Structure Operations

Subsections

• Related Structures
• Numerical Invariants
• Ring Predicates and Booleans

Related Structures

Parent(R) : AlgChtr -> Pow

Category(R) : AlgChtr -> Cat

Group(R) : AlgChtr -> Grp

Given the ring R of class functions on a finite group G, return G.

Centre(x) : AlgChtrElt -> Grp

The centre of the character x of G, i.e. the subgroup of G consisting of those classes C of G for which |x(g)|, g in C, is equal to the degree of x.

CoefficientField(x) : AlgChtrElt -> Rng

The (minimal) coefficient field Q_m of the class function x.

Kernel(x) : AlgChtrElt -> Grp

The kernel of the character x of G, i.e. the normal subgroup of G consisting of those elements g for which x(g) = x(1).

Numerical Invariants

Characteristic(R) : AlgChtr -> RngIntElt

Ring Predicates and Booleans

IsCommutative(F) : FldFun -> BoolElt

IsUnitary(F) : FldFun -> BoolElt

IsFinite(F) : FldFun -> BoolElt

IsOrdered(F) : FldFun -> BoolElt

IsField(F) : FldFun -> BoolElt

IsEuclideanDomain(F) : FldFun -> BoolElt

IsPID(F) : FldFun -> BoolElt

IsUFD(F) : FldFun -> BoolElt

IsDivisionRing(F) : FldFun -> BoolElt

IsEuclideanRing(F) : FldFun -> BoolElt

IsPrincipalIdealRing(F) : FldFun -> BoolElt

IsDomain(F) : FldFun -> BoolElt

F eq G : FldFun, Rng -> BoolElt

F ne G : FldFun, Rng -> BoolElt