12
x1**2 + x2**2 - 1;
x3**2 + x4**2 - 1;
x5**2 + x6**2 - 1;
x7**2 + x8**2 - 1;
x9**2 + x10**2 - 1;
x11**2 + x12**2 - 1;
3*x3 + 2*x5 + x7 - 3.9701;
3*x1*x4 + 2*x1*x6 + x1*x8 - 1.7172;
3*x2*x4 + 2*x2*x6 + x2*x8 - 4.0616;
x3*x9 + x5*x9 + x7*x9 - 1.9791;
x2*x4*x9 + x2*x6*x9 + x2*x8*x9 + x1*x10 - 1.9115;
- x3*x10*x11 - x5*x10*x11 - x7*x10*x11 + x4*x12 + x6*x12 + x8*x12 - 0.4077;
TITLE : a sparse system, known as benchmark D1
ROOT COUNTS :
total degree : 4068
3-homogeneous Bezout number : 320
with partition : {x1 x2 }{x3 x4 x5 x6 x7 x8 }{x9 x10 }{x11 x12 }
mixed volume : 192
REFERENCES :
H. Hong and V. Stahl:
`Safe Starting Regions by Fixed Points and Tightening',
Computing 53(3-4): 322-335, 1995.
NOTE :
The system is deficient w.r.t. the face normals
(1,1,0,0, 0,0,0,0, 0,0,0,0)
(0,0,1,1, 1,1,1,1, 0,0,0,0)
(0,0,2,2, 2,2,2,2, -2,0,1,1)
(0,0,2,2, 2,2,0,0, -2,0,1,1)
(0,0,2,2, 0,0,2,2, -2,0,1,1)
(0,0,0,0, 2,2,2,2, -2,0,1,1)
THE SOLUTIONS :
48 12
===========================================================
solution 1 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -3.89415083856842E-01 -2.87322206334911E-50
x2 : -9.21062371647419E-01 -7.21646471724893E-50
x3 : 5.75259014495853E-01 4.44748047759341E-48
x4 : -8.17971311380332E-01 3.93430965325571E-48
x5 : 8.08477989701551E-01 -8.55284707229503E-48
x6 : -5.88526414163492E-01 -7.52650542361962E-48
x7 : 6.27366977109340E-01 4.10536659470161E-48
x8 : -7.78723748214146E-01 3.76325271180981E-48
x9 : 9.84086361717633E-01 -2.40548823908298E-50
x10 : 1.77690834545149E-01 -3.42113882891801E-49
x11 : 9.40301932754719E-01 1.49674823765163E-49
x12 : -3.40341409848611E-01 3.10040706370695E-49
== err : 8.640E-16 = rco : 3.391E-02 = res : 8.882E-16 ==
solution 2 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 3.89415083856842E-01 -1.37091205084606E-30
x2 : 9.21062371647419E-01 -1.81857028142917E-31
x3 : -3.08457430339590E+00 -1.12748434939333E+00
x4 : -1.18298149617247E+00 2.93986783637120E+00
x5 : 5.51926701023123E+00 2.78748170612766E+00
x6 : 2.82446248609853E+00 -5.44700306623820E+00
x7 : 2.18528888972524E+00 -2.19251036407534E+00
x8 : 2.30971002700246E+00 2.07440262336281E+00
x9 : 4.22761702728453E-01 4.87287884168481E-02
x10 : 9.07833668459021E-01 -2.26921145125288E-02
x11 : 6.32896057637868E-01 5.02771683764591E-03
x12 : 7.74264004141422E-01 -4.10973795558809E-03
== err : 7.460E-15 = rco : 3.843E-03 = res : 3.553E-15 ==
solution 3 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -3.89415083856842E-01 1.72523275534842E-30
x2 : -9.21062371647419E-01 3.54433146416023E-31
x3 : -3.08457430339590E+00 -1.12748434939333E+00
x4 : 1.18298149617247E+00 -2.93986783637120E+00
x5 : 5.51926701023123E+00 2.78748170612766E+00
x6 : -2.82446248609853E+00 5.44700306623820E+00
x7 : 2.18528888972524E+00 -2.19251036407534E+00
x8 : -2.30971002700246E+00 -2.07440262336281E+00
x9 : 4.22761702728453E-01 4.87287884168481E-02
x10 : -9.07833668459021E-01 2.26921145125288E-02
x11 : -6.32896057637867E-01 -5.02771683764594E-03
x12 : -7.74264004141422E-01 4.10973795558812E-03
== err : 8.150E-15 = rco : 3.843E-03 = res : 5.024E-15 ==
solution 4 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 3.89415083856842E-01 3.74187059412907E-50
x2 : 9.21062371647419E-01 4.27642353614751E-50
x3 : 5.75259014495853E-01 1.79609788518196E-48
x4 : 8.17971311380332E-01 -1.71056941445901E-48
x5 : 8.08477989701551E-01 -3.59219577036391E-48
x6 : 5.88526414163492E-01 3.07902494602621E-48
x7 : 6.27366977109340E-01 1.53951247301310E-48
x8 : 7.78723748214146E-01 -1.53951247301310E-48
x9 : 9.84086361717633E-01 -8.68648530779963E-51
x10 : -1.77690834545149E-01 1.44329294344979E-49
x11 : -9.40301932754719E-01 0.00000000000000E+00
x12 : 3.40341409848611E-01 -7.48374118825815E-50
== err : 8.640E-16 = rco : 3.225E-02 = res : 8.882E-16 ==
solution 5 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -3.89415083856842E-01 3.07902494602621E-48
x2 : -9.21062371647419E-01 -1.36845553156720E-48
x3 : 5.75259014495853E-01 2.87375661629113E-47
x4 : -8.17971311380332E-01 1.83579958778635E-47
x5 : 8.08477989701551E-01 -5.75494802158566E-47
x6 : -5.88526414163493E-01 -4.37905770101505E-47
x7 : 6.27366977109341E-01 3.01060216944785E-47
x8 : -7.78723748214146E-01 8.89496095518683E-48
x9 : 9.84086361717633E-01 -6.84227765783602E-49
