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

## Synopsis

• Usage:
resMinFlag(D, k)
• Inputs:
• Outputs:

## 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

• differentialModule(Complex) -- converts a complex into a differential module
• unfold -- converts a differential module into a 1-periodic complex
• resDM -- uses a "killing cycles"-style construction to find a free resolution of a differential module
• foldComplex -- converts a chain complex into a differential module
• minimizeDM -- minimizes a square matrix or a differential module

## Ways to use resMinFlag :

• resMinFlag(DifferentialModule,ZZ)

## For the programmer

The object resMinFlag is .