Macaulay2 » Documentation
Packages » MatrixFactorizations :: map(ZZdFactorization,ZZdFactorization,ZZ)
next | previous | forward | backward | up | index | toc

# 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)

## See also

- ZZdFactorizationMap -- the class of all maps between ZZ/d-graded factorizations
- isWellDefined(ZZdFactorizationMap) -- whether a map of ZZ/d-graded factorizations is well-defined
- degree(ZZdFactorizationMap) -- get the degree of a map of ZZ/d-graded factorizations
- isCommutative(ZZdFactorizationMap) -- whether a ZZ/d-graded factorization map commutes with the differentials
- source(ZZdFactorizationMap) -- get the source of a map of ZZ/d-graded factorizations
- target(ZZdFactorizationMap) -- get the target of a map of ZZ/d-graded factorizations
- id _ ZZdFactorization -- the identity map of a ZZ/d-graded factorization

## Ways to use this method:

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

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/MatrixFactorizations/MatrixFactorizationsDOC.m2:2572:0.