x10 : 1.77690834545150E-01 1.36845553156720E-48
x11 : -9.99733562617972E-01 4.06260235934014E-49
x12 : -2.30825426497600E-02 -1.36845553156720E-48
== err : 7.994E-16 = rco : 3.370E-02 = res : 5.412E-16 ==
solution 6 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 3.89415083856842E-01 3.87145567347627E-32
x2 : 9.21062371647419E-01 8.26799056619022E-31
x3 : -3.08457430339590E+00 -1.12748434939333E+00
x4 : -1.18298149617247E+00 2.93986783637120E+00
x5 : 5.51926701023123E+00 2.78748170612766E+00
x6 : 2.82446248609853E+00 -5.44700306623820E+00
x7 : 2.18528888972524E+00 -2.19251036407534E+00
x8 : 2.30971002700246E+00 2.07440262336281E+00
x9 : 4.22761702728453E-01 4.87287884168482E-02
x10 : 9.07833668459021E-01 -2.26921145125288E-02
x11 : -7.34696844899792E-01 -1.63682788488653E-02
x12 : -6.78824208644993E-01 1.77155185002992E-02
== err : 1.078E-14 = rco : 3.904E-03 = res : 1.005E-14 ==
solution 7 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -3.89415083856842E-01 -1.03822132541497E-31
x2 : -9.21062371647419E-01 -2.02427767924878E-32
x3 : -3.08457430339590E+00 -1.12748434939333E+00
x4 : 1.18298149617247E+00 -2.93986783637120E+00
x5 : 5.51926701023123E+00 2.78748170612766E+00
x6 : -2.82446248609853E+00 5.44700306623820E+00
x7 : 2.18528888972524E+00 -2.19251036407534E+00
x8 : -2.30971002700246E+00 -2.07440262336281E+00
x9 : 4.22761702728453E-01 4.87287884168481E-02
x10 : -9.07833668459021E-01 2.26921145125288E-02
x11 : 7.34696844899792E-01 1.63682788488653E-02
x12 : 6.78824208644992E-01 -1.77155185002992E-02
== err : 7.992E-15 = rco : 3.904E-03 = res : 1.589E-14 ==
solution 8 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 3.89415083856842E-01 -4.10536659470161E-48
x2 : 9.21062371647419E-01 4.10536659470161E-48
x3 : 5.75259014495853E-01 2.18952885050753E-47
x4 : 8.17971311380332E-01 -6.56858655152258E-47
x5 : 8.08477989701551E-01 -4.37905770101505E-47
x6 : 5.88526414163493E-01 0.00000000000000E+00
x7 : 6.27366977109341E-01 -2.18952885050753E-47
x8 : 7.78723748214146E-01 6.56858655152258E-47
x9 : 9.84086361717633E-01 -1.02634164867540E-47
x10 : -1.77690834545150E-01 -6.84227765783602E-47
x11 : 9.99733562617972E-01 -1.71056941445901E-49
x12 : 2.30825426497600E-02 -5.20013101995538E-47
== err : 6.930E-16 = rco : 3.199E-02 = res : 2.220E-16 ==
solution 9 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 3.89415083856842E-01 1.56574904758305E-30
x2 : 9.21062371647419E-01 -5.88271702973549E-31
x3 : -1.66814300276215E+00 2.60968969868373E+00
x4 : -2.74607605173298E+00 -1.58529317041035E+00
x5 : 3.42882833936714E+00 -5.05527774520946E+00
x6 : 5.12313078715411E+00 3.38341539896057E+00
x7 : 2.11687232955215E+00 2.28148639436773E+00
x8 : 2.40165709157283E+00 -2.01095128669009E+00
x9 : 5.09486080364478E-01 2.15618991998569E-02
x10 : -8.60843598054382E-01 1.27613047635804E-02
x11 : 8.57813431291869E-01 4.79408655973425E-03
x12 : -5.14045817407173E-01 8.00012703626073E-03
== err : 6.791E-15 = rco : 4.642E-03 = res : 7.105E-15 ==
solution 10 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -3.89415083856842E-01 -1.07004234414235E-31
x2 : -9.21062371647419E-01 -1.24459966309488E-31
x3 : -1.66814300276214E+00 2.60968969868372E+00
x4 : 2.74607605173297E+00 1.58529317041035E+00
x5 : 3.42882833936714E+00 -5.05527774520945E+00
x6 : -5.12313078715411E+00 -3.38341539896057E+00
x7 : 2.11687232955215E+00 2.28148639436773E+00
x8 : -2.40165709157283E+00 2.01095128669009E+00
x9 : 5.09486080364479E-01 2.15618991998569E-02
x10 : 8.60843598054382E-01 -1.27613047635804E-02
x11 : -8.57813431291869E-01 -4.79408655973423E-03
x12 : 5.14045817407173E-01 -8.00012703626069E-03
== err : 7.173E-15 = rco : 4.642E-03 = res : 7.105E-15 ==
solution 11 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 3.89415083856842E-01 4.30220786767705E-32
x2 : 9.21062371647419E-01 2.33215602623103E-31
x3 : -1.66814300276215E+00 2.60968969868373E+00
x4 : -2.74607605173297E+00 -1.58529317041035E+00
x5 : 3.42882833936714E+00 -5.05527774520946E+00
x6 : 5.12313078715411E+00 3.38341539896057E+00
x7 : 2.11687232955215E+00 2.28148639436773E+00
x8 : 2.40165709157283E+00 -2.01095128669009E+00
x9 : 5.09486080364479E-01 2.15618991998569E-02
x10 : -8.60843598054382E-01 1.27613047635804E-02
x11 : -7.77847414131604E-01 -1.58035359040089E-03
x12 : 6.28458211691578E-01 -1.95601542129298E-03
