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# target(ZZdFactorizationMap) -- get the target of a map of ZZ/d-graded factorizations

- Function: target
- Usage:
    `C = target f`
- Inputs:
  - f, a map of ZZ/d-graded factorizations,
- Outputs:
  - C, a ZZ/d graded factorization,

## Description

Given a ZZ/d-graded factorization map $f : C \to D$ this method returns the ZZ/d-graded factorization $D$.

    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 = randomFactorizationMap(C, D, Cycle=>true)

              4                                                                                                                     8
    o6 = 0 : S  <----------------------------------------------------------------------------------------------------------------- S  : 0
                   {3} | -20a-4b+47c -33a-29b+30c 45a-43b+33c -45a-20b+12c -42a+30b+5c  16a+33b+41c  29a-8b+20c   -21a+9b+16c  |
                   {3} | -43a-39b+7c 39a+36b+41c  2a+16b-23c  -39a-15b-41c -48a+12b-18c -17a-14b-42c -10a+9b+40c  -47a-3b-16c  |
                   {3} | -33a+3b+13c 13a-29b-30c  14a-39b+29c 41a-40b-15c  -11a-22b-21c -41a-46b+5c  24a+42b+3c   -38a+24b-47c |
                   {3} | 39a-14b-7c  18a+19b+47c  24a+34b+8c  25a-8b-15c   -18a-14b+5c  -a+42b+38c   -22a+25b-23c -13a-46b+30c |

              4                                                                                                                      8
         1 : S  <------------------------------------------------------------------------------------------------------------------ S  : 1
                   {4} | -11a-15b+38c 33a+14b-15c  -13a-9b-23c  -14a+3b-18c 41a-12b-7c   -41a+39b-5c  24a-36b-30c  -38a-16b+39c |
                   {4} | 42a+8b-42c   -20a+42b-41c -33a+25b+9c  45a-46b+22c 45a-14b+7c   -16a-14b+18c -29a+19b+19c 21a+34b+19c  |
                   {4} | -48a+40b+41c 43a-46b+12c  -39a+42b+38c -2a+24b+25c -39a-22b+47c -17a+3b-5c   -10a-29b-8c  -47a-39b-18c |
                   {4} | -18a+20b-5c  -39a+33b+15c -18a-8b-34c  -24a+9b+18c 25a+30b-13c  -a-4b-21c    -22a-29b-24c -13a-43b-15c |

    o6 : ZZdFactorizationMap

    i7 : source f

          8      8      8
    o7 = S  <-- S  <-- S

         0      1      0

    o7 : ZZdFactorization

    i8 : assert isWellDefined f

    i9 : assert isFactorizationMorphism f

    i10 : assert(source f == D)

    i11 : assert(target f == C)

The differential in a factorization is a map of factorizations.

    i12 : use S

    o12 = S

    o12 : PolynomialRing

    i13 : F = randomTailMF(a^3 + b^3 + c^3)

           15      15      15
    o13 = S   <-- S   <-- S

          0       1       0

    o13 : ZZdFactorization

    i14 : source dd^F == F

    o14 = true

    i15 : target dd^F == F

    o15 = true

    i16 : degree dd^F == -1

    o16 = true

## See also

- Making ZZdFactorizations -- Information about the basic constructors
- source(ZZdFactorizationMap) -- get the source of a map of ZZ/d-graded factorizations
- randomFactorizationMap(ZZdFactorization,ZZdFactorization) -- a random map of ZZ/d-graded factorizations

## Ways to use this method:

- target(ZZdFactorizationMap) -- get the target of a map of ZZ/d-graded factorizations

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/MatrixFactorizations/MatrixFactorizationsDOC.m2:2879:0.