12
s1**2 + c1**2 - 1;
s2**2 + c2**2 - 1;
s3**2 + c3**2 - 1;
s4**2 + c4**2 - 1;
s5**2 + c5**2 - 1;
s6**2 + c6**2 - 1;
s2*c5*s6 - s3*c5*s6 - s4*c5*s6 + c2*c6 + c3*c6 + c4*c6 - 0.4077;
c1*c2*s5 + c1*c3*s5 + c1*c4*s5 + s1*c5 - 1.9115;
s2*s5 + s3*s5 + s4*s5 - 1.9791;
c1*c2 + c1*c3 + c1*c4 + c1*c2 + c1*c3 + c1*c2 - 4.0616;
s1*c2 + s1*c3 + s1*c4 + s1*c2 + s1*c3 + s1*c2 - 1.7172;
s2 + s3 + s4 + s2 + s3 + s2 - 3.9701;
TITLE : kinematics problem
ROOT COUNTS :
total degree : 4608
4-homogeneous Bezout number = 320.
with partition : {s1 c1 }{s2 c2 s3 c3 s4 c4 }{s5 c5 }{s6 c6 }
mixed volume : 192
REFERENCES :
P. Van Hentenryck, D. McAllester and D. Kapur:
`Solving Polynomial Systems Using a Branch and Prune Approach'
SIAM J. Numerical Analysis, Vol. 34, No. 2, pp 797-827, 1997.
H. Hong and V. Stahl:
`Safe Starting Regions by Fixed Points and Tightening'
Computing 53(3-4): 322-335, 1995.
THE SOLUTIONS :
48 12
===========================================================
solution 1 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : 3.89415083856842E-01 7.43554779769399E-31
c1 : 9.21062371647420E-01 -4.69637677015175E-31
s2 : 8.12447299105426E-01 5.16786840383107E-01
c2 : 9.06404061572963E-01 -4.63217333728468E-01
s3 : 1.23611304332968E+00 -1.24952222803037E+00
c3 : 1.46469772617762E+00 1.05451841454651E+00
s4 : -9.39467983975633E-01 9.48683934911419E-01
c4 : -1.23891712639201E+00 -7.19384827907607E-01
s5 : 1.71925348920786E+00 -3.34751466405344E-01
c5 : 4.06076515006418E-01 1.41727631460228E+00
s6 : 4.23667748161563E-01 2.26075213480995E-01
c6 : 9.39157471197499E-01 -1.01985853861664E-01
== err : 5.571E-15 = rco : 4.123E-02 = res : 1.110E-15 ==
solution 2 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : -3.89415083856842E-01 -1.18072606435204E-30
c1 : -9.21062371647420E-01 -3.50923201498787E-31
s2 : -3.08457430339590E+00 -1.12748434939333E+00
c2 : 1.18298149617247E+00 -2.93986783637119E+00
s3 : 5.51926701023123E+00 2.78748170612766E+00
c3 : -2.82446248609854E+00 5.44700306623819E+00
s4 : 2.18528888972524E+00 -2.19251036407534E+00
c4 : -2.30971002700246E+00 -2.07440262336281E+00
s5 : 4.22761702728453E-01 4.87287884168480E-02
c5 : -9.07833668459021E-01 2.26921145125287E-02
s6 : -3.30199010468440E-01 7.54084055570752E-02
c6 : -9.47283466803091E-01 -2.62854591772632E-02
== err : 9.493E-15 = rco : 3.996E-03 = res : 7.944E-15 ==
solution 3 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : 3.89415083856842E-01 8.27588134152995E-31
c1 : 9.21062371647420E-01 -1.44611330308050E-31
s2 : 8.12447299105426E-01 5.16786840383107E-01
c2 : 9.06404061572963E-01 -4.63217333728468E-01
s3 : 1.23611304332968E+00 -1.24952222803037E+00
c3 : 1.46469772617762E+00 1.05451841454651E+00
s4 : -9.39467983975633E-01 9.48683934911419E-01
c4 : -1.23891712639201E+00 -7.19384827907607E-01
s5 : 1.71925348920786E+00 -3.34751466405344E-01
c5 : 4.06076515006418E-01 1.41727631460228E+00
s6 : -8.61466466923939E-01 -3.64813495876627E-01
c6 : -7.52059005889243E-01 4.17885552753148E-01
== err : 5.571E-15 = rco : 3.290E-02 = res : 1.110E-15 ==
solution 4 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : -3.89415083856842E-01 4.02930062304817E-31
c1 : -9.21062371647420E-01 6.56787281431271E-31
s2 : -3.08457430339590E+00 -1.12748434939333E+00
c2 : 1.18298149617247E+00 -2.93986783637119E+00
s3 : 5.51926701023123E+00 2.78748170612766E+00
c3 : -2.82446248609853E+00 5.44700306623819E+00
s4 : 2.18528888972524E+00 -2.19251036407534E+00
c4 : -2.30971002700246E+00 -2.07440262336281E+00
s5 : 4.22761702728453E-01 4.87287884168480E-02
c5 : -9.07833668459021E-01 2.26921145125287E-02
s6 : 4.01843190733972E-01 -8.02819201166972E-02
c6 : 9.19889752968952E-01 3.50702275287029E-02
== err : 7.525E-15 = rco : 3.881E-03 = res : 3.553E-15 ==
solution 5 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : -3.89415083856842E-01 1.52372162131122E-31
c1 : -9.21062371647420E-01 2.08273397831169E-31
s2 : -1.66814300276214E+00 -2.60968969868373E+00
c2 : 2.74607605173298E+00 -1.58529317041035E+00
s3 : 3.42882833936714E+00 5.05527774520946E+00
c3 : -5.12313078715411E+00 3.38341539896057E+00
s4 : 2.11687232955215E+00 -2.28148639436773E+00
c4 : -2.40165709157283E+00 -2.01095128669009E+00
s5 : 5.09486080364478E-01 -2.15618991998570E-02
c5 : 8.60843598054382E-01 1.27613047635805E-02
