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isFree(ZZdFactorization) -- whether a ZZ/d-graded factorization consists of free modules

Description

This method checks whether the given representation of each module $C_i$ is free. To determine whether the factorization $C$ is isomorphic to a free factorization, use prune.

The following example demonstrates that the presentation of a module might not reveal the property of being free.

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

      2      2      2
o2 = S  <-- S  <-- S
                    
     0      1      0

o2 : ZZdFactorization
 
i3 : M' = coker (M++M)_[0]

o3 = cokernel | 1 0 | <-- cokernel | 1 0 | <-- cokernel | 1 0 |
              | 0 1 |              | 0 1 |              | 0 1 |
              | 0 0 |              | 0 0 |              | 0 0 |
              | 0 0 |              | 0 0 |              | 0 0 |
                                                
     0                    1                    0

o3 : ZZdFactorization
 
i4 : prune M'

      2      2      2
o4 = S  <-- S  <-- S
                    
     0      1      0

o4 : ZZdFactorization
 
i5 : assert not isFree M'
 
i6 : assert isFree prune M

See also

Ways to use this method:

The source of this document is in MatrixFactorizations/MatrixFactorizationsDOC.m2:5332:0.