i1 : R = ZZ/101[a,b,c,d]/ideal{a^3,b^3,c^3-d^4} o1 = R o1 : QuotientRing |
i2 : A = koszulComplexDGA(R) o2 = {Ring => R } Underlying algebra => R[T ..T ] 1 4 Differential => {a, b, c, d} o2 : DGAlgebra |
i3 : A.diff o3 = map(R[T ..T ],R[T ..T ],{a, b, c, d, a, b, c, d}) 1 4 1 4 o3 : RingMap R[T ..T ] <--- R[T ..T ] 1 4 1 4 |
i4 : prune homology(1,A) o4 = cokernel | d c b a 0 0 0 0 0 0 0 0 | | 0 0 0 0 d c b a 0 0 0 0 | | 0 0 0 0 0 0 0 0 d c b a | 3 o4 : R-module, quotient of R |
i5 : B = adjoinVariables(A,{a^2*T_1}) o5 = {Ring => R } Underlying algebra => R[T ..T ] 1 5 2 Differential => {a, b, c, d, a T } 1 o5 : DGAlgebra |
i6 : B.diff 2 o6 = map(R[T ..T ],R[T ..T ],{a, b, c, d, a T , a, b, c, d}) 1 5 1 5 1 o6 : RingMap R[T ..T ] <--- R[T ..T ] 1 5 1 5 |
i7 : prune homology(1,B) o7 = cokernel | d c b a 0 0 0 0 | | 0 0 0 0 d c b a | 2 o7 : R-module, quotient of R |
The object adjoinVariables is a method function.