s6 : -5.50180407961115E-01 2.65168683281356E-01
c6 : 8.91295858167372E-01 1.63683711765720E-01
== err : 5.368E-15 = rco : 4.424E-03 = res : 1.421E-14 ==
solution 6 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : -3.89415083856842E-01 3.59925302899856E-31
c1 : -9.21062371647420E-01 6.01691585860594E-31
s2 : -1.66814300276214E+00 -2.60968969868373E+00
c2 : 2.74607605173298E+00 -1.58529317041035E+00
s3 : 3.42882833936714E+00 5.05527774520946E+00
c3 : -5.12313078715411E+00 3.38341539896057E+00
s4 : 2.11687232955215E+00 -2.28148639436773E+00
c4 : -2.40165709157283E+00 -2.01095128669009E+00
s5 : 5.09486080364478E-01 -2.15618991998571E-02
c5 : 8.60843598054382E-01 1.27613047635805E-02
s6 : 4.66761459278284E-01 -2.34817061898099E-01
c6 : -9.22704020497345E-01 -1.18785170585817E-01
== err : 8.764E-15 = rco : 4.478E-03 = res : 1.005E-14 ==
solution 7 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : 3.89415083856842E-01 1.08281829476888E-30
c1 : 9.21062371647420E-01 3.43478743748823E-31
s2 : -3.08457430339590E+00 -1.12748434939333E+00
c2 : -1.18298149617247E+00 2.93986783637119E+00
s3 : 5.51926701023123E+00 2.78748170612766E+00
c3 : 2.82446248609853E+00 -5.44700306623819E+00
s4 : 2.18528888972524E+00 -2.19251036407534E+00
c4 : 2.30971002700246E+00 2.07440262336281E+00
s5 : 4.22761702728453E-01 4.87287884168481E-02
c5 : 9.07833668459021E-01 -2.26921145125288E-02
s6 : -4.01843190733972E-01 8.02819201166972E-02
c6 : -9.19889752968952E-01 -3.50702275287029E-02
== err : 8.527E-15 = rco : 3.881E-03 = res : 5.024E-15 ==
solution 8 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : -3.89415083856842E-01 -7.80184136256078E-31
c1 : -9.21062371647420E-01 1.04184090966962E-32
s2 : 8.12447299105426E-01 5.16786840383107E-01
c2 : -9.06404061572963E-01 4.63217333728468E-01
s3 : 1.23611304332968E+00 -1.24952222803037E+00
c3 : -1.46469772617762E+00 -1.05451841454651E+00
s4 : -9.39467983975633E-01 9.48683934911419E-01
c4 : 1.23891712639201E+00 7.19384827907607E-01
s5 : 1.71925348920786E+00 -3.34751466405344E-01
c5 : -4.06076515006418E-01 -1.41727631460228E+00
s6 : 8.61466466923939E-01 3.64813495876627E-01
c6 : 7.52059005889243E-01 -4.17885552753148E-01
== err : 5.571E-15 = rco : 3.977E-02 = res : 1.110E-15 ==
solution 9 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : 3.89415083856842E-01 2.33893526194247E-31
c1 : 9.21062371647420E-01 2.88527590435391E-31
s2 : -3.08457430339590E+00 -1.12748434939333E+00
c2 : -1.18298149617247E+00 2.93986783637119E+00
s3 : 5.51926701023123E+00 2.78748170612766E+00
c3 : 2.82446248609854E+00 -5.44700306623819E+00
s4 : 2.18528888972524E+00 -2.19251036407534E+00
c4 : 2.30971002700246E+00 2.07440262336281E+00
s5 : 4.22761702728453E-01 4.87287884168481E-02
c5 : 9.07833668459021E-01 -2.26921145125288E-02
s6 : 3.30199010468440E-01 -7.54084055570751E-02
c6 : 9.47283466803091E-01 2.62854591772632E-02
== err : 6.034E-15 = rco : 3.996E-03 = res : 3.553E-15 ==
solution 10 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : -3.89415083856842E-01 -6.44778291352428E-31
c1 : -9.21062371647420E-01 5.53495702086169E-31
s2 : 8.12447299105426E-01 5.16786840383107E-01
c2 : -9.06404061572963E-01 4.63217333728468E-01
s3 : 1.23611304332968E+00 -1.24952222803037E+00
c3 : -1.46469772617762E+00 -1.05451841454651E+00
s4 : -9.39467983975633E-01 9.48683934911419E-01
c4 : 1.23891712639201E+00 7.19384827907607E-01
s5 : 1.71925348920786E+00 -3.34751466405344E-01
c5 : -4.06076515006418E-01 -1.41727631460228E+00
s6 : -4.23667748161564E-01 -2.26075213480995E-01
c6 : -9.39157471197499E-01 1.01985853861664E-01
== err : 5.571E-15 = rco : 4.176E-02 = res : 1.110E-15 ==
solution 11 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : 3.89415083856842E-01 -7.97834684292006E-32
c1 : 9.21062371647420E-01 -2.69033276898011E-31
s2 : -1.66814300276214E+00 -2.60968969868373E+00
c2 : -2.74607605173297E+00 1.58529317041035E+00
s3 : 3.42882833936714E+00 5.05527774520946E+00
c3 : 5.12313078715411E+00 -3.38341539896057E+00
s4 : 2.11687232955215E+00 -2.28148639436773E+00
c4 : 2.40165709157283E+00 2.01095128669009E+00
s5 : 5.09486080364479E-01 -2.15618991998570E-02
c5 : -8.60843598054382E-01 -1.27613047635804E-02
s6 : -4.66761459278284E-01 2.34817061898099E-01
c6 : 9.22704020497345E-01 1.18785170585816E-01
== err : 5.986E-15 = rco : 4.478E-03 = res : 1.281E-14 ==
