i1 : R = ZZ/101[a,b,c]/ideal{a^3+b^3+c^3,a*b*c} o1 = R o1 : QuotientRing |
i2 : K1 = koszulComplexDGA(ideal vars R,Variable=>"Y") o2 = {Ring => R } Underlying algebra => R[Y , Y , Y ] 1 2 3 Differential => {a, b, c} o2 : DGAlgebra |
i3 : K2 = koszulComplexDGA(ideal {b,c},Variable=>"T") o3 = {Ring => R } Underlying algebra => R[T , T ] 1 2 Differential => {b, c} o3 : DGAlgebra |
i4 : f = dgAlgebraMap(K2,K1,matrix{{0,T_1,T_2}}) o4 = map(R[T , T ],R[Y , Y , Y ],{0, T , T , a, b, c}) 1 2 1 2 3 1 2 o4 : DGAlgebraMap |
i5 : g = dgAlgebraMap(K1,K2,matrix{{Y_2,Y_3}}) o5 = map(R[Y , Y , Y ],R[T , T ],{Y , Y , a, b, c}) 1 2 3 1 2 2 3 o5 : DGAlgebraMap |
i6 : toComplexMap g 1 1 o6 = 0 : R <--------- R : 0 | 1 | 3 2 1 : R <--------------- R : 1 {1} | 0 0 | {1} | 1 0 | {1} | 0 1 | 3 1 2 : R <------------- R : 2 {2} | 0 | {2} | 0 | {2} | 1 | o6 : ChainComplexMap |
i7 : HHg = HH g Finding easy relations : -- used 0.0134072 seconds ZZ ---[a, b, c] ZZ 101 o7 = map(---[X , X ],------------[X ],{X , 0, 0, 0}) 101 1 2 3 1 1 (c, b, a ) ZZ ---[a, b, c] ZZ 101 o7 : RingMap ---[X , X ] <--- ------------[X ] 101 1 2 3 1 (c, b, a ) |
One can also supply the second argument (a ZZ) in order to obtain the map on homology in a specified degree. (This is currently not available).