katsura -- an example of a 0-dimensional square polynomial system

Synopsis

Usage:

katsura(n,kk)
Inputs:
- n, an integer, the number of variables
- kk, a ring, the coefficient ring
Outputs:
- a list, of polynomials in the system

Description

This system was solved in May 2020, using solveSystem in Macaulay2 v1.15 with an Intel(R) Core(TM) i5-5250U CPU at 1.60GHz.

There were 512 solutions found in 2.804 seconds with 10 variables.

The unknowns stand for the values (in [0,1]) of a distribution function of a field created by a mixture of a ferro-antiferro-magnetic bond at some points.

i1 : katsura(10,QQ)

                                                           2     2     2  
o1 = {a + 2b + 2c + 2d + 2e + 2f + 2g + 2h + 2i + 2j - 1, a  + 2b  + 2c  +
     ------------------------------------------------------------------------
       2     2     2     2     2     2     2                                 
     2d  + 2e  + 2f  + 2g  + 2h  + 2i  + 2j  - a, 2a*b + 2b*c + 2c*d + 2d*e +
     ------------------------------------------------------------------------
                                            2                              
     2e*f + 2f*g + 2g*h + 2h*i + 2i*j - b, b  + 2a*c + 2b*d + 2c*e + 2d*f +
     ------------------------------------------------------------------------
                                                                             
     2e*g + 2f*h + 2g*i + 2h*j - c, 2b*c + 2a*d + 2b*e + 2c*f + 2d*g + 2e*h +
     ------------------------------------------------------------------------
                       2                                                   
     2f*i + 2g*j - d, c  + 2b*d + 2a*e + 2b*f + 2c*g + 2d*h + 2e*i + 2f*j -
     ------------------------------------------------------------------------
                                                             2              
     e, 2c*d + 2b*e + 2a*f + 2b*g + 2c*h + 2d*i + 2e*j - f, d  + 2c*e + 2b*f
     ------------------------------------------------------------------------
                                                                             
     + 2a*g + 2b*h + 2c*i + 2d*j - g, 2d*e + 2c*f + 2b*g + 2a*h + 2b*i + 2c*j
     ------------------------------------------------------------------------
           2
     - h, e  + 2d*f + 2c*g + 2b*h + 2a*i + 2b*j - i}

o1 : List

Ways to use katsura :

katsura(ZZ,Ring)

For the programmer

The object katsura is a method function.