BGGL -- Exterior module to linear complex

Synopsis

Usage:

L = BGGL(P,S)
Inputs:
- P, a module, module over an exterior algebra
- S, a ring, polynomial ring on the same number of vars
Outputs:
- L, a chain complex, linear chain complex over S corresponding to P

Implements the left adjoint BGG functor. The more primitive function SymExt does this only for linearly presented exterior modules.

i1 : E = ZZ/101[a,b,c,d, SkewCommutative => true]

o1 = E

o1 : PolynomialRing, 4 skew commutative variable(s)

i2 : P = E^1/ideal(a*b,c)

o2 = cokernel | ab c |

                            1
o2 : E-module, quotient of E

i3 : betti res P

            0 1 2 3  4  5
o3 = total: 1 2 4 7 11 16
         0: 1 1 1 1  1  1
         1: . 1 3 6 10 15

o3 : BettiTally

i4 : hf(0..3, P)

o4 = {1, 3, 2, 0}

o4 : List

i5 : S = ZZ/101[x,y,z,w]

o5 = S

o5 : PolynomialRing

i6 : betti BGGL(P,S)

            -2 -1 0
o6 = total:  2  3 1
         0:  2  3 1

o6 : BettiTally

This script really belongs in the BGG package.