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, a module, 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

Ways to use setupModules:

setupModules(List,Module)

For the programmer

The object setupModules is a method function.

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

Synopsis

Description

See also

Ways to use setupModules:

For the programmer