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export{"wright"}
wright = method()
wright (Ring) := kk -> (
x := symbol x;
R := kk[x_1..x_5];
{ x_1^2-x_1+x_2+x_3+x_4+x_5-10,
x_2^2+x_1-x_2+x_3+x_4+x_5-10,
x_3^2+x_1+x_2-x_3+x_4+x_5-10,
x_4^2+x_1+x_2+x_3-x_4+x_5-10,
x_5^2+x_1+x_2+x_3+x_4-x_5-10
}
)
beginDocumentation()
doc ///
Key
wright
(wright, Ring)
Headline
system of A.H. Wright
Usage
wright(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 32 solutions found in 0.0944 seconds (with a Bezout bound of 32).
Reference: "Computation of all solutions to a system of polynomial equations" by M. Kojima and S. Mizuno (pages 131-157),
"Finding all solutions to a system of polynomial equations" by A.H. Wright (pages 125-133), and "A simple homotopy method for determining all isolated solutions to
polynomial systems" by W. Zulehner (pages 167-177).
See also: http://homepages.math.uic.edu/~jan/Demo/wright.html.
Example
wright(QQ)
///
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