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

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 ChainComplexExtras.m2:1000:0.

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

Description

See also

Functions with optional argument named LengthLimit:

Further information