== err : 6.119E-15 = rco : 4.613E-03 = res : 3.553E-15 ==
solution 12 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -3.89415083856842E-01 -5.02603258121557E-33
x2 : -9.21062371647419E-01 1.44662346941344E-31
x3 : -1.66814300276214E+00 2.60968969868373E+00
x4 : 2.74607605173297E+00 1.58529317041035E+00
x5 : 3.42882833936714E+00 -5.05527774520946E+00
x6 : -5.12313078715411E+00 -3.38341539896057E+00
x7 : 2.11687232955215E+00 2.28148639436773E+00
x8 : -2.40165709157283E+00 2.01095128669009E+00
x9 : 5.09486080364479E-01 2.15618991998570E-02
x10 : 8.60843598054382E-01 -1.27613047635805E-02
x11 : 7.77847414131604E-01 1.58035359040086E-03
x12 : -6.28458211691578E-01 1.95601542129294E-03
== err : 7.868E-15 = rco : 4.613E-03 = res : 7.944E-15 ==
solution 13 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -3.89415083856842E-01 8.75811540203011E-46
x2 : -9.21062371647419E-01 7.77720647700274E-44
x3 : 6.26140621849592E-01 1.70935991872198E-40
x4 : -7.79710152344964E-01 1.24659511386336E-40
x5 : 6.07900231883578E-01 -3.02052686582143E-40
x6 : -7.94013418070433E-01 -2.66896910709162E-40
x7 : 8.75877670684069E-01 9.12077144459737E-41
x8 : -4.82533217506370E-01 1.59277188649016E-40
x9 : 9.37998305193623E-01 1.74433632839153E-41
x10 : -3.46639841123160E-01 4.52899663669781E-41
x11 : -8.62987387721747E-01 -2.04253264159985E-41
x12 : -5.05225463167876E-01 3.39898955506628E-41
== err : 6.388E-15 = rco : 8.154E-03 = res : 8.882E-16 ==
solution 14 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 3.89415083856842E-01 -6.37590801267792E-44
x2 : 9.21062371647419E-01 -1.60974161089313E-43
x3 : 6.26140621849592E-01 6.36750022189197E-41
x4 : 7.79710152344963E-01 -4.71733115030306E-41
x5 : 6.07900231883578E-01 -1.13718172976888E-40
x6 : 7.94013418070433E-01 1.01162538736537E-40
x7 : 8.75877670684069E-01 3.60526068901489E-41
x8 : 4.82533217506370E-01 -6.00876781502482E-41
x9 : 9.37998305193623E-01 6.23297556931679E-42
x10 : 3.46639841123161E-01 -1.58290674530131E-41
x11 : 8.62987387721747E-01 7.10738581105547E-42
x12 : 5.05225463167876E-01 -1.18157486511869E-41
== err : 3.535E-15 = rco : 8.043E-03 = res : 8.882E-16 ==
solution 15 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -3.89415083856842E-01 2.42599796636234E-44
x2 : -9.21062371647419E-01 -1.03345761743955E-44
x3 : 6.26140621849592E-01 1.31834159523679E-41
x4 : -7.79710152344964E-01 9.73061653627153E-42
x5 : 6.07900231883578E-01 -2.33176064463649E-41
x6 : -7.94013418070433E-01 -2.06271133948613E-41
x7 : 8.75877670684069E-01 7.21948968820146E-42
x8 : -4.82533217506370E-01 1.21072187317664E-41
x9 : 9.37998305193623E-01 1.23314264860584E-42
x10 : -3.46639841123160E-01 3.07164623380000E-42
x11 : 9.88193097648288E-01 5.63321982658577E-43
x12 : 1.53213582166468E-01 -3.31827476352117E-42
== err : 1.338E-15 = rco : 8.094E-03 = res : 8.882E-16 ==
solution 16 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 3.89415083856842E-01 1.36188694501568E-44
x2 : 9.21062371647419E-01 3.47697181460595E-44
x3 : 6.26140621849592E-01 6.45718332360876E-41
x4 : 7.79710152344963E-01 -4.64558466892963E-41
x5 : 6.07900231883577E-01 -1.14076905383755E-40
x6 : 7.94013418070434E-01 9.97276091090686E-41
x7 : 8.75877670684069E-01 3.39002124489460E-41
x8 : 4.82533217506370E-01 -6.02670443536817E-41
x9 : 9.37998305193624E-01 6.68139107790073E-42
x10 : 3.46639841123160E-01 -1.73536801821985E-41
x11 : -9.88193097648288E-01 -3.36311631437956E-42
x12 : -1.53213582166467E-01 1.83850358519416E-41
== err : 2.900E-15 = rco : 7.991E-03 = res : 8.882E-16 ==
solution 17 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 3.89415083856842E-01 7.84702303830901E-32
x2 : 9.21062371647419E-01 -1.67588887889235E-30
x3 : 8.12447299105426E-01 5.16786840383107E-01
x4 : 9.06404061572963E-01 -4.63217333728468E-01
x5 : 1.23611304332968E+00 -1.24952222803037E+00
x6 : 1.46469772617762E+00 1.05451841454651E+00
x7 : -9.39467983975633E-01 9.48683934911419E-01
x8 : -1.23891712639201E+00 -7.19384827907607E-01
x9 : 1.71925348920786E+00 -3.34751466405344E-01
x10 : 4.06076515006418E-01 1.41727631460229E+00
x11 : 2.26935708206733E-02 1.44499739394751E+00
x12 : -1.75722813380886E+00 1.86612939232641E-02
== err : 5.686E-15 = rco : 1.917E-02 = res : 9.778E-16 ==
solution 18 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -3.89415083856842E-01 -2.32069012450183E-31