solution 12 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : 3.89415083856842E-01 -2.02259011496046E-31
c1 : 9.21062371647420E-01 -1.81471703246161E-31
s2 : -1.66814300276214E+00 -2.60968969868373E+00
c2 : -2.74607605173298E+00 1.58529317041035E+00
s3 : 3.42882833936714E+00 5.05527774520946E+00
c3 : 5.12313078715411E+00 -3.38341539896057E+00
s4 : 2.11687232955215E+00 -2.28148639436773E+00
c4 : 2.40165709157283E+00 2.01095128669009E+00
s5 : 5.09486080364478E-01 -2.15618991998570E-02
c5 : -8.60843598054382E-01 -1.27613047635805E-02
s6 : 5.50180407961115E-01 -2.65168683281356E-01
c6 : -8.91295858167372E-01 -1.63683711765720E-01
== err : 5.368E-15 = rco : 4.424E-03 = res : 1.421E-14 ==
solution 13 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : -3.89415083856842E-01 5.37680945305336E-72
c1 : -9.21062371647420E-01 3.11288968334668E-71
s2 : 7.30467265581231E-01 -9.23679266040325E-70
c2 : -6.82947709502184E-01 -7.60677042621444E-70
s3 : 5.01061086394408E-01 1.77491309945004E-69
c3 : -8.65411917933452E-01 1.55757680155819E-69
s4 : 7.76576030467492E-01 -7.24454326306137E-70
c4 : -6.30023546308670E-01 -9.68957661434458E-70
s5 : 9.85556337261790E-01 -3.73546762001602E-71
c5 : 1.69347884790821E-01 2.26391976970668E-70
s6 : -9.89421385196769E-01 -2.74500272076935E-71
c6 : -1.45070060713112E-01 1.90169260655361E-70
== err : 1.136E-15 = rco : 2.341E-02 = res : 5.967E-16 ==
solution 14 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : -3.89415083856842E-01 -1.71451025968357E-30
c1 : -9.21062371647419E-01 2.82321487431262E-31
s2 : -3.08457430339590E+00 1.12748434939333E+00
c2 : 1.18298149617247E+00 2.93986783637119E+00
s3 : 5.51926701023123E+00 -2.78748170612766E+00
c3 : -2.82446248609854E+00 -5.44700306623819E+00
s4 : 2.18528888972524E+00 2.19251036407534E+00
c4 : -2.30971002700246E+00 2.07440262336281E+00
s5 : 4.22761702728453E-01 -4.87287884168480E-02
c5 : -9.07833668459021E-01 -2.26921145125288E-02
s6 : -3.30199010468440E-01 -7.54084055570750E-02
c6 : -9.47283466803091E-01 2.62854591772632E-02
== err : 8.816E-15 = rco : 3.996E-03 = res : 1.123E-14 ==
solution 15 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : -3.89415083856842E-01 5.52714787526045E-75
c1 : -9.21062371647420E-01 3.75846055517710E-74
s2 : 7.30467265581230E-01 1.41494985606667E-73
c2 : -6.82947709502185E-01 1.59181858807501E-73
s3 : 5.01061086394409E-01 -3.00676844414168E-73
c3 : -8.65411917933451E-01 -2.82989971213335E-73
s4 : 7.76576030467492E-01 1.59181858807501E-73
c4 : -6.30023546308670E-01 -8.84343660041671E-75
s5 : 9.85556337261790E-01 6.63257745031253E-75
c5 : 1.69347884790822E-01 2.12242478410001E-73
s6 : 9.73527905464624E-01 -5.52714787526045E-75
c6 : -2.28568189566401E-01 -9.94886617546880E-75
== err : 8.407E-16 = rco : 2.388E-02 = res : 2.220E-16 ==
solution 16 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : -3.89415083856842E-01 -2.38933027226999E-30
c1 : -9.21062371647420E-01 -1.60384880690501E-30
s2 : -3.08457430339590E+00 1.12748434939333E+00
c2 : 1.18298149617247E+00 2.93986783637119E+00
s3 : 5.51926701023123E+00 -2.78748170612766E+00
c3 : -2.82446248609854E+00 -5.44700306623819E+00
s4 : 2.18528888972524E+00 2.19251036407534E+00
c4 : -2.30971002700246E+00 2.07440262336281E+00
s5 : 4.22761702728453E-01 -4.87287884168480E-02
c5 : -9.07833668459021E-01 -2.26921145125288E-02
s6 : 4.01843190733972E-01 8.02819201166972E-02
c6 : 9.19889752968952E-01 -3.50702275287030E-02
== err : 9.843E-15 = rco : 3.881E-03 = res : 7.105E-15 ==
solution 17 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : 3.89415083856842E-01 1.92031089696496E-30
c1 : 9.21062371647420E-01 -8.61507960085025E-31
s2 : -3.08457430339590E+00 1.12748434939333E+00
c2 : -1.18298149617247E+00 -2.93986783637119E+00
s3 : 5.51926701023123E+00 -2.78748170612767E+00
c3 : 2.82446248609854E+00 5.44700306623819E+00
s4 : 2.18528888972524E+00 2.19251036407534E+00
c4 : 2.30971002700246E+00 -2.07440262336281E+00
s5 : 4.22761702728452E-01 -4.87287884168479E-02
c5 : 9.07833668459021E-01 2.26921145125287E-02
s6 : -4.01843190733972E-01 -8.02819201166973E-02
c6 : -9.19889752968952E-01 3.50702275287030E-02
== err : 9.407E-15 = rco : 3.881E-03 = res : 3.553E-15 ==
solution 18 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : 3.89415083856842E-01 -2.76357393763022E-76
