4
0.141050018728*i*bx**2*by*y - 0.00097847866344*bx**2*by*y
+ 0.0782395368483*i*bx**2*y**2 + 0.00123918464673*i*bx**2*y
+ 0.00969424108804*bx**2*y**2 + 0.00125705255662*bx**2*y
+ 0.0328315845569*i*bx*by**2*x - 0.0725922104353*bx*by**2*x
+ 0.000160324879058*i*bx*by*x - 0.14642522425*i*bx*by*y
- 0.2391158765*bx*by*x*y - 0.00109445130977*bx*by*x + 0.168022431284*bx*by*y
- 0.0328315845569*i*bx*x*y**2 - 0.000160324879058*i*bx*x*y
- 0.0471003874787*i*bx*y**2 - 0.00105590259776*i*bx*y
- 0.0725922104353*bx*x*y**2 - 0.00109445130977*bx*x*y
- 0.0000135684269291*bx*x + 0.0654830371929*bx*y**2 - 0.000300187113597*bx*y
- 0.0782395368483*i*by**2*x**2 + 0.0471003874787*i*by**2*x
+ 0.00969424108804*by**2*x**2 + 0.0654830371929*by**2*x
- 0.141050018728*i*by*x**2*y - 0.00123918464673*i*by*x**2
+ 0.14642522425*i*by*x*y + 0.00105590259776*i*by*x
- 0.00097847866344*by*x**2*y + 0.00125705255662*by*x**2
+ 0.168022431284*by*x*y - 0.000300187113597*by*x - 0.0888122554974*by*y;
- 0.0249469889303*i*bx**2*by*y + 0.00931583747381*bx**2*by*y
+ 0.0294053156051*i*bx**2*y**2 - 0.00105533016484*i*bx**2*y
+ 0.00786359271692*bx**2*y**2 - 0.0177007048352*bx**2*y
+ 0.0595383104696*i*bx*by**2*x + 0.079236107727*bx*by**2*x
- 0.108418415833*i*bx*by*x + 0.00451693895279*i*bx*by*y
- 0.205718481117*bx*by*x*y + 0.0366433756262*bx*by*x
- 0.00437803776486*bx*by*y - 0.0595383104696*i*bx*x*y**2
+ 0.108418415833*i*bx*x*y - 0.0129569311769*i*bx*y**2
+ 0.00353939806669*i*bx*y + 0.079236107727*bx*x*y**2 + 0.0366433756262*bx*x*y
- 0.0322818097234*bx*x + 0.00301410665727*bx*y**2 + 0.00546021583064*bx*y
- 0.0294053156051*i*by**2*x**2 + 0.0129569311769*i*by**2*x
+ 0.00786359271692*by**2*x**2 + 0.00301410665727*by**2*x
+ 0.0249469889303*i*by*x**2*y + 0.00105533016484*i*by*x**2
- 0.00451693895279*i*by*x*y - 0.00353939806669*i*by*x
+ 0.00931583747381*by*x**2*y - 0.0177007048352*by*x**2
- 0.00437803776486*by*x*y + 0.00546021583064*by*x - 0.0013116146819*by*y;
- 0.0218107478514*i*bx**2*by*y - 0.0227503225264*bx**2*by*y
+ 0.0145785542176*i*bx**2*y**2 + 0.0133382023419*i*bx**2*y
+ 0.0289746279868*bx**2*y**2 - 0.0104815931774*bx**2*y
+ 0.0537999863131*i*bx*by**2*x + 0.112859448991*bx*by**2*x
- 0.124451937985*i*bx*by*x + 0.00929216513796*i*bx*by*y
- 0.249135161545*bx*by*x*y + 0.0288876047041*bx*by*x
+ 0.00595806356335*bx*by*y - 0.0537999863131*i*bx*x*y**2
+ 0.124451937985*i*bx*x*y - 0.00917830603125*i*bx*y**2
- 0.00230902546847*i*bx*y + 0.112859448991*bx*x*y**2 + 0.0288876047041*bx*x*y
- 0.0330774656043*bx*x - 0.00830926429131*bx*y**2 + 0.00563037140451*bx*y
- 0.0145785542176*i*by**2*x**2 + 0.00917830603125*i*by**2*x
+ 0.0289746279868*by**2*x**2 - 0.00830926429131*by**2*x
+ 0.0218107478514*i*by*x**2*y - 0.0133382023419*i*by*x**2
- 0.00929216513796*i*by*x*y + 0.00230902546847*i*by*x
- 0.0227503225264*by*x**2*y - 0.0104815931774*by*x**2
+ 0.00595806356335*by*x*y + 0.00563037140451*by*x - 0.0011195743111*by*y;
- 0.0114868064801*i*bx**2*by*y - 0.0119413549909*bx**2*by*y
- 0.0139828726508*i*bx**2*y**2 + 0.000914652140862*i*bx**2*y
- 0.0209721546687*bx**2*y**2 + 0.00721574419444*bx**2*y
- 0.00930458610211*i*bx*by**2*x + 0.0140687638574*bx*by**2*x
+ 0.00726787677736*i*bx*by*x + 0.00908990049543*i*bx*by*y
+ 0.0363929678175*bx*by*x*y - 0.00210685119583*bx*by*x
- 0.0189904701902*bx*by*y + 0.00930458610211*i*bx*x*y**2
- 0.00726787677736*i*bx*x*y + 0.0207832691669*i*bx*y**2
