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 matrix, 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 |
     +-----------------------+

Ways to use setupRings :

setupRings(Matrix)
setupRings(ZZ,ZZ)

For the programmer

The object setupRings is a method function with options.

setupRings -- Sets up a complete intersection for experiments

Synopsis

Description

See also

Ways to use setupRings :

For the programmer