c1 : 9.21062371647420E-01 9.67250878170578E-76
s2 : 7.30467265581231E-01 -2.60881379712293E-73
c2 : 6.82947709502184E-01 2.07820760109793E-73
s3 : 5.01061086394408E-01 5.04075886223753E-73
c3 : 8.65411917933452E-01 -4.51015266621252E-73
s4 : 7.76576030467492E-01 -2.16664196710209E-73
c4 : 6.30023546308670E-01 2.96255126113960E-73
s5 : 9.85556337261790E-01 -1.07779383567579E-74
c5 : -1.69347884790821E-01 -6.74312040781774E-74
s6 : -9.73527905464624E-01 9.05070464573898E-75
c6 : 2.28568189566400E-01 4.75334717272398E-74
== err : 1.136E-15 = rco : 2.709E-02 = res : 5.967E-16 ==
solution 19 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : 3.89415083856842E-01 -7.28386846774837E-31
c1 : 9.21062371647420E-01 2.24693952239863E-32
s2 : -3.08457430339590E+00 1.12748434939333E+00
c2 : -1.18298149617247E+00 -2.93986783637119E+00
s3 : 5.51926701023123E+00 -2.78748170612766E+00
c3 : 2.82446248609853E+00 5.44700306623819E+00
s4 : 2.18528888972524E+00 2.19251036407534E+00
c4 : 2.30971002700246E+00 -2.07440262336281E+00
s5 : 4.22761702728453E-01 -4.87287884168481E-02
c5 : 9.07833668459021E-01 2.26921145125288E-02
s6 : 3.30199010468440E-01 7.54084055570751E-02
c6 : 9.47283466803091E-01 -2.62854591772632E-02
== err : 8.527E-15 = rco : 3.996E-03 = res : 5.024E-15 ==
solution 20 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : 3.89415083856842E-01 -1.69793982728001E-72
c1 : 9.21062371647420E-01 -9.62165902125338E-72
s2 : 7.30467265581231E-01 3.98449879468375E-70
c2 : 6.82947709502184E-01 -3.16948767758935E-70
s3 : 5.01061086394408E-01 -7.78788400779097E-70
c3 : 8.65411917933452E-01 7.24454326306137E-70
s4 : 7.76576030467492E-01 3.44115804995415E-70
c4 : 6.30023546308670E-01 -4.89006670256642E-70
s5 : 9.85556337261790E-01 2.40541475531335E-71
c5 : -1.69347884790821E-01 1.43758905376374E-70
s6 : 9.89421385196769E-01 -1.50692159671101E-71
c6 : 1.45070060713112E-01 1.04140309406507E-70
== err : 1.136E-15 = rco : 2.650E-02 = res : 5.967E-16 ==
solution 21 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : 3.89415083856842E-01 4.05694422731437E-69
c1 : 9.21062371647420E-01 3.47738076626946E-68
s2 : 5.75259014495853E-01 1.11276184520623E-67
c2 : 8.17971311380332E-01 -2.96736492054994E-67
s3 : 8.08477989701551E-01 -7.41841230137484E-68
c3 : 5.88526414163493E-01 3.70920615068742E-67
s4 : 6.27366977109340E-01 -7.41841230137484E-68
c4 : 7.78723748214146E-01 0.00000000000000E+00
s5 : 9.84086361717633E-01 -3.47738076626946E-69
c5 : -1.77690834545150E-01 -1.71550784469293E-67
s6 : 9.93123154097381E-01 3.92654244857926E-68
c6 : 1.17074338758196E-01 -2.59644430548120E-67
== err : 9.821E-16 = rco : 3.414E-02 = res : 8.882E-16 ==
solution 22 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : -3.89415083856842E-01 1.97051576755269E-68
c1 : -9.21062371647420E-01 1.41123702764436E-67
s2 : 5.75259014495853E-01 2.22552369041245E-67
c2 : -8.17971311380332E-01 8.90209476164981E-67
s3 : 8.08477989701551E-01 -2.96736492054994E-67
c3 : -5.88526414163493E-01 -1.33531421424747E-66
s4 : 6.27366977109340E-01 7.41841230137484E-68
c4 : -7.78723748214146E-01 1.48368246027497E-67
s5 : 9.84086361717633E-01 4.04942596482930E-68
c5 : 1.77690834545150E-01 5.37834891849676E-67
s6 : -9.93123154097381E-01 -1.08957930676443E-67
c6 : -1.17074338758196E-01 7.04749168630610E-67
== err : 9.821E-16 = rco : 3.614E-02 = res : 8.882E-16 ==
solution 23 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : 3.89415083856842E-01 -1.21543267145725E-63
c1 : 9.21062371647420E-01 1.84279896821850E-63
s2 : 5.75259014495853E-01 -9.72346137165803E-63
c2 : 8.17971311380332E-01 -4.86173068582902E-62
s3 : 8.08477989701551E-01 3.88938454866321E-62
c3 : 5.88526414163493E-01 3.88938454866321E-62
s4 : 6.27366977109340E-01 -5.83407682299482E-62
c4 : 7.78723748214146E-01 4.86173068582902E-62
s5 : 9.84086361717633E-01 1.45851920574871E-62
c5 : -1.77690834545150E-01 -1.50713651260700E-61
s6 : -9.67138464698502E-01 2.73472351077882E-62
c6 : 2.54250250935226E-01 9.23728830307513E-62
== err : 9.821E-16 = rco : 3.531E-02 = res : 8.882E-16 ==
solution 24 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : -3.89415083856842E-01 -4.86173068582902E-62
c1 : -9.21062371647419E-01 -1.36128459203212E-61
s2 : 5.75259014495852E-01 -5.13398760423544E-60
