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naiveTruncation(Complex,ZZ) -- compute the hard truncation of a chain complex

Description

This method returns the naive truncation of $C$ by truncating the low homological degrees if $n$ is positive (i.e. from left) and high homological degrees if $n$ is negative (i.e. from right).

i1 : B = QQ[a..d];
 
i2 : C = (koszulComplex vars B)[2]

      1      4      6      4      1
o2 = B  <-- B  <-- B  <-- B  <-- B
                                  
     -2     -1     0      1      2

o2 : Complex
 
i3 : naiveTruncation(C, 10)

o3 = 0
      
     0

o3 : Complex
 
i4 : naiveTruncation(C, 2)

      6      4      1
o4 = B  <-- B  <-- B
                    
     0      1      2

o4 : Complex
 
i5 : naiveTruncation(C, 1)

      4      6      4      1
o5 = B  <-- B  <-- B  <-- B
                           
     -1     0      1      2

o5 : Complex
 
i6 : naiveTruncation(C, 0)

      1      4      6      4      1
o6 = B  <-- B  <-- B  <-- B  <-- B
                                  
     -2     -1     0      1      2

o6 : Complex
 
i7 : naiveTruncation(C,-1)

      1      4      6      4
o7 = B  <-- B  <-- B  <-- B
                           
     -2     -1     0      1

o7 : Complex
 
i8 : naiveTruncation(C,-2)

      1      4      6
o8 = B  <-- B  <-- B
                    
     -2     -1     0

o8 : Complex
 
i9 : naiveTruncation(C,-10)

o9 = 0
      
     0

o9 : Complex

See also

Ways to use this method:

The source of this document is in SpectralSequences.m2:2677:0.