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map(SimplicialModule,SimplicialModule,ZZ) -- make the zero map or identity between simplicial modules

Description

A map of simplicial modules $f : C \rightarrow D$ of degree $d$ is a sequence of maps $f_i : C_i \rightarrow D_{d+i}$.

We construct the zero map between two simplicial modules.

i1 : R = QQ[a,b,c]

o1 = R

o1 : PolynomialRing
 
i2 : C = simplicialModule(freeResolution coker vars R, Degeneracy => true)

      1      4      10      20
o2 = R  <-- R  <-- R   <-- R  <-- ...
                            
     0      1      2       3

o2 : SimplicialModule
 
i3 : D = simplicialModule(freeResolution coker matrix{{a^2, b^2, c^2}}, Degeneracy => true)

      1      4      10      20
o3 = R  <-- R  <-- R   <-- R  <-- ...
                            
     0      1      2       3

o3 : SimplicialModule
 
i4 : f = map(D, C, 0)

o4 = 0

o4 : SimplicialModuleMap
 
i5 : assert isWellDefined f
 
i6 : assert isSimplicialMorphism f
 
i7 : g = map(C, C, 0, Degree => 13)

o7 = 0

o7 : SimplicialModuleMap
 
i8 : assert isWellDefined g
 
i9 : assert(degree g == 13)
 
i10 : assert not isSimplicialMorphism g
 
i11 : assert isCommutative g
 
i12 : assert isHomogeneous g
 
i13 : assert(source g == C)
 
i14 : assert(target g == C)

Using this function to create the identity map is the same as using id _ SimplicialModule.

i15 : assert(map(C, C, 1) === id_C)

See also

Ways to use this method:

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/SimplicialModules/SimplicialModuleDOC.m2:1506:0.