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export{"lorentz"}
lorentz = method()
lorentz (Ring) := kk -> (
x := symbol x;
R := kk[x_1..x_4];
{ x_1*x_2-x_1*x_3-x_4+ 1,
x_2*x_3-x_2*x_4-x_1+ 1,
-x_1*x_3+x_3*x_4-x_2+ 1,
x_1*x_4-x_2*x_4-x_3+ 1
}
)
beginDocumentation()
doc ///
Key
lorentz
(lorentz, Ring)
Headline
equilibrium points of a 4-dimensional Lorentz attractor
Usage
lorentz(kk)
Inputs
kk:Ring
the coefficient ring
Outputs
:List
of the 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 12 solutions found in 0.0562 seconds (with a Bezout bound of 16).
Reference: "Solving polynomial systems" by Tien-Yien Li (pages 33-39).
See also: http://homepages.math.uic.edu/~jan/Demo/lorentz.html.
Example
lorentz(QQ)
///
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