i1 : R = ZZ/101[a,b,c,d]
o1 = R
o1 : PolynomialRing
|
i2 : A = koszulComplexDGA(R)
o2 = {Ring => R }
Underlying algebra => R[T ..T ]
1 4
Differential => {a, b, c, d}
o2 : DGAlgebra
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i3 : S = R/ideal{a^3,a*b*c}
o3 = S
o3 : QuotientRing
|
i4 : B = A ** S
o4 = {Ring => S }
Underlying algebra => S[T ..T ]
1 4
Differential => {a, b, c, d}
o4 : DGAlgebra
|
i5 : Bdd = toComplex B
1 4 6 4 1
o5 = S <-- S <-- S <-- S <-- S
0 1 2 3 4
o5 : ChainComplex
|
i6 : Bdd.dd
1 4
o6 = 0 : S <--------------- S : 1
| a b c d |
4 6
1 : S <----------------------------- S : 2
{1} | -b -c 0 -d 0 0 |
{1} | a 0 -c 0 -d 0 |
{1} | 0 a b 0 0 -d |
{1} | 0 0 0 a b c |
6 4
2 : S <----------------------- S : 3
{2} | c d 0 0 |
{2} | -b 0 d 0 |
{2} | a 0 0 d |
{2} | 0 -b -c 0 |
{2} | 0 a 0 -c |
{2} | 0 0 a b |
4 1
3 : S <-------------- S : 4
{3} | -d |
{3} | c |
{3} | -b |
{3} | a |
o6 : ChainComplexMap
|