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
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i2 : M = coker map(E^2, E^{-1}, matrix"ab;bc")
o2 = cokernel | ab |
| bc |
2
o2 : E-module, quotient of E
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i3 : presentation M
o3 = | ab |
| bc |
2 1
o3 : Matrix E <--- E
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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
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