Number of variables: 5
Variables:  x y z u v
Rank: 3

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

NONSINGULAR SOLUTIONS
---------------
Path number: 0
Component number: 0
Estimated condition number: 1.186789e+01
0.223827723634170447506053169187e1 -0.650507858024091319458701357352e0
0.799032963426681740850461274131e0 0.169834037890692305205342786872e1
0.129037457980681790905056739449e1 0.767118217923605402153728884821e-1
0.173205080756887729352744634145e1 0.126217744835361888865876570445e-28
-0.350787246254301778628617869122e-170 -0.220639859670577482062874338207e-170
Multiplicity: 1
Deflations needed: 0
---------------
Path number: 3
Component number: 0
Estimated condition number: 9.201539e+00
-0.830950703494544369757559239238e0 -0.693746071819102745668207879787e0
-0.212366775460515348072735429290e1 0.139340198453861324700984045262e1
0.175242788508991162959751399990e1 0.135963031495619853999201732928e1
0.173205080756887729352744634147e1 0.126217744835361888865876570445e-28
-0.212774390360477657121595010237e-174 0.211430932676759787512483110217e-174
Multiplicity: 1
Deflations needed: 0
---------------
Path number: 1
Component number: 1
Estimated condition number: 7.964173e+00
0.199016767737112875375623717190e1 0.476867584633307796910445269732e0
0.622395047311394881006171117429e0 0.304075673773021657887082315298e0
0.616566614408689041213664920848e0 -0.184619410147454909148400298002e1
0.471744995585953984362559426652e-174 -0.809369364989492287684648143665e-173
-0.173205080756887729352744634155e1 0.000000000000000000000000000000e0
Multiplicity: 1
Deflations needed: 0
---------------
Path number: 2
Component number: 1
Estimated condition number: 7.880151e+01
-0.473076213599112780304801783605e-1 -0.154218286730233111288991090556e0
-0.126605216585294980416941836079e1 -0.472708109616461273563184858078e0
0.672830927683723010594248126663e0 -0.900328450115978726504486883885e0
0.119548394701402074861751131278e-173 0.712962056125754589333229257879e-174
-0.173205080756887729352744634150e1 -0.126217744835361888865876570445e-28
Multiplicity: 1
Deflations needed: 0
---------------
Path number: 4
Component number: 2
Estimated condition number: 6.647536e+00
-0.260338077853085838659713687375e1 0.458930204177639066581864675882e-1
-0.170613667221459078693518841216e1 0.701801298760228894869725919409e0
0.454347068053987385851209217254e0 0.289832604243968066799480280255e1
-0.335864021279138721288203517229e-106 0.821224482740152411547695176574e-107
0.173205080756887729352744634147e1 -0.126217744835361888865876570445e-28
Multiplicity: 1
Deflations needed: 0
---------------
Path number: 7
Component number: 2
Estimated condition number: 1.551012e+01
0.912444984600424960222225294234e0 -0.459317976956415897231261066804e0
0.168950500405334979105093048610e1 0.522182263200999334518596206254e0
-0.305594732999741512179587422513e0 0.151549458247923479395717527710e1
0.205568098885721828539420176915e-171 0.295301950190440184889436318845e-171
0.173205080756887729352744634153e1 0.126217744835361888865876570445e-28
Multiplicity: 1
Deflations needed: 0
---------------
Path number: 5
Component number: 3
Estimated condition number: 8.398773e+00
0.103018659411351418069638259722e1 0.774381324757798225790492560510e0
0.185255960221487033368960662632e1 -0.739271455737679939976205352949e0
-0.992413853391948343925213929494e0 -0.576157993480803424668007919665e0
-0.173205080756887729352744634155e1 0.000000000000000000000000000000e0
0.259367462020405939900796869536e-173 0.152631713766610257728523923611e-175
Multiplicity: 1
Deflations needed: 0
---------------
Path number: 6
Component number: 3
Estimated condition number: 7.083850e+00
-0.218558886487989023664850963588e1 0.479096946449818534384796256659e0
-0.118821359773919451286021877697e1 -0.129711978159006774537484338556e1
-0.612238734358123269243332622795e0 0.807113930060631988424105917776e0
-0.173205080756887729352744634150e1 0.126217744835361888865876570445e-28
-0.153672678660040890354367206151e-174 0.257161696838762585009622374764e-174
Multiplicity: 1
Deflations needed: 0


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

CONFIG

TrackType: 3;
ImagThreshold: 1.000000000000e-04;
CoeffBound: 8.194187000000e+00;
DegreeBound: 2.000000000000e+00;
SharpenDigits: 24;
RandomSeed: 13423;

END;

INPUT

variable_group x,y,z,u,v;
function f1,f2,crit;
r_squared=x^2+y^2+z^2;
f1=r_squared-1-u^2;
f2=r_squared-4+v^2;
crit=-4*u*v;

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