c2 : -8.17971311380332E-01 -4.51168607644933E-60
s3 : 8.08477989701552E-01 9.64567368068477E-60
c3 : -5.88526414163492E-01 9.49009829873824E-60
s4 : 6.27366977109340E-01 -4.04495993060974E-60
c4 : -7.78723748214147E-01 -5.13398760423544E-60
s5 : 9.84086361717633E-01 -7.04950949445208E-62
c5 : 1.77690834545150E-01 5.83407682299482E-61
s6 : 9.67138464698502E-01 -3.11150763893057E-61
c6 : -2.54250250935226E-01 -1.23001786351474E-60
== err : 1.426E-15 = rco : 3.779E-02 = res : 8.882E-16 ==
solution 25 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : -3.89415083856842E-01 -1.30699200206328E-31
c1 : -9.21062371647420E-01 -1.00601754242529E-31
s2 : -1.66814300276214E+00 2.60968969868373E+00
c2 : 2.74607605173297E+00 1.58529317041035E+00
s3 : 3.42882833936714E+00 -5.05527774520946E+00
c3 : -5.12313078715411E+00 -3.38341539896057E+00
s4 : 2.11687232955215E+00 2.28148639436773E+00
c4 : -2.40165709157283E+00 2.01095128669009E+00
s5 : 5.09486080364479E-01 2.15618991998570E-02
c5 : 8.60843598054382E-01 -1.27613047635805E-02
s6 : 4.66761459278284E-01 2.34817061898099E-01
c6 : -9.22704020497345E-01 1.18785170585816E-01
== err : 4.680E-15 = rco : 4.478E-03 = res : 7.944E-15 ==
solution 26 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : 3.89415083856842E-01 9.86169495326495E-32
c1 : 9.21062371647420E-01 7.90333934964611E-33
s2 : -1.66814300276214E+00 2.60968969868373E+00
c2 : -2.74607605173298E+00 -1.58529317041035E+00
s3 : 3.42882833936714E+00 -5.05527774520946E+00
c3 : 5.12313078715411E+00 3.38341539896057E+00
s4 : 2.11687232955215E+00 2.28148639436773E+00
c4 : 2.40165709157283E+00 -2.01095128669009E+00
s5 : 5.09486080364478E-01 2.15618991998570E-02
c5 : -8.60843598054382E-01 1.27613047635805E-02
s6 : -4.66761459278283E-01 -2.34817061898099E-01
c6 : 9.22704020497345E-01 -1.18785170585816E-01
== err : 5.368E-15 = rco : 4.478E-03 = res : 1.421E-14 ==
solution 27 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : 3.89415083856842E-01 8.22325724561267E-32
c1 : 9.21062371647419E-01 1.79150539365652E-31
s2 : 8.23145787536120E-01 5.60379372510051E-01
c2 : 9.37349006938816E-01 -4.92104772597142E-01
s3 : 1.04914305688734E+00 -9.62741326591088E-01
c3 : 1.22651709460876E+00 8.23513494276851E-01
s4 : -5.97623476383050E-01 2.44344535652022E-01
c4 : -8.55390699351840E-01 -1.70712670762276E-01
s5 : 1.52914291606202E+00 1.89564431625379E-01
c5 : 2.48202441735159E-01 -1.16788177316392E+00
s6 : -4.72806388998190E-01 -8.65404650283140E-02
c6 : 8.86607684872822E-01 -4.61499324564624E-02
== err : 4.792E-15 = rco : 5.481E-02 = res : 9.155E-16 ==
solution 28 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : -3.89415083856842E-01 -8.58598285181072E-32
c1 : -9.21062371647419E-01 -1.50519098652568E-31
s2 : 8.23145787536120E-01 5.60379372510051E-01
c2 : -9.37349006938816E-01 4.92104772597142E-01
s3 : 1.04914305688734E+00 -9.62741326591088E-01
c3 : -1.22651709460876E+00 -8.23513494276851E-01
s4 : -5.97623476383050E-01 2.44344535652022E-01
c4 : 8.55390699351840E-01 1.70712670762276E-01
s5 : 1.52914291606202E+00 1.89564431625379E-01
c5 : -2.48202441735159E-01 1.16788177316392E+00
s6 : 4.72806388998190E-01 8.65404650283140E-02
c6 : -8.86607684872822E-01 4.61499324564624E-02
== err : 4.792E-15 = rco : 4.912E-02 = res : 9.155E-16 ==
solution 29 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : -3.89415083856842E-01 -1.38606669272869E-31
c1 : -9.21062371647420E-01 -1.28287338039757E-31
s2 : -1.66814300276214E+00 2.60968969868373E+00
c2 : 2.74607605173298E+00 1.58529317041035E+00
s3 : 3.42882833936714E+00 -5.05527774520946E+00
c3 : -5.12313078715411E+00 -3.38341539896057E+00
s4 : 2.11687232955215E+00 2.28148639436773E+00
c4 : -2.40165709157283E+00 2.01095128669009E+00
s5 : 5.09486080364478E-01 2.15618991998570E-02
c5 : 8.60843598054382E-01 -1.27613047635805E-02
s6 : -5.50180407961115E-01 -2.65168683281356E-01
c6 : 8.91295858167372E-01 -1.63683711765720E-01
== err : 5.368E-15 = rco : 4.424E-03 = res : 1.421E-14 ==
solution 30 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : 3.89415083856842E-01 4.77672556170894E-32
c1 : 9.21062371647420E-01 -3.01584649379662E-32
s2 : -1.66814300276214E+00 2.60968969868373E+00
c2 : -2.74607605173298E+00 -1.58529317041035E+00
s3 : 3.42882833936714E+00 -5.05527774520946E+00
c3 : 5.12313078715411E+00 3.38341539896057E+00
