Macaulay2 » Documentation
Packages » Complexes :: target(ComplexMap)
next | previous | forward | backward | up | index | toc

# target(ComplexMap) -- get the target of a map of chain complexes

- Function: target
- Usage:
    `C = target f`
- Inputs:
  - f, a map of complexes,
- Outputs:
  - C, a complex,

## Description

Given a complex map $f : C \to D$ this method returns the chain complex $D$.

    i1 : R = ZZ/101[a..d]

    o1 = R

    o1 : PolynomialRing

    i2 : I = ideal(a^2, b^2, c^2)

                 2   2   2
    o2 = ideal (a , b , c )

    o2 : Ideal of R

    i3 : J = I + ideal(a*b*c)

                 2   2   2
    o3 = ideal (a , b , c , a*b*c)

    o3 : Ideal of R

    i4 : FI = freeResolution I

          1      3      3      1
    o4 = R  <-- R  <-- R  <-- R

         0      1      2      3

    o4 : Complex

    i5 : FJ = freeResolution J

          1      4      6      3
    o5 = R  <-- R  <-- R  <-- R

         0      1      2      3

    o5 : Complex

    i6 : f = randomComplexMap(FJ, FI, Cycle=>true)

              1              1
    o6 = 0 : R  <---------- R  : 0
                   | 24 |

              4                        3
         1 : R  <-------------------- R  : 1
                   {2} | 24 0  0  |
                   {2} | 0  24 0  |
                   {2} | 0  0  24 |
                   {3} | 0  0  0  |

              6                        3
         2 : R  <-------------------- R  : 2
                   {4} | 24 0  0  |
                   {4} | 0  0  0  |
                   {4} | 0  0  0  |
                   {4} | 0  24 0  |
                   {4} | 0  0  0  |
                   {4} | 0  0  24 |

              3                    1
         3 : R  <---------------- R  : 3
                   {5} | 24c  |
                   {5} | -24b |
                   {5} | 24a  |

    o6 : ComplexMap

    i7 : target f

          1      4      6      3
    o7 = R  <-- R  <-- R  <-- R

         0      1      2      3

    o7 : Complex

    i8 : assert isWellDefined f

    i9 : assert isComplexMorphism f

    i10 : assert(target f == FJ)

    i11 : assert(source f == FI)

The differential in a complex is a map of chain complexes.

    i12 : kk = coker vars R

    o12 = cokernel | a b c d |

                                 1
    o12 : R-module, quotient of R

    i13 : F = freeResolution kk

           1      4      6      4      1
    o13 = R  <-- R  <-- R  <-- R  <-- R

          0      1      2      3      4

    o13 : Complex

    i14 : target dd^F == F

    o14 = true

    i15 : source dd^F == F

    o15 = true

    i16 : degree dd^F == -1

    o16 = true

## See also

- Making chain complexes -- information about the basic constructors
- source(ComplexMap) -- get the source of a map of chain complexes
- freeResolution(Ideal) -- compute a free resolution of a module or ideal
- randomComplexMap(Complex,Complex) -- a random map of chain complexes

## Ways to use this method:

- target(ComplexMap) -- get the target of a map of chain complexes

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Complexes/ChainComplexMapDoc.m2:679:0.