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resBE -- Buchsbaum-Eisenbud resolution

Synopsis

Usage:

resBE(A)
Inputs:
- A, a matrix, skew-symmetric
Outputs:
- a chain complex,

Description

Returns the Buchsbaum-Eisenbud resolution of the ideal of submaximal pfaffians of a skew-symmetric matrix A. The syzygy matrix will be A.

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

i2 : A=matrix {{0,x_1,x_2,x_3,x_4},{-x_1,0,0,z_1,z_2},{-x_2,0,0,z_3,z_4},{-x_3,-z_1,-z_3,0,0},{-x_4,-z_2,-z_4,0,0}}

o2 = | 0    x_1  x_2  x_3 x_4 |
     | -x_1 0    0    z_1 z_2 |
     | -x_2 0    0    z_3 z_4 |
     | -x_3 -z_1 -z_3 0   0   |
     | -x_4 -z_2 -z_4 0   0   |

             5      5
o2 : Matrix R  <-- R

i3 : resBE A

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

o3 : ChainComplex

See also

resolution -- projective resolution

Ways to use resBE:

resBE(Matrix)

For the programmer

The object resBE is a method function.