toricLL -- computes the BGG functor of a module over the Koszul dual exterior algebra of a multigraded polynomial ring

• Usage:

  toricLL N

• Inputs:
  • N, a module, a module over the Koszul dual exterior algebra of a multigraded polynomial ring
• Outputs:
  • a complex, a complex of modules over a multigraded polynomial ring, the result of applying the BGG functor L to N

i1 : S = ring hirzebruchSurface 3

o1 = S

o1 : PolynomialRing

i2 : E = dualRingToric S

o2 = E

o2 : PolynomialRing, 4 skew commutative variable(s)

i3 : C = toricLL(coker matrix{{e_0, e_1}})

                 1                 2                 1
o3 = (QQ[x ..x ])  <-- (QQ[x ..x ])  <-- (QQ[x ..x ])
          0   3             0   3             0   3
                                          
     -2                -1                0

o3 : Complex