+ 0.000392165732469*i*bx*y + 0.0140687638574*bx*x*y**2
- 0.00210685119583*bx*x*y - 0.000223340726321*bx*x - 0.00631749512119*bx*y**2
+ 0.000524903641698*bx*y + 0.0139828726508*i*by**2*x**2
- 0.0207832691669*i*by**2*x - 0.0209721546687*by**2*x**2
- 0.00631749512119*by**2*x + 0.0114868064801*i*by*x**2*y
- 0.000914652140862*i*by*x**2 - 0.00908990049543*i*by*x*y
- 0.000392165732469*i*by*x - 0.0119413549909*by*x**2*y
+ 0.00721574419444*by*x**2 - 0.0189904701902*by*x*y + 0.000524903641698*by*x
- 0.00192225485187*by*y;
TITLE : Four-bar linkage through five points, 4-dimensional version.
ROOT COUNTS :
total degree : 256
m-homogeneous Bezout bound : 96
with partition : {bx x }{by y }
mixed volume : 36
REFERENCES :
Wampler, C.W.:
"Isotropic coordinates, circularity and Bezout numbers:
planar kinematics from a new perspective" ,
Publication R&D-8188, General Motors Corporation, Research
and Development Center.
Proceedings of the 1996 ASME Design Engineering Technical Conference,
Irvine, California August 18-22, 1996. CD-ROM edited by McCarthy, J.M.,
American society of mechanical engineers.
NOTE : the system should be scaled before solving.
THE SOLUTIONS :
36 4
===========================================================
solution 1 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
bx : 4.10643844279429E-01 3.80097858680397E-01
by : 5.24290008999790E-02 2.98380116830551E-01
y : 5.33809408978755E-02 -3.00741174670343E-01
x : 4.10128328342876E-01 -3.83183749554144E-01
== err : 2.730E-13 = rco : 6.848E-04 = res : 1.371E-18 ==
solution 2 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
bx : 5.32080766527715E-02 5.90752167831680E-01
by : 1.77071366545533E+00 -7.44464236041437E-01
y : 1.77071366545533E+00 7.44464236041427E-01
x : 5.32080766527717E-02 -5.90752167831680E-01
== err : 7.017E-13 = rco : 2.743E-03 = res : 1.536E-16 ==
solution 3 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
bx : 2.51352068853834E-01 5.18006222569402E-01
by : 1.24368653495560E-01 2.98722380938766E-01
y : 4.70269690304145E-02 -9.15586136242007E-02
x : -2.11555520756750E-01 3.12707267556329E-02
== err : 1.815E-14 = rco : 1.613E-02 = res : 1.319E-18 ==
solution 4 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
bx : 4.52037570892197E-01 6.40342628287667E-01
by : 1.58281903528209E-01 3.83166969106441E-01
y : 1.05769256504725E-01 -7.97380822738326E-02
x : 2.02358500001056E-01 -1.61002177558598E-01
== err : 8.563E-15 = rco : 6.807E-02 = res : 2.158E-18 ==
solution 5 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
bx : 4.65117817970906E-01 4.69040702572671E-01
by : -1.29838210703014E-01 3.47552123025764E-01
y : -1.29838210703012E-01 -3.47552123025768E-01
x : 4.65117817970906E-01 -4.69040702572676E-01
== err : 1.562E-14 = rco : 3.349E-02 = res : 1.564E-18 ==
solution 6 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
bx : -2.91350510977198E-01 6.29899792895238E-01
by : 6.22620282693208E-01 1.58754316408417E-01
y : 6.22620282693209E-01 -1.58754316408420E-01
x : -2.91350510977198E-01 -6.29899792895239E-01
== err : 2.173E-14 = rco : 1.471E-02 = res : 9.921E-18 ==
solution 7 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
bx : 4.04563104934930E-01 3.26901584321475E-01
by : 1.05593528207785E-01 2.73116575725835E-01
y : 1.09651154869771E-01 -2.84400945697550E-01
x : 5.08652824588756E-01 -3.02042217618094E-01