x2 : -9.21062371647419E-01 -7.86303112189558E-31
x3 : -1.66814300276214E+00 -2.60968969868373E+00
x4 : 2.74607605173298E+00 -1.58529317041035E+00
x5 : 3.42882833936714E+00 5.05527774520946E+00
x6 : -5.12313078715411E+00 3.38341539896057E+00
x7 : 2.11687232955215E+00 -2.28148639436773E+00
x8 : -2.40165709157283E+00 -2.01095128669009E+00
x9 : 5.09486080364479E-01 -2.15618991998569E-02
x10 : 8.60843598054382E-01 1.27613047635804E-02
x11 : -8.57813431291869E-01 4.79408655973425E-03
x12 : 5.14045817407173E-01 8.00012703626073E-03
== err : 5.674E-15 = rco : 4.642E-03 = res : 7.324E-15 ==
solution 19 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 3.89415083856842E-01 -4.05357743317086E-31
x2 : 9.21062371647419E-01 -9.73898397361824E-31
x3 : 8.23145787536120E-01 5.60379372510051E-01
x4 : 9.37349006938816E-01 -4.92104772597142E-01
x5 : 1.04914305688734E+00 -9.62741326591088E-01
x6 : 1.22651709460876E+00 8.23513494276851E-01
x7 : -5.97623476383049E-01 2.44344535652022E-01
x8 : -8.55390699351840E-01 -1.70712670762276E-01
x9 : 1.52914291606202E+00 1.89564431625379E-01
x10 : 2.48202441735159E-01 -1.16788177316392E+00
x11 : 3.71549559703573E-01 -2.83174538077762E+00
x12 : -3.00061342433028E+00 -3.50639552862555E-01
== err : 5.706E-15 = rco : 5.611E-03 = res : 2.701E-15 ==
solution 20 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 3.89415083856842E-01 5.48584085661725E-31
x2 : 9.21062371647419E-01 -8.08816062679508E-31
x3 : 8.12447299105426E-01 5.16786840383107E-01
x4 : 9.06404061572963E-01 -4.63217333728468E-01
x5 : 1.23611304332968E+00 -1.24952222803037E+00
x6 : 1.46469772617762E+00 1.05451841454651E+00
x7 : -9.39467983975633E-01 9.48683934911419E-01
x8 : -1.23891712639201E+00 -7.19384827907607E-01
x9 : 1.71925348920786E+00 -3.34751466405344E-01
x10 : 4.06076515006418E-01 1.41727631460229E+00
x11 : -6.05809492048029E-02 -5.28028309584329E-01
x12 : 1.12957771194285E+00 -2.83189512889793E-02
== err : 5.285E-15 = rco : 3.780E-02 = res : 8.882E-16 ==
solution 21 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -3.89415083856842E-01 -1.02132701423084E-31
x2 : -9.21062371647419E-01 -3.70667094281775E-31
x3 : -1.66814300276215E+00 -2.60968969868373E+00
x4 : 2.74607605173297E+00 -1.58529317041035E+00
x5 : 3.42882833936714E+00 5.05527774520946E+00
x6 : -5.12313078715411E+00 3.38341539896057E+00
x7 : 2.11687232955215E+00 -2.28148639436773E+00
x8 : -2.40165709157283E+00 -2.01095128669009E+00
x9 : 5.09486080364479E-01 -2.15618991998569E-02
x10 : 8.60843598054382E-01 1.27613047635804E-02
x11 : 7.77847414131604E-01 -1.58035359040091E-03
x12 : -6.28458211691578E-01 -1.95601542129299E-03
== err : 6.032E-15 = rco : 4.613E-03 = res : 7.105E-15 ==
solution 22 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 3.89415083856842E-01 2.66886858450598E-31
x2 : 9.21062371647419E-01 6.46554607154143E-31
x3 : 8.23145787536120E-01 5.60379372510051E-01
x4 : 9.37349006938816E-01 -4.92104772597142E-01
x5 : 1.04914305688734E+00 -9.62741326591088E-01
x6 : 1.22651709460876E+00 8.23513494276851E-01
x7 : -5.97623476383049E-01 2.44344535652022E-01
x8 : -8.55390699351840E-01 -1.70712670762275E-01
x9 : 1.52914291606202E+00 1.89564431625379E-01
x10 : 2.48202441735159E-01 -1.16788177316392E+00
x11 : -1.45894122879726E-01 8.62915178631412E-01
x12 : 1.31623928166929E+00 9.56469350666771E-02
== err : 5.228E-15 = rco : 2.878E-02 = res : 9.114E-16 ==
solution 23 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 3.89415083856842E-01 1.21114722566236E-30
x2 : 9.21062371647419E-01 4.46639148878638E-31
x3 : -1.66814300276214E+00 -2.60968969868373E+00
x4 : -2.74607605173298E+00 1.58529317041035E+00
x5 : 3.42882833936714E+00 5.05527774520946E+00
x6 : 5.12313078715411E+00 -3.38341539896057E+00
x7 : 2.11687232955215E+00 -2.28148639436773E+00
x8 : 2.40165709157283E+00 2.01095128669009E+00
x9 : 5.09486080364479E-01 -2.15618991998570E-02
x10 : -8.60843598054382E-01 -1.27613047635804E-02
x11 : 8.57813431291869E-01 -4.79408655973426E-03
x12 : -5.14045817407173E-01 -8.00012703626075E-03
== err : 1.063E-14 = rco : 4.642E-03 = res : 3.972E-15 ==
solution 24 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -3.89415083856842E-01 3.00266311165013E-32
x2 : -9.21062371647419E-01 2.22990503606788E-30
x3 : 8.12447299105426E-01 5.16786840383107E-01
