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ZZdFactorizationMap | ZZdFactorizationMap -- join or concatenate maps horizontally

Description

Given ZZ/d-graded factorization maps with the same target, this method constructs the associated map from the direct sum of the sources to the target.

First, we define some non-trivial maps of factorizations.

i1 : S = ZZ/101[a,b];
 
i2 : R = S/(a^3+b^3);
 
i3 : m = ideal vars R

o3 = ideal (a, b)

o3 : Ideal of R
 
i4 : use S;
 
i5 : C1 = tailMF m

      2      2      2
o5 = S  <-- S  <-- S
                    
     0      1      0

o5 : ZZdFactorization
 
i6 : C2 = randomTailMF(a^3+b^3, 2, 4, 2)

      4      4      4
o6 = S  <-- S  <-- S
                    
     0      1      0

o6 : ZZdFactorization
 
i7 : D = tailMF (m^2)

      3      3      3
o7 = S  <-- S  <-- S
                    
     0      1      0

o7 : ZZdFactorization
 
i8 : f = randomFactorizationMap(D, C1, InternalDegree => 1)

          3                            2
o8 = 0 : S  <------------------------ S  : 0
               {3} | -13 -28a-47b |
               {3} | -43 38a+2b   |
               {3} | -15 16a+22b  |

          3                       2
     1 : S  <------------------- S  : 1
               {5} | 45  -47 |
               {5} | -34 47  |
               {5} | -48 19  |

o8 : ZZdFactorizationMap
 
i9 : g = randomFactorizationMap(D, C2, InternalDegree => 3)

          3                              4
o9 = 0 : S  <-------------------------- S  : 0
               {3} | -16 -23 -17 36 |
               {3} | 7   39  -11 35 |
               {3} | 15  43  48  11 |

          3                           4
     1 : S  <----------------------- S  : 1
               {5} | 0 0 -38 11  |
               {5} | 0 0 33  46  |
               {5} | 0 0 40  -28 |

o9 : ZZdFactorizationMap
 
i10 : h = f|g

           3                                           6
o10 = 0 : S  <--------------------------------------- S  : 0
                {3} | -13 -28a-47b -16 -23 -17 36 |
                {3} | -43 38a+2b   7   39  -11 35 |
                {3} | -15 16a+22b  15  43  48  11 |

           3                                   6
      1 : S  <------------------------------- S  : 1
                {5} | 45  -47 0 0 -38 11  |
                {5} | -34 47  0 0 33  46  |
                {5} | -48 19  0 0 40  -28 |

o10 : ZZdFactorizationMap
 
i11 : assert isWellDefined h
 
i12 : assert(source h === source f ++ source g)
 
i13 : assert(target h === target f)

See also

Ways to use this method:

The source of this document is in MatrixFactorizations/MatrixFactorizationsDOC.m2:4162:0.