Complexes of Modules over Basic Algebras
Creation
Complex(L, d) : List, RngIntElt -> ModCpx
Complex(f, d) : Map, RngIntElt -> ModCpx
ZeroComplex(A, m, n) : AlgBas, RngIntElt, RngIntElt -> ModCpx
Dual(C) : ModCpx -> ModCpx
Subcomplexes and Quotient Complexes
sub< C | Q > : ModCpx, SeqEnum[ModAlg] -> ModCpx, MapChn
RandomSubcomplex(C,Q) : ModCpx, SeqEnum -> ModCpx, MapChn
quo< C | D > : ModCpx, ModCpx -> ModCpx
Access Functions
Degrees(C) : ModCpx -> RngIntElt
Algebra(C) : ModCpx -> AlgBas
BoundaryMap(C, n) : ModCpx, RngIntElt -> ModMatFldElt
BoundaryMaps(C) : ModCpx -> List
DimensionsOfHomology(C) : ModCpx -> SeqEnum
DimensionOfHomology(C, n) : ModCpx, RngIntElt -> RngIntElt
DimensionsOfTerms(C) : ModCpx -> SeqEnum
Term(C, n) : ModCpx, RngIntElt -> ModAlg
Terms(C) : ModCpx -> SeqEnum
Elementary operations
DirectSum(C, D) : ModCpx, ModCpx -> ModCpx
Homology(C) : ModCpx -> SeqEnum
Homology(C, n) : ModCpx, RngIntElt -> SeqEnum
Prune(C) : ModCpx -> ModCpx
Prune(C,n) : ModCpx, RngIngElt -> ModCpx
Preprune(C) : ModCpx -> ModCpx
Preprune(C,n) : ModCpx, RngIntElt -> ModCpx
Shift(C, n) : ModCpx, RngIntElt -> ModCpx
ShiftToDegreeZero(C) : ModCpx -> ModCpx
Splice(C, D) : ModCpx, ModCpx -> ModCpx
Splice(C, D, f) : ModCpx, ModCpx, ModMatFldElt -> ModCpx
Extensions
LeftExactExtension(C) : ModCpx -> ModCpx
RightExactExtension(C) : ModCpx -> ModCpx
ExactExtension(C) : ModCpx -> ModCpx
LeftZeroExtension(C) : ModCpx -> ModCpx
RightZeroExtension(C) : ModCpx -> ModCpx
ZeroExtension(C) : ModCpx -> ModCpx
EqualizeDegrees(C, D) : ModCpx, ModCpx -> ModCpx, ModCpx
EqualizeDegrees(C, D, n) : ModCpx, ModCpx, RngIntElt -> ModCpx, ModCpx
Predicates
IsExact(C) : ModComplex -> BoolElt
IsShortExactSequence(C) : ModCpx -> BoolElt, RngIntElt
IsExact(C, n) : ModCpx, RngIntElt -> BoolElt
IsZeroComplex(C) : ModCpx -> BoolElt
IsZeroMap(C, n) : ModCpx, RngIntElt -> BoolElt
IsZeroTerm(C, n) : ModCpx, RngIntElt -> BoolElt
Example ModCpx_Complexes (H80E1)
Creation
ChainMap(Q, C, D, n) : SeqEnum, ModCpx, ModCpx, RngIntElt -> ModMatCpxElt
ZeroChainMap(C, D) : ModCpx -> ModMatCpxElt
Access Functions
Degree(f) : ModMatCpxElt -> RngIntElt
ModuleMap(f, n) : ModMatCpxElt, RngIntElt -> ModMatFldElt
Kernel(f) : ModMatCpxElt -> ModCpx, ModMatCpxElt
Cokernel(f) : ModMatCpxElt -> ModCpx, ModMatCpxElt
Image(f) : ModMatCpxElt -> ModCpx, ModMatCpxElt, ModMatCpxElt
Elementary Operations
f + g : ModMatCpxElt , ModMatCpxElt -> ModMatCpxElt
a * g : RngElt , ModMatCpxElt -> ModMatCpxElt
f * g : ModMatCpxElt , ModMatCpxElt -> ModMatCpxElt
Predicates
IsSurjective(f) : MotMatCpxElt -> BoolElt
IsInjective(f) : MotMatCpxElt -> BoolElt
IsZero(f) : MotMatCpxElt -> BoolElt
IsIsomorphism(f) : MotMatCpxElt -> BoolElt
IsShortExactSequence(f, g) : MapChn, MapChn -> BoolElt
IsChainMap(L, C, D, n) : List, ModCpx, ModCpx, RngIntElt -> BoolElt
IsChainMap(f) : MapChn -> BoolElt
IsProperChainMap(f) : MapChn -> BoolElt
HasDefinedModuleMap(C,n) : ModCpx, RngIntElt -> BoolElt
Example ModCpx_Chainmaps (H80E2)
Maps on Homology
InducedMapOnHomology(f,n) : MapChn, RngIntElt -> ModTupFldElt
ConnectingHomomorphism(f,g,n) : MapChn, MapChn, RngIntElt -> ModMatFldElt
LongExactSequenceOnHomology(f,g) : MapChn, MapChn -> ModCpx