x4 : -9.06404061572963E-01 4.63217333728468E-01
x5 : 1.23611304332968E+00 -1.24952222803037E+00
x6 : -1.46469772617762E+00 -1.05451841454651E+00
x7 : -9.39467983975633E-01 9.48683934911419E-01
x8 : 1.23891712639201E+00 7.19384827907607E-01
x9 : 1.71925348920786E+00 -3.34751466405344E-01
x10 : -4.06076515006418E-01 -1.41727631460229E+00
x11 : -2.26935708206733E-02 -1.44499739394751E+00
x12 : 1.75722813380886E+00 -1.86612939232641E-02
== err : 6.627E-15 = rco : 1.844E-02 = res : 9.114E-16 ==
solution 25 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -3.89415083856842E-01 -1.30197206937695E-31
x2 : -9.21062371647419E-01 -3.18158119234600E-31
x3 : 8.23145787536120E-01 5.60379372510051E-01
x4 : -9.37349006938816E-01 4.92104772597142E-01
x5 : 1.04914305688734E+00 -9.62741326591088E-01
x6 : -1.22651709460876E+00 -8.23513494276851E-01
x7 : -5.97623476383049E-01 2.44344535652022E-01
x8 : 8.55390699351840E-01 1.70712670762275E-01
x9 : 1.52914291606202E+00 1.89564431625379E-01
x10 : -2.48202441735159E-01 1.16788177316392E+00
x11 : -3.71549559703573E-01 2.83174538077761E+00
x12 : 3.00061342433027E+00 3.50639552862555E-01
== err : 6.484E-15 = rco : 5.611E-03 = res : 1.601E-15 ==
solution 26 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 3.89415083856842E-01 2.00811454378731E-32
x2 : 9.21062371647419E-01 1.02379814251086E-31
x3 : -1.66814300276214E+00 -2.60968969868373E+00
x4 : -2.74607605173297E+00 1.58529317041035E+00
x5 : 3.42882833936714E+00 5.05527774520946E+00
x6 : 5.12313078715411E+00 -3.38341539896057E+00
x7 : 2.11687232955215E+00 -2.28148639436773E+00
x8 : 2.40165709157283E+00 2.01095128669009E+00
x9 : 5.09486080364479E-01 -2.15618991998569E-02
x10 : -8.60843598054382E-01 -1.27613047635804E-02
x11 : -7.77847414131604E-01 1.58035359040080E-03
x12 : 6.28458211691578E-01 1.95601542129286E-03
== err : 7.932E-15 = rco : 4.613E-03 = res : 7.324E-15 ==
solution 27 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -3.89415083856842E-01 -8.87892302478894E-31
x2 : -9.21062371647419E-01 -1.86923145177691E-31
x3 : 8.12447299105426E-01 5.16786840383107E-01
x4 : -9.06404061572963E-01 4.63217333728468E-01
x5 : 1.23611304332968E+00 -1.24952222803037E+00
x6 : -1.46469772617762E+00 -1.05451841454651E+00
x7 : -9.39467983975633E-01 9.48683934911419E-01
x8 : 1.23891712639201E+00 7.19384827907607E-01
x9 : 1.71925348920786E+00 -3.34751466405344E-01
x10 : -4.06076515006418E-01 -1.41727631460228E+00
x11 : 6.05809492048028E-02 5.28028309584330E-01
x12 : -1.12957771194285E+00 2.83189512889793E-02
== err : 5.330E-15 = rco : 3.798E-02 = res : 9.778E-16 ==
solution 28 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -3.89415083856842E-01 -3.42960581194187E-31
x2 : -9.21062371647419E-01 -8.16111660016590E-31
x3 : 8.23145787536120E-01 5.60379372510051E-01
x4 : -9.37349006938816E-01 4.92104772597142E-01
x5 : 1.04914305688734E+00 -9.62741326591088E-01
x6 : -1.22651709460876E+00 -8.23513494276851E-01
x7 : -5.97623476383049E-01 2.44344535652022E-01
x8 : 8.55390699351840E-01 1.70712670762275E-01
x9 : 1.52914291606202E+00 1.89564431625379E-01
x10 : -2.48202441735159E-01 1.16788177316392E+00
x11 : 1.45894122879726E-01 -8.62915178631412E-01
x12 : -1.31623928166929E+00 -9.56469350666771E-02
== err : 4.968E-15 = rco : 3.083E-02 = res : 9.114E-16 ==
solution 29 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -3.89415083856842E-01 9.56866682505458E-31
x2 : -9.21062371647419E-01 3.71242671323870E-31
x3 : 8.12447299105426E-01 -5.16786840383107E-01
x4 : -9.06404061572963E-01 -4.63217333728468E-01
x5 : 1.23611304332968E+00 1.24952222803037E+00
x6 : -1.46469772617762E+00 1.05451841454651E+00
x7 : -9.39467983975633E-01 -9.48683934911419E-01
x8 : 1.23891712639201E+00 -7.19384827907607E-01
x9 : 1.71925348920786E+00 3.34751466405344E-01
x10 : -4.06076515006418E-01 1.41727631460229E+00
x11 : -2.26935708206749E-02 1.44499739394750E+00
x12 : 1.75722813380886E+00 1.86612939232654E-02
== err : 5.319E-15 = rco : 1.844E-02 = res : 1.093E-15 ==
solution 30 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -3.89415083856842E-01 -6.83319124261855E-32
x2 : -9.21062371647419E-01 -1.71642311902469E-31
x3 : 8.23145787536120E-01 -5.60379372510051E-01
x4 : -9.37349006938816E-01 -4.92104772597142E-01
x5 : 1.04914305688734E+00 9.62741326591088E-01
