Structure Operations

Related Structures

The main structure related to an algebra of symmetric functions is its coefficient ring. An algebra of symmetric functions belongs to the Magma category AlgSym.

BaseRing(L): AlgSym -> Rng

CoefficientRing(L): AlgSym -> Rng

Return the coefficient ring of an algebra of symmetric functions \(L\).

Category(L): AlgSym -> Cat

Parent(L): AlgSym -> Pow

PrimeRing(L): AlgSym -> Rng

Ring Predicates and Booleans

The usual ring functions returning boolean values are available on algebras of symmetric functions.

IsCommutative(L): AlgSym -> BoolElt

IsUnitary(L): AlgSym -> BoolElt

IsFinite(L): AlgSym -> BoolElt

IsOrdered(L): AlgSym -> BoolElt

IsField(L): AlgSym -> BoolElt

IsEuclideanDomain(L): AlgSym -> BoolElt

IsPID(L): AlgSym -> BoolElt

IsUFD(L): AlgSym -> BoolElt

IsDivisionRing(L): AlgSym -> BoolElt

IsEuclideanRing(L): AlgSym -> BoolElt

IsDomain(L): AlgSym -> BoolElt

IsPrincipalIdealRing(L): AlgSym -> BoolElt

L eq M: AlgSym, AlgSym -> BoolElt

L ne M: AlgSym, AlgSym -> BoolElt

Return true if \(L\) and \(M\) are equal (respectively, not equal). Magma considers two algebras to be equal if they are over the same ring.

Predicates on Basis Types

HasSchurBasis(A): AlgSym -> BoolElt

Returns true if \(A\) is an algebra with a Schur basis.

HasHomogeneousBasis(A): AlgSym -> BoolElt

HasElementaryBasis(A): AlgSym -> BoolElt

HasPowerSumBasis(A): AlgSym -> BoolElt

HasMonomialBasis(A): AlgSym -> BoolElt

Returns true if \(A\) is an algebra with a homogeneous, elementary, power sum, or monomial basis respectively.