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 |
The object katsura is a method function.