HH DGAlgebraMap -- Computes the homomorphism in homology associated to a DGAlgebraMap.

Synopsis

• Function: homology
• Usage:
homologyPhi = homology(phi,n)
• Inputs:
• Outputs:
• homologyPhi, , The map on homology defined by phi.

Description

 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 ] 1 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 ], {0, T , T , a, b, c}) 1 2 1 3 1 2 o4 : DGAlgebraMap i5 : g = dgAlgebraMap(K1,K2,matrix{{Y_2,Y_3}}) o5 = map (R[Y ..Y ], R[T ..T ], {Y , Y , a, b, c}) 1 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 0.0163247 seconds ZZ ---[a..c] ZZ 101 o7 = map (---[X ..X ], ----------[X ], {X , 0, 0, 0}) 101 1 2 3 1 1 (c, b, a ) ZZ ---[a..c] ZZ 101 o7 : RingMap ---[X ..X ] <--- ----------[X ] 101 1 2 3 1 (c, b, a )