# setupModules -- Creates a list of modules and maps over complete intersection for experiments

## Synopsis

• Usage:
(MM, kk, p) = setupModules(R,M)
• Inputs:
• R, a list, of complete intersections R_i = S/(f_0..f_(i-1))
• M, , over the ring R_{c-1} where c = length R.
• Outputs:
• MM, a list, of c+1 modules M_i over R_i
• kk, a list, of residue class modules k_i of R_i
• p, a list, of maps, p_i_j: R_j to R_i the projection

## Description

This is useful for setting up an experiment. For example, we conjecture that the regularity of Ext_{R_i}(M_i,k_i) is a non-decreasing function of i. Here ring M = R_{c-1} and M_i = pushForward(p_{(c-1)}_i, M).

 i1 : needsPackage "CompleteIntersectionResolutions" -- for "evenExtModule" o1 = CompleteIntersectionResolutions o1 : Package i2 : R =setupRings(3,2);--codims 0..3, degrees = 2 i3 : MM0 = coker random(R_3^2, R_3^{3: -1}); i4 : (M,kkk,p) = setupModules(R,MM0); i5 : apply(3, j->regularity evenExtModule M_(j+1)) o5 = {1, 2, 3} o5 : List