# 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).

 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 .