# trivialHomologicalTruncation -- return the trivial truncation of a chain complex

## Synopsis

• Usage:
trivialHomologicalTruncation(ChainComplex,d,e)
• Inputs:
• Outputs:

## Description

Given a chain complex

... <- C_{k-1} <- C_k <- C_{k+1} <- ...

return the trivial truncation

0 <- C_d <- C_{d+1} <- ... < C_e <- 0

 i1 : E=ZZ/101[e_0,e_1,SkewCommutative=>true];F=res ideal vars E; i3 : C=dual res (coker transpose F.dd_3,LengthLimit=>8)[-3] 5 4 3 2 1 1 2 3 4 o3 = E <-- E <-- E <-- E <-- E <-- E <-- E <-- E <-- E -5 -4 -3 -2 -1 0 1 2 3 o3 : ChainComplex i4 : C1=trivialHomologicalTruncation(C,-2,2) 2 1 1 2 3 o4 = 0 <-- E <-- E <-- E <-- E <-- E <-- 0 -3 -2 -1 0 1 2 3 o4 : ChainComplex i5 : C2=trivialHomologicalTruncation(C1,-3,3) 2 1 1 2 3 o5 = 0 <-- 0 <-- E <-- E <-- E <-- E <-- E <-- 0 <-- 0 -4 -3 -2 -1 0 1 2 3 4 o5 : ChainComplex i6 : C3=trivialHomologicalTruncation(C2,2,2) 3 o6 = 0 <-- E <-- 0 1 2 3 o6 : ChainComplex

## Ways to use trivialHomologicalTruncation :

• "trivialHomologicalTruncation(ChainComplex,ZZ,ZZ)"

## For the programmer

The object trivialHomologicalTruncation is .