s4 : 2.11687232955215E+00 2.28148639436773E+00
c4 : 2.40165709157283E+00 -2.01095128669009E+00
s5 : 5.09486080364478E-01 2.15618991998570E-02
c5 : -8.60843598054382E-01 1.27613047635805E-02
s6 : 5.50180407961115E-01 2.65168683281356E-01
c6 : -8.91295858167372E-01 1.63683711765720E-01
== err : 6.871E-15 = rco : 4.424E-03 = res : 7.944E-15 ==
solution 31 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : 3.89415083856842E-01 -3.51710436505454E-32
c1 : 9.21062371647419E-01 -2.77075473689231E-31
s2 : 8.23145787536120E-01 5.60379372510051E-01
c2 : 9.37349006938816E-01 -4.92104772597142E-01
s3 : 1.04914305688734E+00 -9.62741326591088E-01
c3 : 1.22651709460876E+00 8.23513494276851E-01
s4 : -5.97623476383050E-01 2.44344535652022E-01
c4 : -8.55390699351840E-01 -1.70712670762276E-01
s5 : 1.52914291606202E+00 1.89564431625379E-01
c5 : 2.48202441735158E-01 -1.16788177316392E+00
s6 : 7.81285014306436E-01 6.00957349607138E-02
c6 : -6.31453818401378E-01 7.43552351419824E-02
== err : 4.847E-15 = rco : 5.552E-02 = res : 9.114E-16 ==
solution 32 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : -3.89415083856842E-01 2.75710572042304E-32
c1 : -9.21062371647419E-01 2.65051806747724E-31
s2 : 8.23145787536120E-01 5.60379372510051E-01
c2 : -9.37349006938816E-01 4.92104772597142E-01
s3 : 1.04914305688734E+00 -9.62741326591088E-01
c3 : -1.22651709460876E+00 -8.23513494276851E-01
s4 : -5.97623476383050E-01 2.44344535652022E-01
c4 : 8.55390699351840E-01 1.70712670762276E-01
s5 : 1.52914291606202E+00 1.89564431625379E-01
c5 : -2.48202441735158E-01 1.16788177316392E+00
s6 : -7.81285014306436E-01 -6.00957349607139E-02
c6 : 6.31453818401378E-01 -7.43552351419825E-02
== err : 4.847E-15 = rco : 4.917E-02 = res : 9.114E-16 ==
solution 33 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : 3.89415083856842E-01 2.65920486866181E-32
c1 : 9.21062371647419E-01 3.38674211387560E-31
s2 : 8.23145787536120E-01 -5.60379372510051E-01
c2 : 9.37349006938816E-01 4.92104772597142E-01
s3 : 1.04914305688734E+00 9.62741326591088E-01
c3 : 1.22651709460876E+00 -8.23513494276851E-01
s4 : -5.97623476383050E-01 -2.44344535652022E-01
c4 : -8.55390699351840E-01 1.70712670762276E-01
s5 : 1.52914291606202E+00 -1.89564431625379E-01
c5 : 2.48202441735158E-01 1.16788177316392E+00
s6 : 7.81285014306436E-01 -6.00957349607138E-02
c6 : -6.31453818401378E-01 -7.43552351419824E-02
== err : 4.847E-15 = rco : 5.552E-02 = res : 9.114E-16 ==
solution 34 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : 3.89415083856842E-01 6.68974142370073E-60
c1 : 9.21062371647420E-01 2.10804642537546E-59
s2 : 6.26140621849592E-01 3.19614064670948E-57
c2 : 7.79710152344964E-01 -2.33985374447579E-57
s3 : 6.07900231883579E-01 -5.65547628452021E-57
c3 : 7.94013418070433E-01 5.03815316895638E-57
s4 : 8.75877670684069E-01 1.73248745335654E-57
c4 : 4.82533217506370E-01 -3.11648605115286E-57
s5 : 9.37998305193623E-01 3.07416954726340E-58
c5 : 3.46639841123162E-01 -6.96977711120448E-58
s6 : 9.42387849717845E-01 5.50114550562925E-58
c6 : 3.34522257412232E-01 -1.40391224668547E-57
== err : 2.441E-15 = rco : 7.794E-03 = res : 2.220E-16 ==
solution 35 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : -3.89415083856842E-01 2.78334081763711E-61
c1 : -9.21062371647419E-01 -1.94469227433161E-61
s2 : 5.64604874232218E-01 -4.48057100006002E-59
c2 : -8.25361336623676E-01 -3.48488855560224E-59
s3 : 7.17403428624498E-01 8.08991986121949E-59
c3 : -6.96657965286994E-01 7.09423741676170E-59
s4 : 8.41478520054349E-01 -2.67589656948029E-59
c4 : -5.40290570237111E-01 -3.98272977783113E-59
s5 : 9.32004841587325E-01 -3.18929532990384E-60
c5 : -3.62445823893427E-01 -1.08902767362570E-59
s6 : 9.99735569944520E-01 1.86690458335834E-60
c6 : -2.29954384108199E-02 1.68021412502251E-59
== err : 8.866E-16 = rco : 8.519E-03 = res : 8.882E-16 ==
solution 36 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : -3.89415083856842E-01 6.59826499123333E-31
c1 : -9.21062371647420E-01 -5.46918320578315E-31
s2 : 8.12447299105426E-01 -5.16786840383107E-01
c2 : -9.06404061572963E-01 -4.63217333728468E-01
s3 : 1.23611304332968E+00 1.24952222803037E+00
c3 : -1.46469772617762E+00 1.05451841454651E+00
s4 : -9.39467983975633E-01 -9.48683934911419E-01
c4 : 1.23891712639201E+00 -7.19384827907607E-01
