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ExampleSystems (missing documentation) :: cyclic

cyclic -- an example of a square polynomial system

Description

Cyclic n-roots is a popular benchmark problem. It has finitely many solutions iff n is square free. In this case the number of solutions is less than the Bezout bound.

i1 : F = cyclic(5,QQ)

o1 = {a + b + c + d + e, a*b + b*c + c*d + a*e + d*e, a*b*c + b*c*d + a*b*e +
     ------------------------------------------------------------------------
     a*d*e + c*d*e, a*b*c*d + a*b*c*e + a*b*d*e + a*c*d*e + b*c*d*e,
     ------------------------------------------------------------------------
     a*b*c*d*e - 1}

o1 : List
i2 : sols = solveSystem F;
i3 : #sols

o3 = 70

Ways to use cyclic :