Macaulay2 » Documentation
Packages » ChainComplexExtras :: isQuasiIsomorphism(...,Concentration=>...)
next | previous | forward | backward | up | index | toc

isQuasiIsomorphism(...,Concentration=>...) -- Option to check quasi-isomorphism only up to a certain homological degree

Description

Useful, for example, when checking whether a map is a resolution of a complex in cases where the actual resolution is infinite. Only the upper bound of the Concentration tuple participates in the cone-exactness check on the ChainComplexMap overload. This option is inherited from the Complexes package's isQuasiIsomorphism; the legacy LengthLimit option of this package has been retired in favour of it. Migration: the previous LengthLimit => n is now Concentration => (-infinity, n).

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, Concentration => (-infinity, 10))

o7 = true
 
i8 : isQuasiIsomorphism(m, Concentration => (-infinity, 12))

o8 = false

See also

Further information

  • Default value: (-infinity,infinity)
  • Function: isQuasiIsomorphism -- whether a map of complexes is a quasi-isomorphism
  • Option key: Concentration (missing documentation)

The source of this document is in ChainComplexExtras.m2:1289:0.