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export{"eco8"}
eco8 = method()
eco8 (Ring) := kk -> (
x := symbol x;
R := kk[x_1..x_8];
{ (x_1 + x_1*x_2 + x_2*x_3 + x_3*x_4 + x_4*x_5 + x_5*x_6 + x_6*x_7)*x_8 - 1,
(x_2 + x_1*x_3 + x_2*x_4 + x_3*x_5 + x_4*x_6 + x_5*x_7)*x_8 - 2,
(x_3 + x_1*x_4 + x_2*x_5 + x_3*x_6 + x_4*x_7)*x_8 - 3,
(x_4 + x_1*x_5 + x_2*x_6 + x_3*x_7)*x_8 - 4,
(x_5 + x_1*x_6 + x_2*x_7)*x_8 - 5,
(x_6 + x_1*x_7)*x_8 - 6,
x_7*x_8 - 7,
x_1 + x_2 + x_3 + x_4 + x_5 + x_6 + x_7 + 1 }
)
beginDocumentation()
doc ///
Key
eco8
(eco8,Ring)
Headline
an 8-dimensional economics problem
Usage
eco8(kk)
Inputs
kk:Ring
the coefficient ring
Outputs
:List
of 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 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.
Example
eco8(QQ)
///
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