map(ZZdFactorization,ZZdFactorization,ZZ) -- make the zero map or identity between ZZ/d-graded factorizations

Function: map
Usage:

f = map(D, C, 0)

f = map(C, C, 1)
Inputs:
- C, a ZZ/d graded factorization,
- D, a ZZ/d graded factorization,
- 0, an integer, or 1
Optional inputs:
- Degree => an integer, default value null, the degree of the resulting map
- DegreeLift => ..., default value null, unused
- DegreeMap => ..., default value null, unused
Outputs:
- f, a map of ZZ/d-graded factorizations, the zero map from $C$ to $D$ or the identity map from $C$ to $C$

Description

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

We construct the zero map between two factorizations.

i1 : S = ZZ/101[a,b,c]

o1 = S

o1 : PolynomialRing

i2 : R = S/(a^2+b^2+c^2);

i3 : m = ideal vars R

o3 = ideal (a, b, c)

o3 : Ideal of R

i4 : C = tailMF m

      4      4      4
o4 = S  <-- S  <-- S
                    
     0      1      0

o4 : ZZdFactorization

i5 : D = tailMF (m^2)

      8      8      8
o5 = S  <-- S  <-- S
                    
     0      1      0

o5 : ZZdFactorization

i6 : f = map(D, C, 0)

o6 = 0

o6 : ZZdFactorizationMap

i7 : assert isWellDefined f

i8 : assert isFactorizationMorphism f

i9 : g = map(C, C, 0, Degree => 13)

o9 = 0

o9 : ZZdFactorizationMap

i10 : assert isWellDefined g

i11 : assert(degree g == 13)

i12 : assert not isFactorizationMorphism g

i13 : assert isCommutative g

i14 : assert isHomogeneous g

i15 : assert(source g == C)

i16 : assert(target g == C)

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

i17 : assert(map(C, C, 1) === id_C)

map(ZZdFactorization,ZZdFactorization,ZZ) -- make the zero map or identity between ZZ/d-graded factorizations

The source of this document is in MatrixFactorizations/MatrixFactorizationsDOC.m2:2572:0.