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# isQuasiIsomorphism(...,LengthLimit=>...) -- Option to check quasi-isomorphism only up to a certain point

- Usage:
    `t = isQuasiIsomorphism(F, LengthLimit => n)`
- Inputs:
  - F, a chain complex map,
  - n, an integer,
- Outputs:
  - t, a Boolean value,

## Description

Useful, for example, when checking whether a map is a resolution of a complex in cases where the actual resolution is infinite

    i1 : kk= ZZ/101

    o1 = kk

    o1 : QuotientRing

    i2 : S = kk[a,b,c]

    o2 = S

    o2 : PolynomialRing

    i3 : R = S/ideal(a^3)

    o3 = R

    o3 : QuotientRing

    i4 : M = R^1/ideal(a)

    o4 = cokernel | a |

                                1
    o4 : R-module, quotient of R

    i5 : C = chainComplex{map(M,R^0,0)}

    o5 = M <-- 0

         0     1

    o5 : ChainComplex

    i6 : m=cartanEilenbergResolution (C, LengthLimit => 10)

                                        1
    o6 = 0 : cokernel | a | <--------- R  : 0
                               | 1 |

                       1
         1 : 0 <----- R  : 1
                  0

    o6 : ChainComplexMap

    i7 : isQuasiIsomorphism(m, LengthLimit=> 10)

    o7 = true

    i8 : isQuasiIsomorphism(m, LengthLimit => 12)

    o8 = false

## See also

- isExact(ChainComplex)

## Functions with optional argument named LengthLimit:

- cartanEilenbergResolution(...,LengthLimit=>...) -- How many steps to compute
- isExact(ChainComplex,LengthLimit=>...) -- Option to check exactness only up to a particular homological degree
- isQuasiIsomorphism(...,LengthLimit=>...) -- Option to check quasi-isomorphism only up to a certain point
- koszulComplex(...,LengthLimit=>...) -- How many steps to compute
- `minimalBetti(...,LengthLimit=>...)` -- see minimalBetti -- minimal betti numbers of (the minimal free resolution of) a homogeneous ideal or module
- resolution(...,LengthLimit=>...) -- stop when the resolution reaches this length
- resolutionOfChainComplex(...,LengthLimit=>...) -- How many steps to compute
- taylorResolution(...,LengthLimit=>...) -- How many steps to compute

## Further information

- Default value: infinity
- Function: isQuasiIsomorphism -- Test to see if the ChainComplexMap is a quasi-isomorphism.
- Option key: LengthLimit -- an optional argument

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/ChainComplexExtras.m2:1000:0.