x6 : -1.22651709460876E+00 8.23513494276851E-01
x7 : -5.97623476383049E-01 -2.44344535652022E-01
x8 : 8.55390699351840E-01 -1.70712670762276E-01
x9 : 1.52914291606202E+00 -1.89564431625379E-01
x10 : -2.48202441735159E-01 -1.16788177316392E+00
x11 : -3.71549559703573E-01 -2.83174538077761E+00
x12 : 3.00061342433028E+00 -3.50639552862555E-01
== err : 4.903E-15 = rco : 5.611E-03 = res : 1.776E-15 ==
solution 31 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 3.89415083856842E-01 6.62726235031100E-56
x2 : 9.21062371647419E-01 1.19800511717160E-55
x3 : 5.64604874232219E-01 3.78467659143914E-53
x4 : 8.25361336623675E-01 -2.70800135421939E-53
x5 : 7.17403428624497E-01 -6.59055751267851E-53
x6 : 6.96657965286995E-01 5.67701488715871E-53
x7 : 8.41478520054349E-01 1.94127807922956E-53
x8 : 5.40290570237111E-01 -3.39315832335923E-53
x9 : 9.32004841587325E-01 3.79283322202414E-54
x10 : 3.62445823893426E-01 -9.54325778444784E-54
x11 : -9.85432012846133E-01 -2.01876606978704E-54
x12 : -1.70069832886432E-01 1.00326556195477E-53
== err : 1.253E-15 = rco : 9.022E-03 = res : 8.882E-16 ==
solution 32 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -3.89415083856842E-01 1.16654194966947E-30
x2 : -9.21062371647419E-01 8.06183769302334E-31
x3 : 8.12447299105426E-01 -5.16786840383107E-01
x4 : -9.06404061572963E-01 -4.63217333728468E-01
x5 : 1.23611304332968E+00 1.24952222803037E+00
x6 : -1.46469772617762E+00 1.05451841454651E+00
x7 : -9.39467983975633E-01 -9.48683934911419E-01
x8 : 1.23891712639201E+00 -7.19384827907607E-01
x9 : 1.71925348920786E+00 3.34751466405344E-01
x10 : -4.06076515006418E-01 1.41727631460229E+00
x11 : 6.05809492048028E-02 -5.28028309584329E-01
x12 : -1.12957771194285E+00 -2.83189512889792E-02
== err : 5.344E-15 = rco : 3.798E-02 = res : 4.965E-16 ==
solution 33 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -3.89415083856842E-01 2.64172633303269E-31
x2 : -9.21062371647419E-01 6.21009803524653E-31
x3 : 8.23145787536120E-01 -5.60379372510051E-01
x4 : -9.37349006938816E-01 -4.92104772597142E-01
x5 : 1.04914305688734E+00 9.62741326591088E-01
x6 : -1.22651709460876E+00 8.23513494276851E-01
x7 : -5.97623476383049E-01 -2.44344535652022E-01
x8 : 8.55390699351840E-01 -1.70712670762275E-01
x9 : 1.52914291606202E+00 -1.89564431625379E-01
x10 : -2.48202441735159E-01 -1.16788177316392E+00
x11 : 1.45894122879726E-01 8.62915178631412E-01
x12 : -1.31623928166929E+00 9.56469350666772E-02
== err : 5.188E-15 = rco : 3.083E-02 = res : 9.114E-16 ==
solution 34 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 3.89415083856842E-01 -4.07831529249908E-55
x2 : 9.21062371647419E-01 -1.22349458774972E-54
x3 : 5.64604874232219E-01 3.00164005527932E-52
x4 : 8.25361336623676E-01 -2.28385656379948E-52
x5 : 7.17403428624497E-01 -5.32464844588680E-52
x6 : 6.96657965286995E-01 4.85482652419090E-52
x7 : 8.41478520054349E-01 1.68352855274362E-52
x8 : 5.40290570237111E-01 -2.81893153017536E-52
x9 : 9.32004841587325E-01 2.83850744357936E-53
x10 : 3.62445823893426E-01 -7.42253383234832E-53
x11 : 8.55915113396959E-01 3.42578484569923E-53
x12 : 5.17116349247122E-01 -5.70964140949871E-53
== err : 1.388E-15 = rco : 8.418E-03 = res : 8.882E-16 ==
solution 35 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 3.89415083856842E-01 -1.20818676970718E-30
x2 : 9.21062371647419E-01 -8.58408097143961E-31
x3 : 8.12447299105426E-01 -5.16786840383107E-01
x4 : 9.06404061572963E-01 4.63217333728468E-01
x5 : 1.23611304332968E+00 1.24952222803037E+00
x6 : 1.46469772617762E+00 -1.05451841454651E+00
x7 : -9.39467983975633E-01 -9.48683934911419E-01
x8 : -1.23891712639201E+00 7.19384827907607E-01
x9 : 1.71925348920786E+00 3.34751466405344E-01
x10 : 4.06076515006418E-01 -1.41727631460229E+00
x11 : 2.26935708206742E-02 -1.44499739394751E+00
x12 : -1.75722813380886E+00 -1.86612939232648E-02
== err : 5.239E-15 = rco : 1.917E-02 = res : 9.778E-16 ==
solution 36 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -3.89415083856842E-01 -3.77562782938391E-56
x2 : -9.21062371647419E-01 -1.56760244055433E-55
x3 : 5.64604874232219E-01 -9.05385994934795E-53
x4 : -8.25361336623676E-01 -6.77000338554847E-53
x5 : 7.17403428624498E-01 1.61175020359564E-52
x6 : -6.96657965286995E-01 1.44535493966167E-52
x7 : 8.41478520054349E-01 -5.13867726854884E-53
x8 : -5.40290570237111E-01 -8.48289580839808E-53
