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ChainComplexExtras :: trivialHomologicalTruncation

trivialHomologicalTruncation -- return the trivial truncation of a chain complex

Synopsis

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=removeZeroTrailingTerms C2

      2      1      1      2      3
o6 = E  <-- E  <-- E  <-- E  <-- E
                                  
     -2     -1     0      1      2

o6 : ChainComplex
i7 : C4=trivialHomologicalTruncation(C3,2,2)

            3
o7 = 0 <-- E  <-- 0
                   
     1     2      3

o7 : ChainComplex

Ways to use trivialHomologicalTruncation :

For the programmer

The object trivialHomologicalTruncation is a method function.