s5 : 1.71925348920786E+00 3.34751466405344E-01
c5 : -4.06076515006418E-01 1.41727631460228E+00
s6 : 8.61466466923939E-01 -3.64813495876627E-01
c6 : 7.52059005889243E-01 4.17885552753148E-01
== err : 5.571E-15 = rco : 3.977E-02 = res : 1.110E-15 ==
solution 37 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : 3.89415083856842E-01 -8.29044990954045E-32
c1 : 9.21062371647419E-01 -1.73616168931533E-31
s2 : 8.23145787536120E-01 -5.60379372510051E-01
c2 : 9.37349006938816E-01 4.92104772597142E-01
s3 : 1.04914305688734E+00 9.62741326591088E-01
c3 : 1.22651709460876E+00 -8.23513494276851E-01
s4 : -5.97623476383050E-01 -2.44344535652022E-01
c4 : -8.55390699351840E-01 1.70712670762276E-01
s5 : 1.52914291606202E+00 -1.89564431625379E-01
c5 : 2.48202441735159E-01 1.16788177316392E+00
s6 : -4.72806388998190E-01 8.65404650283140E-02
c6 : 8.86607684872822E-01 4.61499324564624E-02
== err : 4.792E-15 = rco : 5.481E-02 = res : 9.155E-16 ==
solution 38 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : 3.89415083856842E-01 2.66422841583430E-60
c1 : 9.21062371647419E-01 7.08840333993871E-60
s2 : 6.26140621849592E-01 4.77927573339736E-58
c2 : 7.79710152344964E-01 -3.68402504449380E-58
s3 : 6.07900231883578E-01 -8.76200551122849E-58
c3 : 7.94013418070433E-01 7.56718657787915E-58
s4 : 8.75877670684069E-01 2.78791084448179E-58
c4 : 4.82533217506370E-01 -4.48057100006002E-58
s5 : 9.37998305193623E-01 4.23165038894558E-59
c5 : 3.46639841123161E-01 -4.97841222228891E-59
s6 : -9.98546109059359E-01 -5.91186451396809E-60
c6 : 5.39042492055606E-02 2.88747908892757E-58
== err : 1.294E-15 = rco : 7.789E-03 = res : 8.882E-16 ==
solution 39 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : -3.89415083856842E-01 -5.41247361508309E-63
c1 : -9.21062371647419E-01 5.54541156352372E-62
s2 : 5.64604874232218E-01 -6.06743989591461E-60
c2 : -8.25361336623676E-01 -4.90062453131565E-60
s3 : 7.17403428624498E-01 1.12014275001501E-59
c3 : -6.96657965286994E-01 9.95682444457783E-60
s4 : 8.41478520054349E-01 -3.65602147574342E-60
c4 : -5.40290570237111E-01 -5.44513836812850E-60
s5 : 9.32004841587325E-01 -5.83407682299482E-61
c5 : -3.62445823893427E-01 -1.82801073787171E-60
s6 : -9.32692979738753E-01 6.02854605042798E-61
c6 : -3.60671326204408E-01 -2.33363072919793E-60
== err : 8.866E-16 = rco : 8.396E-03 = res : 8.882E-16 ==
solution 40 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : -3.89415083856842E-01 7.81187069306404E-31
c1 : -9.21062371647420E-01 -6.58925198626858E-31
s2 : 8.12447299105426E-01 -5.16786840383107E-01
c2 : -9.06404061572963E-01 -4.63217333728468E-01
s3 : 1.23611304332968E+00 1.24952222803037E+00
c3 : -1.46469772617762E+00 1.05451841454651E+00
s4 : -9.39467983975633E-01 -9.48683934911419E-01
c4 : 1.23891712639201E+00 -7.19384827907607E-01
s5 : 1.71925348920786E+00 3.34751466405344E-01
c5 : -4.06076515006418E-01 1.41727631460228E+00
s6 : -4.23667748161564E-01 2.26075213480995E-01
c6 : -9.39157471197499E-01 -1.01985853861664E-01
== err : 5.571E-15 = rco : 4.176E-02 = res : 1.110E-15 ==
solution 41 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : 3.89415083856842E-01 -7.74043219236920E-31
c1 : 9.21062371647420E-01 6.46767250013048E-31
s2 : 8.12447299105426E-01 -5.16786840383107E-01
c2 : 9.06404061572963E-01 4.63217333728468E-01
s3 : 1.23611304332968E+00 1.24952222803037E+00
c3 : 1.46469772617762E+00 -1.05451841454651E+00
s4 : -9.39467983975633E-01 -9.48683934911419E-01
c4 : -1.23891712639201E+00 7.19384827907607E-01
s5 : 1.71925348920786E+00 3.34751466405344E-01
c5 : 4.06076515006418E-01 -1.41727631460228E+00
s6 : 4.23667748161564E-01 -2.26075213480995E-01
c6 : 9.39157471197499E-01 1.01985853861664E-01
== err : 5.571E-15 = rco : 4.123E-02 = res : 1.110E-15 ==
solution 42 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : 3.89415083856842E-01 -3.88938454866321E-62
c1 : 9.21062371647419E-01 6.80642296016062E-62
s2 : 5.64604874232218E-01 -1.94469227433161E-59
c2 : 8.25361336623676E-01 1.50908120488133E-59
s3 : 7.17403428624498E-01 3.48488855560224E-59
c3 : 6.96657965286994E-01 -3.11150763893057E-59
s4 : 8.41478520054349E-01 -1.09291705817436E-59
c4 : 5.40290570237111E-01 1.71132920141181E-59
s5 : 9.32004841587325E-01 -1.94469227433161E-60
c5 : 3.62445823893427E-01 5.83407682299482E-60
s6 : 9.32692979738753E-01 -2.72256918406425E-60