x9 : 9.32004841587325E-01 -8.70720314948553E-54
x10 : -3.62445823893426E-01 -2.25123004145949E-53
x11 : 9.85432012846133E-01 -3.98655319841785E-54
x12 : 1.70069832886432E-01 2.42659759903695E-53
== err : 3.538E-15 = rco : 9.182E-03 = res : 8.882E-16 ==
solution 37 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 3.89415083856842E-01 5.25160343062428E-32
x2 : 9.21062371647419E-01 1.29539369892075E-31
x3 : 8.23145787536120E-01 -5.60379372510051E-01
x4 : 9.37349006938816E-01 4.92104772597142E-01
x5 : 1.04914305688734E+00 9.62741326591088E-01
x6 : 1.22651709460876E+00 -8.23513494276851E-01
x7 : -5.97623476383049E-01 -2.44344535652022E-01
x8 : -8.55390699351840E-01 1.70712670762275E-01
x9 : 1.52914291606202E+00 -1.89564431625379E-01
x10 : 2.48202441735159E-01 1.16788177316392E+00
x11 : 3.71549559703572E-01 2.83174538077761E+00
x12 : -3.00061342433028E+00 3.50639552862554E-01
== err : 7.193E-15 = rco : 5.611E-03 = res : 9.930E-16 ==
solution 38 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 3.89415083856842E-01 -5.17046206738971E-31
x2 : 9.21062371647419E-01 1.21651594044325E-30
x3 : 8.12447299105426E-01 -5.16786840383107E-01
x4 : 9.06404061572963E-01 4.63217333728468E-01
x5 : 1.23611304332968E+00 1.24952222803037E+00
x6 : 1.46469772617762E+00 -1.05451841454651E+00
x7 : -9.39467983975633E-01 -9.48683934911419E-01
x8 : -1.23891712639201E+00 7.19384827907607E-01
x9 : 1.71925348920786E+00 3.34751466405344E-01
x10 : 4.06076515006418E-01 -1.41727631460229E+00
x11 : -6.05809492048029E-02 5.28028309584329E-01
x12 : 1.12957771194285E+00 2.83189512889793E-02
== err : 5.283E-15 = rco : 3.780E-02 = res : 9.114E-16 ==
solution 39 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -3.89415083856842E-01 6.19903924459860E-54
x2 : -9.21062371647419E-01 2.62643504836941E-53
x3 : 5.64604874232219E-01 2.02545450686674E-51
x4 : -8.25361336623675E-01 1.44078722653407E-51
x5 : 7.17403428624497E-01 -3.59152757918639E-51
x6 : -6.96657965286995E-01 -3.04862224744891E-51
x7 : 8.41478520054349E-01 1.02316774058217E-51
x8 : -5.40290570237111E-01 1.75400184099800E-51
x9 : 9.32004841587325E-01 2.27080595486349E-52
x10 : -3.62445823893426E-01 6.21208985353460E-52
x11 : -8.55915113396959E-01 -2.92333640166334E-52
x12 : -5.17116349247122E-01 4.90702895993489E-52
== err : 1.160E-15 = rco : 8.391E-03 = res : 8.882E-16 ==
solution 40 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 3.89415083856842E-01 -1.46083718121979E-31
x2 : 9.21062371647419E-01 -3.42783096084109E-31
x3 : 8.23145787536120E-01 -5.60379372510051E-01
x4 : 9.37349006938816E-01 4.92104772597142E-01
x5 : 1.04914305688734E+00 9.62741326591088E-01
x6 : 1.22651709460876E+00 -8.23513494276851E-01
x7 : -5.97623476383049E-01 -2.44344535652022E-01
x8 : -8.55390699351840E-01 1.70712670762276E-01
x9 : 1.52914291606202E+00 -1.89564431625379E-01
x10 : 2.48202441735159E-01 1.16788177316392E+00
x11 : -1.45894122879726E-01 -8.62915178631412E-01
x12 : 1.31623928166929E+00 -9.56469350666770E-02
== err : 4.903E-15 = rco : 2.878E-02 = res : 9.114E-16 ==
solution 41 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 3.89415083856842E-01 2.09906533045255E-30
x2 : 9.21062371647419E-01 1.19318895541342E-30
x3 : -3.08457430339590E+00 1.12748434939333E+00
x4 : -1.18298149617247E+00 -2.93986783637120E+00
x5 : 5.51926701023123E+00 -2.78748170612766E+00
x6 : 2.82446248609853E+00 5.44700306623820E+00
x7 : 2.18528888972524E+00 2.19251036407534E+00
x8 : 2.30971002700246E+00 -2.07440262336281E+00
x9 : 4.22761702728453E-01 -4.87287884168481E-02
x10 : 9.07833668459021E-01 2.26921145125288E-02
x11 : 6.32896057637867E-01 -5.02771683764590E-03
x12 : 7.74264004141422E-01 4.10973795558808E-03
== err : 8.150E-15 = rco : 3.843E-03 = res : 5.024E-15 ==
solution 42 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 3.89415083856842E-01 -3.22740331715972E-31
x2 : 9.21062371647419E-01 -1.33554077462447E-30
x3 : -3.08457430339590E+00 1.12748434939333E+00
x4 : -1.18298149617247E+00 -2.93986783637120E+00
x5 : 5.51926701023123E+00 -2.78748170612766E+00
x6 : 2.82446248609853E+00 5.44700306623820E+00
x7 : 2.18528888972524E+00 2.19251036407534E+00
x8 : 2.30971002700246E+00 -2.07440262336281E+00
x9 : 4.22761702728453E-01 -4.87287884168482E-02
x10 : 9.07833668459021E-01 2.26921145125288E-02
x11 : -7.34696844899792E-01 1.63682788488653E-02
