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isExact(ChainComplex,LengthLimit=>...) -- Option to check exactness only up to a particular homological degree

Description

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 : n =resolutionOfChainComplex (C, LengthLimit => 10)

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

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

o6 : ChainComplexMap
i7 : isExact(cone n, LengthLimit=> 10)

o7 = true
i8 : isExact(cone n, LengthLimit=> 12)

o8 = false

See also

Functions with optional argument named LengthLimit:

Further information


The source of this document is in /build/reproducible-path/macaulay2-1.25.05+ds/M2/Macaulay2/packages/ChainComplexExtras.m2:1026:0.