BGG :: bgg

# bgg -- the ith differential of the complex R(M)

## Synopsis

• Usage:
bgg(i,M,E)
• Inputs:
• i, an integer, the cohomological index
• E, , exterior algebra
• Outputs:
• , a matrix representing the ith differential

## Description

This function takes as input an integer i and a finitely generated graded S-module M, and returns the ith map in R(M), which is an adjoint of the multiplication map between M_i and M_{i+1}.
 i1 : S = ZZ/32003[x_0..x_2];  i2 : E = ZZ/32003[e_0..e_2, SkewCommutative=>true]; i3 : M = coker matrix {{x_0^2, x_1^2, x_2^2}}; i4 : bgg(1,M,E) o4 = {-2} | e_1 e_0 0 | {-2} | e_2 0 e_0 | {-2} | 0 e_2 e_1 | 3 3 o4 : Matrix E <--- E i5 : bgg(2,M,E) o5 = {-3} | e_2 e_1 e_0 | 1 3 o5 : Matrix E <--- E