x12 : -6.78824208644992E-01 -1.77155185002992E-02
== err : 1.079E-14 = rco : 3.904E-03 = res : 1.005E-14 ==
solution 43 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 3.89415083856842E-01 7.48374118825815E-50
x2 : 9.21062371647419E-01 9.62195295633190E-50
x3 : 7.30467265581230E-01 -1.47108969643474E-47
x4 : 6.82947709502185E-01 1.20595143719360E-47
x5 : 5.01061086394409E-01 2.90796800458031E-47
x6 : 8.65411917933452E-01 -2.53164273339933E-47
x7 : 7.76576030467492E-01 -1.35134983742261E-47
x8 : 6.30023546308670E-01 1.36845553156720E-47
x9 : 9.85556337261790E-01 -3.10040706370695E-49
x10 : -1.69347884790821E-01 -1.28292706084425E-48
x11 : 9.99515580871569E-01 -2.23175853292698E-49
x12 : 3.11223969991191E-02 -1.11187011939835E-48
== err : 2.320E-15 = rco : 2.869E-02 = res : 8.882E-16 ==
solution 44 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 3.89415083856842E-01 -4.52692997467398E-54
x2 : 9.21062371647419E-01 -6.72922023262348E-54
x3 : 7.30467265581230E-01 -2.40131204422346E-52
x4 : 6.82947709502185E-01 2.92333640166334E-52
x5 : 5.01061086394409E-01 4.90702895993489E-52
x6 : 8.65411917933451E-01 -5.42905331737477E-52
x7 : 7.76576030467492E-01 -2.50571691571143E-52
x8 : 6.30023546308670E-01 2.53181813358343E-52
x9 : 9.85556337261790E-01 2.61012178719941E-54
x10 : -1.69347884790821E-01 6.78631664671847E-53
x11 : -9.42471422417144E-01 -2.74062787655938E-53
x12 : 3.34286730109057E-01 -7.56935318287829E-53
== err : 1.617E-15 = rco : 2.814E-02 = res : 8.882E-16 ==
solution 45 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -3.89415083856842E-01 1.01142219253977E-53
x2 : -9.21062371647419E-01 1.99021786273955E-53
x3 : 7.30467265581230E-01 -3.54976563059120E-52
x4 : -6.82947709502185E-01 -3.54976563059120E-52
x5 : 5.01061086394409E-01 6.26429228927858E-52
x6 : -8.65411917933451E-01 6.26429228927858E-52
x7 : 7.76576030467492E-01 -1.87928768678358E-52
x8 : -6.30023546308671E-01 -2.08809742975953E-52
x9 : 9.85556337261790E-01 7.11156229129527E-54
x10 : 1.69347884790821E-01 -3.84992963611913E-53
x11 : 9.42471422417144E-01 5.83199086827368E-54
x12 : -3.34286730109057E-01 1.68026590050962E-53
== err : 8.670E-16 = rco : 2.351E-02 = res : 8.882E-16 ==
solution 46 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -3.89415083856842E-01 -3.20731765211063E-49
x2 : -9.21062371647419E-01 -2.56585412168851E-49
x3 : 7.30467265581230E-01 8.55284707229503E-48
x4 : -6.82947709502185E-01 7.18439154072782E-48
x5 : 5.01061086394409E-01 -1.50530108472392E-47
x6 : -8.65411917933451E-01 -1.30003275498884E-47
x7 : 7.76576030467492E-01 5.81593600916062E-48
x8 : -6.30023546308671E-01 7.18439154072782E-48
x9 : 9.85556337261790E-01 1.28292706084425E-49
x10 : 1.69347884790821E-01 -1.02634164867540E-48
x11 : -9.99515580871569E-01 -4.27642353614751E-50
x12 : -3.11223969991190E-02 -5.13170824337701E-49
== err : 8.670E-16 = rco : 2.320E-02 = res : 8.882E-16 ==
solution 47 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -3.89415083856842E-01 -1.24869330394630E-30
x2 : -9.21062371647419E-01 6.94844296724591E-31
x3 : -3.08457430339590E+00 1.12748434939333E+00
x4 : 1.18298149617247E+00 2.93986783637119E+00
x5 : 5.51926701023123E+00 -2.78748170612766E+00
x6 : -2.82446248609853E+00 -5.44700306623820E+00
x7 : 2.18528888972524E+00 2.19251036407534E+00
x8 : -2.30971002700246E+00 2.07440262336281E+00
x9 : 4.22761702728453E-01 -4.87287884168481E-02
x10 : -9.07833668459021E-01 -2.26921145125288E-02
x11 : 7.34696844899792E-01 -1.63682788488654E-02
x12 : 6.78824208644993E-01 1.77155185002993E-02
== err : 8.757E-15 = rco : 3.904E-03 = res : 5.024E-15 ==
solution 48 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -3.89415083856842E-01 9.57929243962447E-31
x2 : -9.21062371647419E-01 -1.90052524829610E-31
x3 : -3.08457430339590E+00 1.12748434939333E+00
x4 : 1.18298149617247E+00 2.93986783637119E+00
x5 : 5.51926701023123E+00 -2.78748170612766E+00
x6 : -2.82446248609853E+00 -5.44700306623820E+00
x7 : 2.18528888972524E+00 2.19251036407534E+00
x8 : -2.30971002700246E+00 2.07440262336281E+00
x9 : 4.22761702728453E-01 -4.87287884168481E-02
x10 : -9.07833668459021E-01 -2.26921145125288E-02
x11 : -6.32896057637868E-01 5.02771683764590E-03
x12 : -7.74264004141422E-01 -4.10973795558809E-03
== err : 7.918E-15 = rco : 3.843E-03 = res : 1.281E-14 ==