lorentz -- equilibrium points of a 4-dimensional Lorentz attractor

Synopsis

Usage:

lorentz(kk)
Inputs:
- kk, a ring, the coefficient ring
Outputs:
- a list, of the 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 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.

i1 : lorentz(QQ)

o1 = {x x  - x x  - x  + 1, x x  - x x  - x  + 1, - x x  + x x  - x  + 1,
       1 2    1 3    4       2 3    2 4    1         1 3    3 4    2     
     ------------------------------------------------------------------------
     x x  - x x  - x  + 1}
      1 4    2 4    3

o1 : List

Ways to use lorentz :

lorentz(Ring)

For the programmer

The object lorentz is a method function.