tateResolution -- finite piece of the Tate resolution

Synopsis

• Usage:

  tateResolution(m,E,l,h)

• Inputs:
  • m, a matrix, a presentation matrix for a module
  • E, a polynomial ring, exterior algebra
  • l, an integer, lower cohomological degree
  • h, an integer, upper bound on the cohomological degree
• Outputs:
  • a chain complex, a finite piece of the Tate resolution

Description

i1 : S = ZZ/32003[x_0..x_2]; 

i2 : E = ZZ/32003[e_0..e_2, SkewCommutative=>true];

i3 : m = matrix{{x_0,x_1}};

             1       2
o3 : Matrix S  <--- S

i4 : regularity coker m

o4 = 0

i5 : T = tateResolution(m,E,-2,4)

      1      1      1      1      1      1      1
o5 = E  <-- E  <-- E  <-- E  <-- E  <-- E  <-- E
                                                
     0      1      2      3      4      5      6

o5 : ChainComplex

i6 : betti T

            0 1 2 3 4 5 6
o6 = total: 1 1 1 1 1 1 1
        -4: 1 1 1 1 1 1 1

o6 : BettiTally

i7 : T.dd_1

o7 = {-4} | e_2 |

             1       1
o7 : Matrix E  <--- E

See also

• symExt -- the first differential of the complex R(M)