# isQuism -- Test to see if the ChainComplexMap is a quasiisomorphism.

## Synopsis

• Usage:
isQuism(phi)
• Inputs:
• phi,
• Outputs:
• Boolean

## Description

A quasiisomorphism is a chain map that is an isomorphism in homology.Mapping cones currently do not work properly for complexes concentratedin one degree, so isQuism could return bad information in that case.
 i1 : R = ZZ/101[a,b,c] o1 = R o1 : PolynomialRing i2 : kRes = res coker vars R 1 3 3 1 o2 = R <-- R <-- R <-- R <-- 0 0 1 2 3 4 o2 : ChainComplex i3 : multBya = extend(kRes,kRes,matrix{{a}}) 1 1 o3 = 0 : R <--------- R : 0 | a | 3 3 1 : R <----------------- R : 1 {1} | a b c | {1} | 0 0 0 | {1} | 0 0 0 | 3 3 2 : R <----- R : 2 0 1 1 3 : R <----- R : 3 0 4 : 0 <----- 0 : 4 0 o3 : ChainComplexMap i4 : isQuism(multBya) o4 = false i5 : F = extend(kRes,kRes,matrix{{1_R}}) 1 1 o5 = 0 : R <--------- R : 0 | 1 | 3 3 1 : R <----------------- R : 1 {1} | 1 0 0 | {1} | 0 1 0 | {1} | 0 0 1 | 3 3 2 : R <----------------- R : 2 {2} | 1 0 0 | {2} | 0 1 0 | {2} | 0 0 1 | 1 1 3 : R <------------- R : 3 {3} | 1 | 4 : 0 <----- 0 : 4 0 o5 : ChainComplexMap i6 : isQuism(F) o6 = true

## Ways to use isQuism :

• "isQuism(ChainComplexMap)"

## For the programmer

The object isQuism is .