Creation
BasicAlgebra(Q) : SeqEnum[Tup] -> AlgBas
BasicAlgebra(G, k) : GrpPerm, FldFin -> AlgBas
BasicAlgebra(F,R,s,P): AlgFr, SeqEnum, RngIntElt, SeqEnum -> AlgBas
BasicAlgebra(F,R) : AlgFr, SeqEnum -> AlgBas
TensorProduct(A, B) : AlgBas, AlgBas-> AlgBas
Access Functions
NumberOfProjectives(B) : AlgBas -> RngIntElt
B . i : AlgBas, RngIntElt -> AlgBasElt
BaseRing(B) : AlgBas -> Rng
VectorSpace(B) : AlgBas -> ModTupFld
Dimension(B) : AlgBas -> RngIntElt
Basis(B) : AlgBas -> SeqEnum
Generators(B) : AlgBas -> SeqEnum
IdempotentGenerators(B) : AlgBas -> SeqEnum
IdempotentPositions(B) : AlgBas -> SeqEnum
NonIdempotentGenerators(B) : AlgBas -> SeqEnum
Random(B) : AlgBas -> AlgBasElt
NumberOfGenerators(B) : AlgBas -> RngIntElt
DimensionsOfProjectiveModules(B) : AlgBas -> SeqEnum
DimensionsOfInjectiveModules(B) : AlgBas -> SeqEnum
Elementary Operations
a + b : AlgBasElt, AlgBasElt -> AlgBasElt
a * b : AlgBasElt, AlgBasElt -> AlgBasElt
a ^ n : AlgBasElt, RngIntElt -> AlgBasElt
Example AlgBas_BasicAlgebras (H71E1)
Example AlgBas_BasicAlgebras-2 (H71E2)
Example AlgBas_BasicAlgebras-3 (H71E3)
Indecomposable Projective Modules
ProjectiveModule(B, i) : AlgBas, RngIntElt -> ModRng
PathTree(B, i) : AlgBas, RngIntElt -> ModRng
ActionGenerator(B, i) : AlgBas, RngIntElt -> SeqEnum
IdempotentActionGenerators(B, i) : AlgBas, RngIntElt -> SeqEnum
NonIdempotentActionGenerators(B, i) : AlgBas, RngIntElt -> SeqEnum
Injection(B, i, v) : AlgBas, RngIntElt, ModRngElt -> AlgBasElt
Creation
AModule(B, Q) : AlgBas, SeqEnum[AlgMatElt] -> ModRng
ProjectiveModule(B, S) : AlgBas, SeqEnum[RngIntElt] -> ModAlg, SeqEnum, SeqEnum
IrreducibleModule(B, i) : AlgBas, RngIntElt -> ModAlg
ZeroModule(B) : AlgBas -> ModAlg
RightRegularModule(B) : AlgBas -> ModAlg
RegularRepresentation(v) : AlgBasElt -> AlgMatElt
JacobsonRadical(M) : ModAlg -> ModAlg
Socle(M) : ModAlg -> ModAlg
Access Functions
Algebra(M) : ModAlg -> AlgBas
Dimension(M) : ModAlg -> RngIntElt
Action(M) : ModAlg -> AlgMat
Predicates
IsSemisimple(M) : ModAlg -> BoolElt, SeqEnum
IsProjective(M) : ModAlg -> BoolElt, SeqEnum
IsInjective(M) : ModAlg -> BoolElt, SeqEnum
Elementary Operations
m * b : ModAlgElt, AlgBasElt -> ModAlgElt
Example AlgBas_AModules (H71E4)
Example AlgBas_AModules-2 (H71E5)
Creation
AHom(M, N) : ModAlg, ModAlg -> ModMatFld
PHom(M,N) : ModAlg, ModAlg -> ModMatFld
ZeroMap(M, N) : ModAlg, ModAlg -> ModMatFld
LiftHomomorphism(x, n) : ModAlgElt, RngIntElt -> ModMatFldElt
LiftHomomorphism(X, N) : SeqEnum[ModAlgElt], SeqEnum[RngIntElt] -> ModMatFldElt
Pushout(M, f1, N1, f2, N2) : ModAlg, ModMatFldElt, ModAlg, ModMatFldElt, ModAlg -> ModAlg, ModMatFldElt, ModMatFldElt
Pullback(f1, M1, f2, M2, N) : ModAlg, ModMatFldElt, ModAlg, ModMatFldElt, ModAlg -> ModAlg, ModMatFldElt, ModMatFldElt
Access Functions
IsModuleHomomorphism(f) : ModMatFldElt -> BoolElt
Domain(f) : ModMatFldElt -> ModAlg