== err : 2.732E-13 = rco : 3.205E-03 = res : 2.638E-18 ==
solution 8 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
bx : 4.07453650855699E-01 6.59241121559313E-01
by : 1.72945324245810E-01 4.23116907682134E-01
y : 9.81794420987430E-02 -1.23330096820087E-01
x : 1.61242793312879E-01 -1.90369017262101E-01
== err : 1.405E-14 = rco : 6.171E-02 = res : 2.882E-18 ==
solution 9 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
bx : 1.61242793312878E-01 1.90369017262103E-01
by : 9.81794420987426E-02 1.23330096820085E-01
y : 1.72945324245810E-01 -4.23116907682136E-01
x : 4.07453650855697E-01 -6.59241121559313E-01
== err : 1.326E-14 = rco : 5.351E-02 = res : 1.666E-18 ==
solution 10 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
bx : 1.20647775356082E+00 -9.36345185074867E-02
by : 3.24771126236157E-01 2.14184210010077E-01
y : 3.24771126236148E-01 -2.14184210010030E-01
x : 1.20647775356070E+00 9.36345185077011E-02
== err : 2.089E-13 = rco : 1.015E-03 = res : 1.399E-17 ==
solution 11 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
bx : 1.13337718253528E+00 -5.38858398089683E-02
by : 1.99684727474357E-01 2.33955256182626E-01
y : 1.99684727474357E-01 -2.33955256182626E-01
x : 1.13337718253528E+00 5.38858398089658E-02
== err : 2.462E-13 = rco : 5.978E-03 = res : 1.490E-17 ==
solution 12 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
bx : 1.72266423705274E+00 -3.81388672899821E-01
by : 4.18469707410531E-01 1.98044029985402E-01
y : 4.18469707410533E-01 -1.98044029985418E-01
x : 1.72266423705279E+00 3.81388672899719E-01
== err : 2.174E-13 = rco : 7.201E-04 = res : 6.597E-17 ==
solution 13 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
bx : 4.87403732141600E-01 1.68688910021504E-01
by : 1.34373580768024E-01 2.59259706384777E-01
y : 1.44652288859644E-01 -2.67024928868181E-01
x : 5.81051048294509E-01 -2.71102828840313E-01
== err : 5.562E-13 = rco : 3.499E-03 = res : 2.267E-18 ==
solution 14 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
bx : 5.08652824588712E-01 3.02042217618121E-01
by : 1.09651154869742E-01 2.84400945697570E-01
y : 1.05593528207758E-01 -2.73116575725840E-01
x : 4.04563104934882E-01 -3.26901584321581E-01
== err : 3.311E-13 = rco : 2.684E-03 = res : 2.782E-18 ==
solution 15 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
bx : 3.34803931333403E-01 1.60553319642052E-01
by : 4.12749367461024E-02 5.72686811005432E-02
y : 2.76331602391193E-02 8.68452347612911E-02
x : -9.27794256887926E-04 -5.90051132524531E-05
== err : 8.711E-16 = rco : 1.374E-02 = res : 7.063E-20 ==
solution 16 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
bx : 5.83182363049177E-01 3.26733607777418E-01
by : 1.47323765616800E-01 2.85540999011355E-01
y : 1.21094670303097E-01 -2.49156335673215E-01
x : 3.76623768704033E-01 -1.58903307729672E-01
== err : 4.764E-13 = rco : 2.056E-03 = res : 2.274E-18 ==
solution 17 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
bx : -2.51207564750122E-01 -2.25329652796196E-01
by : 4.15766144217165E-02 9.41891746850768E-02
y : 1.16247295058443E-01 -3.66309789144711E-01
x : 1.11256875354288E-01 -7.35865844321103E-01
== err : 3.856E-14 = rco : 1.531E-02 = res : 1.403E-18 ==
solution 18 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
bx : 6.54269902031446E-02 3.28326558145372E-01
by : -1.42177193321312E-01 -7.31524928134020E-02
y : 2.19375120413220E-01 -6.11788889109238E-01
