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CompleteIntersectionResolutions :: TateResolution

TateResolution -- TateResolution of a module over an exterior algebra

Synopsis

Description

Forms an interval, lower..upper, of a doubly infinite free resolution of a a Cohen-Macaulay module over a Gorenstein ring, such as any module over an exterior algebra (actually, any module over any ring.)
i1 : E = ZZ/101[a,b,c, SkewCommutative=>true]

o1 = E

o1 : PolynomialRing
i2 : M = coker map(E^2, E^{-1}, matrix"ab;bc")

o2 = cokernel | ab |
              | bc |

                            2
o2 : E-module, quotient of E
i3 : presentation M

o3 = | ab |
     | bc |

             2       1
o3 : Matrix E  <--- E
i4 : TateResolution(M,2,7)

             0  1  2 3 4 5 6 7 8 9
o4 = total: 22 16 11 7 4 2 1 2 5 9
        -8: 21 15 10 6 3 1 . . . .
        -7:  1  1  1 1 1 1 1 . . .
        -6:  .  .  . . . . . 2 5 9

o4 : BettiTally

Ways to use TateResolution :