-- -*- M2-comint -*- hash: 11913268809499872385

i1 : Q = QQ[x,y,z,w]

o1 = Q

o1 : PolynomialRing

i2 : I = ideal (w^2, y*w+z*w, x*w, y*z+z^2, y^2+z*w, x*y+x*z, x^2+z*w)

             2                         2   2                    2
o2 = ideal (w , y*w + z*w, x*w, y*z + z , y  + z*w, x*y + x*z, x  + z*w)

o2 : Ideal of Q

i3 : R = Q/I

o3 = R

o3 : QuotientRing

i4 : KR = koszulComplexDGA R

o4 = {Ring => R                      }
      Underlying algebra => R[T ..T ]
                               1   4
      Differential => {x, y, z, w}

o4 : DGAlgebra

i5 : cxKR = toComplex KR

      1      4      6      4      1
o5 = R  <-- R  <-- R  <-- R  <-- R
                                  
     0      1      2      3      4

o5 : Complex

i6 : HKR = HH(KR)
 -- used 0.176348s (cpu); 0.145378s (thread); 0s (gc)
Finding easy relations           : 
o6 = HKR

o6 : QuotientRing

i7 : degList = first entries vars Q / degree / first

o7 = {1, 1, 1, 1}

o7 : List

i8 : M = Ext^4(Q^1/I,Q^{-(sum degList)}) ** R

o8 = cokernel {-2} | 0     z2-zw 0      0  -w 0  z x 0    0  0 |
              {-2} | 0     zw    -z2-zw 0  0  -w w 0 -y-z x  x |
              {-2} | z2+zw 0     0      -w 0  -x 0 w 0    -z y |

                            3
o8 : R-module, quotient of R

i9 : HKM = homologyModule(KR,M);

i10 : hsHKR = value numerator reduceHilbert hilbertSeries HKR

              2     2 4     2 3     3 5     3 4     4 6
o10 = 1 + 7T T  + 6T T  + 8T T  + 8T T  + 3T T  + 3T T
            0 1     0 1     0 1     0 1     0 1     0 1

o10 : ZZ[T ..T ]
          0   1

i11 : hsHKM = value numerator reduceHilbert hilbertSeries HKM

        -2             -1     2       2     3 2
o11 = 3T   + 3T  + 8T T   + 8T T  + 6T  + 7T T
        1      0     0 1      0 1     0     0 1

o11 : ZZ[T ..T ]
          0   1

i12 : AA = ring hsHKR

o12 = AA

o12 : PolynomialRing

i13 : e = numgens Q

o13 = 4

i14 : hsHKR == T_0^e*T_1^e*sub(hsHKM, {T_0 => T_0^(-1), T_1 => T_1^(-1)})

o14 = false

i15 : 
