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

Description

A ZZ/d-graded factorization map $f : C \to D$ of degree $d$ is a sequence of of maps $f_i : C_i \to D_{i+d}$. This method returns $d$.

The degree of the differential of a factorization is always -1.

i1 : S = ZZ/101[a,b,c];
 
i2 : F = randomTailMF(a^3 + b^3 + c^3)

      6      6      6
o2 = S  <-- S  <-- S
                    
     0      1      0

o2 : ZZdFactorization
 
i3 : assert(degree dd^F == -1)
 
i4 : R = S/(a^2+b^2+c^2);
 
i5 : m = ideal vars R

o5 = ideal (a, b, c)

o5 : Ideal of R
 
i6 : C = tailMF m

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

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

      8      8      8
o7 = S  <-- S  <-- S
                    
     0      1      0

o7 : ZZdFactorization
 
i8 : f = randomFactorizationMap(C, D, Cycle=>true, Degree => -1)

          4                                               8
o8 = 1 : S  <------------------------------------------- S  : 0
               {4} | 30  30  42  -24 27  30  1   33  |
               {4} | -27 12  47  -30 30  -24 38  28  |
               {4} | 30  1   33  -27 -24 -30 -30 -42 |
               {4} | 24  -38 -28 30  30  -27 12  47  |

          4                                              8
     0 : S  <------------------------------------------ S  : 1
               {3} | 30  27 -12 -47 -30 -24 38  28  |
               {3} | 24  30 1   33  27  30  30  42  |
               {3} | -27 30 30  42  24  -30 -1  -33 |
               {3} | -30 24 -38 -28 -30 27  -12 -47 |

o8 : ZZdFactorizationMap
 
i9 : assert(degree f == -1)

See also

Ways to use this method:

The source of this document is in MatrixFactorizations/MatrixFactorizationsDOC.m2:2915:0.