Number of variables: 3
Variables:  x y z
Rank: 1

----------DIMENSION 2----------

NONSINGULAR SOLUTIONS
---------------
Path number: 0
Component number: 0
Estimated condition number: 1.000000e+00
0.176666586201415084108043587340e1 0.408439369901079221763591182583e0
-0.880355174945141279729536756802e0 -0.139928680262500099223734811422e1
-0.122411561077233477893723157748e1 -0.237577710027010463601800121102e0
Multiplicity: 1
Deflations needed: 0
---------------
Path number: 1
Component number: 0
Estimated condition number: 1.000000e+00
-0.143667968732422813473330289743e1 0.106850213432673560681771404275e1
0.190956172320737973604613955197e1 0.222288105684909774117959547275e0
-0.701278649409889919289394881035e0 -0.134594257845380627719489542855e0
Multiplicity: 1
Deflations needed: 0
---------------
Path number: 2
Component number: 0
Estimated condition number: 1.000000e+00
0.124844304069879534154190238675e1 -0.140885964041589717397782188145e1
-0.169457274890379613584681005726e1 0.278026979597582189855570756603e0
-0.126094460823408415460124139557e1 0.681058332005019007675627102239e-1
Multiplicity: 1
Deflations needed: 0
---------------
Path number: 3
Component number: 0
Estimated condition number: 1.000000e+00
-0.159977310817499902097563126140e1 0.211020399852192052466971290709e0
0.146549605945026733146483699780e1 0.960160350130052088971377534689e0
-0.730887635154161817417740898240e0 0.450259328690460630220778041630e-2
Multiplicity: 1
Deflations needed: 0


*************** input file needed to reproduce this run ***************

CONFIG

TrackType: 3;
CoeffBound: 4.165454000000e+01;
DegreeBound: 4.000000000000e+00;
SharpenDigits: 20;
SecurityMaxNorm: 1.000000000000e+10;
RandomSeed: 13423;

END;

INPUT

constant R,r;
R=2;
r=0.5;
variable_group x,y,z;
function f1;
f1=(x^2+y^2+z^2+R^2-r^2)^2-4*R^2*(x^2+y^2);

END;


*************** version information ***************
Bertini(TM) v1.5.1
GMP v6.1.1, MPFR v3.1.4-p1

Authors:
D.J. Bates, J.D. Hauenstein,
A.J. Sommese, C.W. Wampler

