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 |