A filter problem

                                                         filter [1]
Fabien Seyfert (INRIA, MIAOU)

Related to a filter design problem.

Characteristics:

• Number of variables: 9.

• The number of complex roots is 192.

Example 1:

vars:= [a,b,m[1],m[2],m[3],m[4],m[5],m[6],m[7]];
[ m[2]*m[4]*m[6]-1/100, a*m[4]*b-7/500, a^2+m[1]^2-2/25,
b^2+m[7]^2-37/50, m[3]^2+m[5]^2+m[4]^2+m[2]^2+m[6]^2-9401/10000,
m[4]^2*m[6]^2+m[2]^2*m[4]^2+m[3]^2*m[6]^2+m[2]^2*m[5]^2+m[3]^2*m[5]^2
+m[2]^2*m[6]^2-38589/1000000,
m[1]*m[3]*m[5]*m[7]-m[6]*m[1]*m[3]*b+m[2]*m[6]*a*b-m[2]*a*m[5]*m[7]+81/10000,
 -m[1]*m[2]*m[3]*m[4]*b-a*m[4]*m[5]*m[6]*m[7]+a*m[4]*b*m[6]^2
+a*m[2]^2*m[4]*b+39/25000,
-m[4]^2*m[7]^2-m[3]^2*m[7]^2+2*m[5]*m[6]*b*m[7]-m[2]^2*m[7]^2-m[5]^2*m[7]^2
-m[3]^2*b^2-b^2*m[6]^2-m[2]^2*b^2+27173/40000 ];

Problem: Find an approximation of the (resp. real ) roots.

References

[1] D. Bini and B. Mourrain. Polynomial test suite. 1996.