Coercion
Example FldRat_Coercion (H20E1)
Homomorphisms
Example FldRat_homomorphism (H20E2)
Creation of Structures
Rationals() : -> FldRat
MaximalOrder(Q) : FldRat -> RngInt
FieldOfFractions(Q) : FldRat -> FldRat
Completion(Q, P) : FldRat, RngInt -> FldLoc, Map
Creation of Elements
a / b : RngIntElt, RngIntElt -> FldRatElt
Q ! [a] : FldRat, RngElt -> FldRatElt
Q ! [a, b] : FldRat, RngIntElt, RngIntElt -> FldRatElt
Q ! a : FldRat, RngIntElt -> FldRatElt
RootOfUnity(n, Q) : RngIntElt, FldRat -> FldRatElt
Random(Q, m) : FldRat, RngIntElt -> FldRatElt
Related Structures
IntegralBasis(Q) : FldRat -> [ FldRatElt ]
MinimalField(q) : FldRatElt -> FldRat
MinimalField(S) : SetEnum -> FldRat
BaseField(Q) : FldRat -> FldRat
Basis(Q) : FldRat -> [FldRatElt]
UnitGroup(Q) : FldRat -> GrpAb, Map
ClassGroup(Q) : FldRat -> GrpAb, Map
AutomorphismGroup(Q) : FldRat -> GrpPerm, PowMapAut, Map
Algebra(Q, Q) : FldRat, Fld -> AlgAss, Map
VectorSpace(Q, Q) : FldRat, Fld -> ModTupFld, Map
Decomposition(Q, p) : FldRat, RngIntElt -> []
Numerical Invariants
Conductor(Q) : FldRat -> RngIntElt
Degree(Q) : FldRat -> RngIntElt
Discriminant(Q) : FldRat -> RngIntElt
DefiningPolynomial(Q) : FldRat -> RngUPolElt
Signature(Q) : FldRat -> RngIntElt, RngIntElt
Numerator and Denominator
Numerator(q) : FldRatElt -> RngIntElt
Denominator(q) : FldRatElt -> RngIntElt
Example FldRat_numerator (H20E3)
Predicates on Ring Elements
IsIntegral(q) : FldRatElt -> BoolElt
Conjugates, Norm and Trace
ComplexConjugate(q) : FldRatElt -> FldRatElt
Conjugate(q) : FldRatElt -> FldRatElt
Norm(q) : FldRatElt -> FldRatElt
Trace(q) : FldRatElt -> FldRatElt
MinimalPolynomial(q) : FldRatElt -> RngUPolElt
Absolute Value and Sign
AbsoluteValue(q) : FldRatElt -> FldRatElt
Sign(q) : FldRatElt -> RngIntElt
Height(q) : FldRatElt -> RngIntElt
Rounding and Truncating
Ceiling(q) : FldRatElt -> RngIntElt
Floor(q) : FldRatElt -> RngIntElt
Round(q) : FldRatElt -> RngIntElt
Truncate(q) : FldRatElt -> RngIntElt
Qround(q, M) : FldRatElt, RngIntElt -> FldRatElt
Rational Reconstruction
RationalReconstruction(s) : RngIntResElt -> BoolElt, FldRatElt
Valuation
Valuation(x, p) : FldRatElt, RngIntElt -> RngIntElt, FldRatElt
Sequence Conversions
ElementToSequence(a) : FldRatElt -> [FldRatElt]
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Version: V2.19 of
Wed Apr 24 15:09:57 EST 2013