c6 : 3.60671326204408E-01 8.24549524316601E-60
== err : 1.037E-15 = rco : 8.356E-03 = res : 8.882E-16 ==
solution 43 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : -3.89415083856842E-01 5.34547288906900E-60
c1 : -9.21062371647419E-01 1.19793044098827E-59
s2 : 6.26140621849592E-01 -7.76632306677071E-58
c2 : -7.79710152344964E-01 -5.97409466674670E-58
s3 : 6.07900231883578E-01 1.43378272001921E-57
c3 : -7.94013418070433E-01 1.27447352890596E-57
s4 : 8.75877670684069E-01 -4.97841222228891E-58
c4 : -4.82533217506370E-01 -8.16459604455382E-58
s5 : 9.37998305193623E-01 -7.34315802787615E-59
c5 : -3.46639841123161E-01 -1.04546656668067E-58
s6 : 9.98546109059359E-01 -5.91186451396809E-60
c6 : -5.39042492055606E-02 4.87884397784314E-58
== err : 1.294E-15 = rco : 7.703E-03 = res : 8.882E-16 ==
solution 44 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : -3.89415083856842E-01 1.14177279211430E-32
c1 : -9.21062371647419E-01 -1.60213698622844E-31
s2 : 8.23145787536120E-01 -5.60379372510051E-01
c2 : -9.37349006938816E-01 -4.92104772597142E-01
s3 : 1.04914305688734E+00 9.62741326591088E-01
c3 : -1.22651709460876E+00 8.23513494276851E-01
s4 : -5.97623476383050E-01 -2.44344535652022E-01
c4 : 8.55390699351840E-01 -1.70712670762276E-01
s5 : 1.52914291606202E+00 -1.89564431625379E-01
c5 : -2.48202441735158E-01 -1.16788177316392E+00
s6 : 4.72806388998190E-01 -8.65404650283140E-02
c6 : -8.86607684872822E-01 -4.61499324564624E-02
== err : 4.847E-15 = rco : 4.912E-02 = res : 9.114E-16 ==
solution 45 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : 3.89415083856842E-01 -6.66476887123257E-31
c1 : 9.21062371647420E-01 4.32071674722514E-31
s2 : 8.12447299105426E-01 -5.16786840383107E-01
c2 : 9.06404061572963E-01 4.63217333728468E-01
s3 : 1.23611304332968E+00 1.24952222803037E+00
c3 : 1.46469772617762E+00 -1.05451841454651E+00
s4 : -9.39467983975633E-01 -9.48683934911419E-01
c4 : -1.23891712639201E+00 7.19384827907607E-01
s5 : 1.71925348920786E+00 3.34751466405344E-01
c5 : 4.06076515006418E-01 -1.41727631460228E+00
s6 : -8.61466466923939E-01 3.64813495876627E-01
c6 : -7.52059005889243E-01 -4.17885552753148E-01
== err : 5.571E-15 = rco : 3.290E-02 = res : 1.110E-15 ==
solution 46 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : 3.89415083856842E-01 -2.19507140465180E-60
c1 : 9.21062371647420E-01 -2.00303304256156E-60
s2 : 5.64604874232218E-01 -2.48920611114446E-57
c2 : 8.25361336623676E-01 1.80218522446859E-57
s3 : 7.17403428624498E-01 4.42083005339256E-57
c3 : 6.96657965286995E-01 -3.86324788449620E-57
s4 : 8.41478520054349E-01 -1.34914971224030E-57
c4 : 5.40290570237110E-01 2.35976739336495E-57
s5 : 9.32004841587325E-01 -2.48920611114446E-58
c5 : 3.62445823893427E-01 6.17323115563825E-58
s6 : -9.99735569944520E-01 -2.86258702781613E-59
c6 : 2.29954384108199E-02 -1.32425765112885E-57
== err : 2.523E-15 = rco : 8.471E-03 = res : 2.220E-16 ==
solution 47 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : -3.89415083856842E-01 -5.78545951613653E-61
c1 : -9.21062371647420E-01 -5.76115086270739E-61
s2 : 6.26140621849592E-01 8.11481192233093E-58
c2 : -7.79710152344964E-01 5.82474230007803E-58
s3 : 6.07900231883579E-01 -1.43876113224150E-57
c3 : -7.94013418070433E-01 -1.25953829223910E-57
s4 : 8.75877670684069E-01 4.40589481672569E-58
c4 : -4.82533217506370E-01 7.86589131121648E-58
s5 : 9.37998305193623E-01 8.21438016677671E-59
c5 : -3.46639841123162E-01 1.81712046113545E-58
s6 : -9.42387849717845E-01 -1.44996255974165E-58
c6 : -3.34522257412232E-01 3.62179489171519E-58
== err : 1.598E-15 = rco : 7.735E-03 = res : 4.441E-16 ==
solution 48 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
s1 : -3.89415083856842E-01 -3.03926886110161E-32
c1 : -9.21062371647419E-01 -2.94747654855477E-31
s2 : 8.23145787536120E-01 -5.60379372510051E-01
c2 : -9.37349006938816E-01 -4.92104772597142E-01
s3 : 1.04914305688734E+00 9.62741326591088E-01
c3 : -1.22651709460876E+00 8.23513494276851E-01
s4 : -5.97623476383050E-01 -2.44344535652022E-01
c4 : 8.55390699351840E-01 -1.70712670762276E-01
s5 : 1.52914291606202E+00 -1.89564431625379E-01
c5 : -2.48202441735158E-01 -1.16788177316392E+00
s6 : -7.81285014306436E-01 6.00957349607139E-02
c6 : 6.31453818401378E-01 7.43552351419825E-02
== err : 4.847E-15 = rco : 4.917E-02 = res : 9.114E-16 ==