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 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 .