Introduction
Representation
Coercion Example FldRat_Coercion (H20E1)
Homomorphisms Example FldRat_homomorphism (H20E2)
Creation Functions
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
Structure Operations
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
Ring Predicates and Booleans
Element Operations
Parent and Category
Arithmetic Operators
Numerator and Denominator Numerator(q) : FldRatElt -> RngIntElt Denominator(q) : FldRatElt -> RngIntElt Example FldRat_numerator (H20E3)
Equality and Membership
Predicates on Ring Elements IsIntegral(q) : FldRatElt -> BoolElt
Comparison
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] [Next][Prev] [Right] [____] [Up] [Index] [Root]
