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).

See also: http://homepages.math.uic.edu/~jan/Demo/eco8.html.

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

Ways to use eco8 :

eco8(Ring)

For the programmer

The object eco8 is a method function.