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export{"wood"}
wood = method()
wood (Ring) := kk -> (
x := symbol x;
R := kk[x_1..x_4];
{ 200*x_1^3-200*x_1*x_2+x_1-1,
-100*x_1^2+ 1.10100000000000e02*x_2+ 9.9*x_4-20,
180*x_3^3-180*x_3*x_4+x_3-1,
-90*x_3^2+ 9.9*x_2+ 1.00100000000000e02*x_4-20
}
)
beginDocumentation()
doc ///
Key
wood
(wood, Ring)
Headline
system derived from optimizing the Wood function
Usage
wood(kk)
Inputs
kk:Ring
the coefficient ring
Outputs
:List
of the polynomials in the system
Description
Text
This system was solved in May 2020, using @TO 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.
Example
wood(RR_53)
///
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