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# setupRings -- Sets up a complete intersection for experiments

## Synopsis

• Usage:
R = setupRings(c,d)
R = setupRings(ff)
• Inputs:
• c, an integer, desired codimension
• d, an integer, degree of homogeneous generators
• ff, , a regular sequence
• Optional inputs:
• Characteristic => ..., default value 101
• Randomize => ..., default value true
• Outputs:
• R, a list, List of rings R_0..R_c with R_i = S/(f_0..f_(i-1))

## Description

Makes a complete intersection f_0..f_{c-1} = x_0^d..x_{c-1}^d or, when Random=>true (the default), random linear combinations of these, in the polynomial ring ZZ/p[x_0..x_{c-1}], where p can be set by the optional argument Characteristic=>p. By default, p = 101.

 i1 : netList setupRings(2,2) +----------------------------+ | ZZ | o1 = |---[x ..x ] | |101 0 1 | +----------------------------+ | ZZ | |---[x ..x ] | |101 0 1 | |----------- | | 2 2 | |24x - 36x | | 0 1 | +----------------------------+ | ZZ | | ---[x ..x ] | | 101 0 1 | |----------------------------| | 2 2 2 2 | |(24x - 36x , - 30x - 29x )| | 0 1 0 1 | +----------------------------+ i2 : netList setupRings(2,2,Characteristic=>5) +-----------------------+ |ZZ | o2 = |--[x ..x ] | | 5 0 1 | +-----------------------+ |ZZ | |--[x ..x ] | | 5 0 1 | |---------- | | 2 2 | | 2x - 2x | | 0 1 | +-----------------------+ | ZZ | | --[x ..x ] | | 5 0 1 | |-----------------------| | 2 2 2 2 | |(2x - 2x , - x - 2x )| | 0 1 0 1 | +-----------------------+