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View File Name : eco8.m2

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)
    ///