to use bnf_certify, unless user requests not to.
other) |
List of all possible composite fields formed from self and other.
[v=None]) |
Returns the discriminant of the ring of integers of the number field, or if v is specified, the determinant of the trace pairing on the elements of the list v.
INPUT: v (optional) -- list of element of this number field OUTPUT: Integer if v is omitted, and Rational otherwise.
[v=None]) |
Returns the discriminant of the ring of integers of the number field, or if v is specified, the determinant of the trace pairing on the elements of the list v.
INPUT: v (optional) -- list of element of this number field OUTPUT: Integer if v is omitted, and Rational otherwise.
n) |
Ideal factorization of the principal ideal of the ring of integers generated by n.
) |
Return a list of elements of this number field that are a basis for the full ring of integers.
sage: x = PolynomialRing(QQ).gen() sage: K = NumberField(x**5+10*x+1) sage: K.integral_basis() [1, a, a^2, a^3, a^4]
Next we compute the ring of integers of a cubic field in which 2 is an "essential discriminant divisor", so the ring of integers is not generated by a single element.
sage: K = NumberField(x**3 + x**2 - 2*x + 8) sage: K.integral_basis() [1, a, 1/2*a^2 + 1/2*a]
) |
PARI big number field corresponding to this field.
) |
PARI number field corresponding to this field.
) |
PARI polynomial corresponding to polynomial that defines this field.
v) |
Returns the trace pairing on the elements of the list v.
[new_var=None]) |
Returns or sets the name of the generator of the number field.
If the optional string argument new_var is given, then the name of the number field generator is set to new_var. If it is not given, this function returns the current name of the generator.
INPUT: new_value -- optional str OUTPUT: str -- the name of the generator
Instances of class NumberField also have the following special methods:
x) |
Coerce x into this number field.
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