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Complexes :: map(Complex,Complex,ZZ)

map(Complex,Complex,ZZ) -- make the zero map or identity between chain complexes

Synopsis

Description

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

We construct the zero map between two chain complexes.

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

o1 = R

o1 : PolynomialRing
i2 : C = freeResolution coker vars R

      1      3      3      1
o2 = R  <-- R  <-- R  <-- R
                           
     0      1      2      3

o2 : Complex
i3 : D = freeResolution coker matrix{{a^2, b^2, c^2}}

      1      3      3      1
o3 = R  <-- R  <-- R  <-- R
                           
     0      1      2      3

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

o4 = 0

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

o7 = 0

o7 : ComplexMap
i8 : assert isWellDefined g
i9 : assert(degree g == 13)
i10 : assert not isComplexMorphism 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 _ Complex.

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

See also