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KustinMiller :: shiftComplex

shiftComplex -- Shift the indexing of a chain complex

Synopsis

Description

Shifts the chain complex cc by p, i.e., returns a new chain complex CS with csi = cci+p and the same differentials as cc.

i1 : R = QQ[x_1..x_4,z_1..z_4, T]

o1 = R

o1 : PolynomialRing
i2 : I =  ideal(z_2*z_3-z_1*z_4,x_4*z_3-x_3*z_4,x_2*z_2-x_1*z_4,x_4*z_1-x_3*z_2,x_2*z_1-x_1*z_3)

o2 = ideal (z z  - z z , x z  - x z , x z  - x z , x z  - x z , x z  - x z )
             2 3    1 4   4 3    3 4   2 2    1 4   4 1    3 2   2 1    1 3

o2 : Ideal of R
i3 : cc = res I

      1      5      5      1
o3 = R  <-- R  <-- R  <-- R  <-- 0
                                  
     0      1      2      3      4

o3 : ChainComplex
i4 : betti cc

            0 1 2 3
o4 = total: 1 5 5 1
         0: 1 . . .
         1: . 5 5 .
         2: . . . 1

o4 : BettiTally
i5 : cs=shiftComplex(cc,-3)

      1      5      5      1
o5 = R  <-- R  <-- R  <-- R  <-- 0
                                  
     3      4      5      6      7

o5 : ChainComplex
i6 : betti cs

            3 4 5 6
o6 = total: 1 5 5 1
        -3: 1 . . .
        -2: . 5 5 .
        -1: . . . 1

o6 : BettiTally

See also

Ways to use shiftComplex :

  • shiftComplex(ChainComplex,ZZ)