Codomain(f) : ModMatFldElt -> ModAlg
Kernel(f) : ModMatFldElt -> ModAlg,ModMatFldElt
Cokernel(f) : ModMatFldElt -> ModAlg,ModMatFldElt
Projective Covers
ProjectiveCover(M) : ModAlg -> ModAlg, ModMatFldElt, SeqEnum[ModMatFldElt], SeqEnum[ModMatFldElt], SeqEnum[RngIntElt]
ProjectiveResolution(M, n) : ModAlg, RngIntElt -> ModCpx, ModMatFldElt
CompactProjectiveResolution(M, n) : ModAlg, RngIntElt -> Rec
SyzygyModule(M, n) : ModAlg, RngIntElt -> ModAlg
SimpleHomologyDimensions(M) : ModAlg -> SeqEnum
Example AlgBas_Homomorphisms (H71E6)
Example AlgBas_Homomorphisms-2 (H71E7)
Creation
OppositeAlgebra(B) : AlgBas -> AlgBas
Dual(M) : ModAlg -> ModAlg
BaseChangeMatrix(A) : AlgBas -> ModAlg
Injective Modules
InjectiveModule(B, i) : AlgBas, RngIntElt -> ModAlg
InjectiveHull(M) : ModAlg -> ModAlg, ModMatFldElt, SeqEnum[ModMatFldElt], SeqEnum[ModMatFldElt], SeqEnum[RngIntElt]
InjectiveResolution(M, n) : ModAlg, RngIntElt -> ModCpx, ModMatFldElt
CompactInjectiveResolution(M, n) : ModAlg, RngIntElt -> Rec
InjectiveSyzygyModule(M, n) : ModAlg, RngIntElt -> ModAlg
SimpleCohomologyDimensions(M) : ModAlg -> SeqEnum
Example AlgBas_Opposite (H71E8)
Cohomology
CohomologyRingGenerators(P) : Rec -> Rec
CohomologyRightModuleGenerators(P, Q, CQ) : Rec, Rec, Rec -> Rec
CohomologyLeftModuleGenerators(P, CP, Q) : Tup, Tup, Tup -> Tup
DegreesOfCohomologyGenerators(C) : Rec -> SeqEnum
CohomologyGeneratorToChainMap(P,Q,C,n) : ModCpx, ModCpx, rec, RngIntElt -> MapChn
CohomologyGeneratorToChainMap(P, C, n) : ModCpx, Tup, RngIntElt -> MapChn
Example AlgBas_Cohomology-2 (H71E9)
Access Functions
Group(A) :AlgBasGrpP -> Grp
PCGroup(A) :AlgBasGrpP -> Grp
PCMap(A) : AlgBasGrpP -> Map
AModule(M) : ModGrp -> ModAlg
GModule(M) : AlgBasGrpP -> ModGrp, ModGrp
GModule(M) : ModAlgBas -> ModGrp
Projective Resolutions
ResolutionData(A) : AlgBasGrpP -> Rec
CompactProjectiveResolutionPGroup(M, n) : ModAlgBas, RngIntElt -> Rec
ProjectiveResolutionPGroup(PR) : Rec -> ModCpx
ProjectiveResolution(M, n) : ModAlgBas, RngIntElt -> ModCpx, ModMatFldElt
ProjectiveResolution(PR) : Rec -> ModCpx, ModMatFldElt
Cohomology Generators
AllCompactChainMaps(PR) : Rec -> Rec
CohomologyElementToChainMap(P, d, n) : ModCpx ,RngIntElt, RngIntElt -> MapChn
CohomologyElementToCompactChainMap(PR, d, n): Rec, RngIntElt, RngIntElt -> ModMatFldElt
Cohomology Rings
CohomologyRing(k, n) : ModAlgBas, RngIntElt -> Rec
MinimalRelations(R) : Rec -> SeqEnum
Restrictions and inflations
RestrictionData(A,B) : AlgBasGrpP, AlgBasGrpP -> ModMatFldElt, ModMatFldElt, SeqEnum
RestrictResolution(PR, RD) : Rec, Rec -> ModCpx
RestrictionChainMap(P1,P2) : Rec, Rec -> MapChn
RestrictionOfGenerators(PR1, PR2, AC1, AC2, REL2) : Rec, Rec, Rec, Rec, Rec -> SeqEnum
InflationMap(PR2, PR1, AC2, AC1, REL1, theta) : Rec, Rec, Rec, Rec, Rec -> SeqEnum
Example AlgBas_CohomologyRing (H71E10)