Construction of a Free Algebra
FreeAlgebra(R, M) : Rng, MonFP -> AlgFP
Example AlgFP_FreeAlgebra (H70E1)
Accessing an Algebra
CoefficientRing(A) : Alg -> Rng
Monoid(A) : Alg -> MonFP
Specification of a Word
A ! e : AlgFP, MonFPElt -> AlgFPElt
Elementary Operators for Elements
u + v : AlgFPElt, AlgFPElt -> AlgFPElt
u - v : AlgFPElt, AlgFPElt -> AlgFPElt
u * v : AlgFPElt, AlgFPElt -> AlgFPElt
u ^ n : AlgFPElt, RngIntElt -> AlgFPElt
Boolean Operators for Elements
u eq v : AlgFPElt, AlgFPElt -> BoolElt
u ne v : AlgFPElt, AlgFPElt -> BoolElt
u lt v : AlgFPElt, AlgFPElt -> BoolElt
u le v : AlgFPElt, AlgFPElt -> BoolElt
u ge v : AlgFPElt, AlgFPElt -> BoolElt
u gt v : AlgFPElt, AlgFPElt -> BoolElt
IsZero(u) : AlgFPElt -> BoolElt
IsScalar(u) : AlgFPElt -> BoolElt
Elementary Functions for Elements
# u : AlgFPElt -> RngIntElt
Support(u) : AlgFPElt -> [ MonElt ]
LeadingCoefficient(u) : AlgFPElt -> RngElt
MonomialCoefficient(u, m) : AlgFPElt, MonElt -> RngElt
Specification of a Relation
w_1 = w_2 : AlgFPElt, AlgFPElt -> Rel
LHS(r) : Rel -> AlgFPElt
RHS(r) : Rel -> AlgFPElt
Construction of a Quotient: Specification of a Presentation
quo< F | relations > : AlgFP, Rel, .., Rel -> AlgFP
A / I : AlgFP, AlgFPIdl -> AlgFP
Construction of a Subalgebra
sub<A | L_1, ..., L_r> : AlgFP, AlgFPElt, ..., AlgFPElt -> AlgFP
ideal<A | L_1, ..., L_r> : AlgFP, AlgFPElt, ..., AlgFPElt -> AlgFP
lideal<A | L_1, ..., L_r> : AlgFP, AlgFPElt, ..., AlgFPElt -> AlgFP
rideal<A | L_1, ..., L_r> : AlgFP, AlgFPElt, ..., AlgFPElt -> AlgFP
Accessing the Defining Generators and Relations
A . i : AlgFP, RngIntElt -> AlgFPElt
Generators(A) : AlgFP -> { AlgFPElt }
NumberOfGenerators(A) : AlgFP -> RngIntElt
Parent(u) : AlgFPElt -> AlgFP
Relations(A) : AlgFP -> [ Rel ]
Vector Enumeration
Example AlgFP_Abstract (H70E2)
The Quotient Module Command
QuotientModule(A, S) : AlgFP, AlgFP -> AlgFP
Weights
QuotientModule(A, S) : AlgFP, AlgFP -> AlgFP
Limits
QuotientModule(A, S) : AlgFP, AlgFP -> AlgFP
Logging
QuotientModule(A, S) : AlgFP, AlgFP -> AlgFP
Miscellaneous
QuotientModule(A, S) : AlgFP, AlgFP -> AlgFP
Example AlgFP_PermutationActionD8 (H70E3)
Example AlgFP_Quotient (H70E4)