# eco8 -- an 8-dimensional economics problem

## Synopsis

• Usage:
eco8(kk)
• Inputs:
• kk, a ring, the coefficient ring
• Outputs:
• a list, of 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 64 solutions found in 9.197 seconds (with a Bezout bound of 1458).

Reference: "Solving polynomial systems using continuation for engineering and scientific problems" by Alexander Morgan (p 148).

 i1 : eco8(QQ) o1 = {x x x + x x x + x x x + x x x + x x x + x x x + x x - 1, x x x 1 2 8 2 3 8 3 4 8 4 5 8 5 6 8 6 7 8 1 8 1 3 8 ------------------------------------------------------------------------ + x x x + x x x + x x x + x x x + x x - 2, x x x + x x x + x x x 2 4 8 3 5 8 4 6 8 5 7 8 2 8 1 4 8 2 5 8 3 6 8 ------------------------------------------------------------------------ + x x x + x x - 3, x x x + x x x + x x x + x x - 4, x x x + 4 7 8 3 8 1 5 8 2 6 8 3 7 8 4 8 1 6 8 ------------------------------------------------------------------------ x x x + x x - 5, x x x + x x - 6, x x - 7, x + x + x + x + x + 2 7 8 5 8 1 7 8 6 8 7 8 1 2 3 4 5 ------------------------------------------------------------------------ x + x + 1} 6 7 o1 : List