next | previous | forward | backward | up | top | index | toc | Macaulay2 website
ExampleSystems :: katsura

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

Synopsis

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

o1 : List

Ways to use katsura :

For the programmer

The object katsura is a method function.