wood -- system derived from optimizing the Wood function

Synopsis

Usage:

wood(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 9 solutions found in 0.141 seconds (with a Bezout bound of 36).

Reference: "Testing unconstrained optimization software" by J.J. More, B.S. Garbow and K.E. Hilstrom (pages 17-41).

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

i1 : wood(RR_53)

          3                           2                             3  
o1 = {200x  - 200x x  + x  - 1, - 100x  + 110.1x  + 9.9x  - 20, 180x  -
          1       1 2    1            1         2       4           3  
     ------------------------------------------------------------------------
                            2
     180x x  + x  - 1, - 90x  + 9.9x  + 100.1x  - 20}
         3 4    3           3       2         4

o1 : List

Ways to use wood :

wood(Ring)

For the programmer

The object wood is a method function.