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export { "katsura" }
katsura = method()
katsura (ZZ,Ring) := (n,kk) -> (
n = n-1;
R := kk[vars(0..n)];
L := gens R;
u := i -> (
if i < 0 then i = -i;
if i <= n then L_i else 0_R
);
f1 := -1 + sum for i from -n to n list u i;
toList prepend(f1, apply(0..n-1, i ->
- u i + sum(-n..n, j -> (u j) * (u (i-j)))
))
)
beginDocumentation()
doc ///
Key
katsura
(katsura,ZZ,Ring)
Headline
an example of a 0-dimensional square polynomial system
Usage
katsura(n,kk)
Inputs
n:ZZ
the number of variables
kk:Ring
the coefficient ring
Outputs
:List
of polynomials in the system
Description
Text
This system was solved in May 2020, using @TO 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.
Example
katsura(10,QQ)
///
-* TEST ///
F = katsura(10,QQ)
sols = solveSystem F
assert(#sols==512)
/// *-
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