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resMinFlag -- gives a minimal free flag resolution of a differential module of degree 0

Synopsis

Description

Let $R$ be a positively graded ring with $R_0$ a field. Given a differential module $D$ of degree 0 with finitely generated homology, this method gives a portion of the minimal free flag resolution of $D$, using Algorithm 2.11 from the accompanying paper for this package, "The multigraded BGG correspondence in Macaulay2". As this resolution will often be infinite, the integer $k$ indicates how many steps of this algorithm will be applied.

i1 : R = ZZ/101[x, y];
i2 : k = coker vars R;
i3 : f = map(k, k, 0);

o3 : Matrix k <-- k
i4 : D = differentialModule(f);
i5 : F = resMinFlag(D, 3);
i6 : F.dd_0

o6 = {0} | 0 y x 0  |
     {1} | 0 0 0 x  |
     {1} | 0 0 0 -y |
     {2} | 0 0 0 0  |

             4      4
o6 : Matrix R  <-- R

See also

Ways to use resMinFlag :

For the programmer

The object resMinFlag is a method function.