Introduction
Example AlgSym_inf-invar (H146E1)
Creation of Symmetric Function Algebras
SymmetricFunctionAlgebra(R) : Rng -> AlgSym
SymmetricFunctionAlgebraSchur(R) : Rng -> AlgSym
SymmetricFunctionAlgebraHomogeneous(R) : Rng -> AlgSym
SymmetricFunctionAlgebraPower(R) : Rng -> AlgSym
SymmetricFunctionAlgebraElementary(R) : Rng -> AlgSym
SymmetricFunctionAlgebraMonomial(R) : Rng -> AlgSym
Example AlgSym_creation (H146E2)
Creation of Symmetric Functions
A . P : AlgSym, [ RngIntElt ] -> AlgSymElt
A . i : AlgSym, RngIntElt -> AlgSymElt
Example AlgSym_elt-create (H146E3)
IsCoercible(A, f) : AlgSym, RngMPolElt -> BoolElt, AlgSymElt
Example AlgSym_poly bang (H146E4)
A ! r : AlgSym, RngElt -> AlgSymElt
Example AlgSym_elt-create-scalar (H146E5)
A ! m : AlgSym, AlgSymElt -> AlgSymElt
Example AlgSym_elt-create-change_basis (H146E6)
Example AlgSym_change-basis-2 (H146E7)
Related Structures
BaseRing(L) : AlgSym -> Rng
Ring Predicates and Booleans
L eq M : AlgSym, AlgSym -> BoolElt
Predicates on Basis Types
HasSchurBasis(A): AlgSym -> BoolElt
HasHomogeneousBasis(A): AlgSym -> BoolElt
Print Styles
A ` PrintStyle : AlgSym -> MonStgElt
Example AlgSym_print-style (H146E8)
Multiplication
a * b : AlgSymElt, AlgSymElt -> AlgSymElt
Example AlgSym_mult (H146E9)
Plethysm
a ~ b : AlgSymElt, AlgSymElt -> AlgSymElt
Example AlgSym_pleth (H146E10)
Boolean Operators
IsHomogeneous(s): AlgSymElt -> BoolElt
s eq t : AlgSymElt, AlgSymElt -> BoolElt
Accessing Elements
Coefficient(s, p) : AlgSymElt, SeqEnum -> RngElt
Support(s) : AlgSymElt -> [SeqEnum], [RngElt]
Length(s) : AlgSymElt -> RngIntElt
Example AlgSym_support (H146E11)
Degree(s) : AlgSymElt -> RngIntElt
Multivariate Polynomials
P ! s : RngMPol, AlgSymElt -> RngMPolElt
Example AlgSym_symmetric polynomials and symmetric functions (H146E12)
Example AlgSym_ChangeOfAlphabet (H146E13)
Frobenius Homomorphism
Frobenius(s) : AlgSymElt -> AlgSymElt
Example AlgSym_Frobenius automorphism (H146E14)
Inner Product
InnerProduct(a,b): AlgSymElt, AlgSymElt -> RngElt
Example AlgSym_Inner-Product (H146E15)
Combinatorial Objects
Tableaux(sf, m): AlgSymElt, RngIntElt -> SetMulti
Symmetric Group Character
SymmetricCharacter(sf): AlgSymElt -> AlgChtrElt
Example AlgSym_symmetric-polynomials-and-symmetric-functions (H146E16)
Restrictions
RestrictDegree(a, n): AlgSymElt, RngIntElt -> AlgSymElt
RestrictPartitionLength(a, n): AlgSymElt, RngIntElt -> AlgSymElt
RestrictParts(a, n): AlgSymElt, RngIntElt -> AlgSymElt
Transition Matrices from Schur Basis
SchurToMonomialMatrix(n): RngIntElt -> AlgMatElt
Example AlgSym_creation (H146E17)
SchurToHomogeneousMatrix(n): RngIntElt -> AlgMatElt
SchurToPowerSumMatrix(n): RngIntElt -> AlgMatElt
SchurToElementaryMatrix(n): RngIntElt -> AlgMatElt
Example AlgSym_trans (H146E18)
Transition Matrices from Monomial Basis
MonomialToSchurMatrix(n): RngIntElt -> AlgMatElt
MonomialToHomogeneousMatrix(n): RngIntElt -> AlgMatElt
MonomialToPowerSumMatrix(n): RngIntElt -> AlgMatElt
MonomialToElementaryMatrix(n): RngIntElt -> AlgMatElt
Transition Matrices from Homogeneous Basis
HomogeneousToSchurMatrix(n): RngIntElt -> AlgMatElt
Example AlgSym_HS (H146E19)
HomogeneousToMonomialMatrix(n): RngIntElt -> AlgMatElt
Example AlgSym_hm (H146E20)
HomogeneousToPowerSumMatrix(n): RngIntElt -> AlgMatElt
HomogeneousToElementaryMatrix(n): RngIntElt -> AlgMatElt
Example AlgSym_HE (H146E21)
Transition Matrices from Power Sum Basis
PowerSumToSchurMatrix(n): RngIntElt -> AlgMatElt
Example AlgSym_character-table (H146E22)
PowerSumToMonomialMatrix(n): RngIntElt -> AlgMatElt
PowerSumToHomogeneousMatrix(n): RngIntElt -> AlgMatElt
PowerSumToElementaryMatrix(n): RngIntElt -> AlgMatElt
Transition Matrices from Elementary Basis
ElementaryToSchurMatrix(n): RngIntElt -> AlgMatElt
ElementaryToMonomialMatrix(n): RngIntElt -> AlgMatElt
Example AlgSym_em (H146E23)
ElementaryToHomogeneousMatrix(n): RngIntElt -> AlgMatElt
ElementaryToPowerSumMatrix(n): RngIntElt -> AlgMatElt
Bibliography
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Wed Apr 24 15:09:57 EST 2013