x : 2.45198947851124E-01 -6.65270362439401E-01
== err : 2.442E-14 = rco : 2.094E-02 = res : 3.387E-18 ==
solution 19 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
bx : 5.37811114617499E-01 1.06123913485911E+00
by : -8.05270439018544E-02 3.54549317702269E-01
y : -8.05270439018706E-02 -3.54549317702240E-01
x : 5.37811114617305E-01 -1.06123913485912E+00
== err : 4.157E-13 = rco : 9.883E-04 = res : 8.416E-18 ==
solution 20 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
bx : -5.58958929302595E-02 6.12044754158337E-01
by : 5.65894334352614E-01 1.69263337604556E-01
y : 5.65894334352614E-01 -1.69263337604557E-01
x : -5.58958929302592E-02 -6.12044754158337E-01
== err : 2.210E-14 = rco : 2.081E-02 = res : 1.164E-17 ==
solution 21 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
bx : 5.81836051396954E-01 2.07715961874054E+00
by : -1.84578856236882E-01 4.13983006171997E-01
y : -1.84578856236869E-01 -4.13983006172020E-01
x : 5.81836051397287E-01 -2.07715961874052E+00
== err : 7.079E-13 = rco : 2.843E-04 = res : 1.300E-16 ==
solution 22 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
bx : 8.80525457171034E-134 -4.40262728585517E-134
by : 5.50328410731896E-134 -2.20131364292758E-134
y : 1.64073107336195E-01 -6.71013948070856E-01
x : 1.12544599120311E+00 3.19900099153871E-02
== err : 1.000E+00 = rco : 7.636E-135 = res : 0.000E+00 ==
solution 23 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
bx : -2.11555520756749E-01 -3.12707267556321E-02
by : 4.70269690304146E-02 9.15586136242007E-02
y : 1.24368653495560E-01 -2.98722380938766E-01
x : 2.51352068853835E-01 -5.18006222569401E-01
== err : 1.903E-14 = rco : 1.462E-02 = res : 8.619E-19 ==
solution 24 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
bx : 4.67889490684491E-01 3.90288499946566E-01
by : 6.25290402357431E-02 2.92856254019974E-01
y : 6.13303869027975E-02 -2.92357825283943E-01
x : 4.50483816913761E-01 -3.86539581083285E-01
== err : 2.953E-13 = rco : 7.149E-03 = res : 2.743E-18 ==
solution 25 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
bx : 3.76623768704082E-01 1.58903307729661E-01
by : 1.21094670303104E-01 2.49156335673218E-01
y : 1.47323765616801E-01 -2.85540999011346E-01
x : 5.83182363049188E-01 -3.26733607777395E-01
== err : 4.512E-13 = rco : 2.529E-03 = res : 2.579E-18 ==
solution 26 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
bx : 4.33564833462993E-01 3.27856655510231E-01
by : 1.22819657745345E-01 2.94837409933799E-01
y : 7.32532369536364E-02 -1.75269267542269E-01
x : 2.43134627508992E-02 -3.19180931825397E-01
== err : 1.599E-14 = rco : 2.959E-02 = res : 1.222E-18 ==
solution 27 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
bx : 4.46198075780247E-02 3.66755463488267E-01
by : 8.46054145410421E-02 2.21230007269951E-01
y : 1.30151402978545E-01 -3.38695015590422E-01
x : 4.22897870112585E-01 -3.59147292155791E-01
== err : 1.607E-14 = rco : 1.294E-02 = res : 3.080E-18 ==
solution 28 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
bx : 2.02358500001057E-01 1.61002177558596E-01
by : 1.05769256504725E-01 7.97380822738339E-02
y : 1.58281903528209E-01 -3.83166969106440E-01
x : 4.52037570892199E-01 -6.40342628287667E-01
== err : 8.436E-15 = rco : 6.948E-02 = res : 9.139E-19 ==
solution 29 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
bx : 4.50483816913784E-01 3.86539581083297E-01
by : 6.13303869027928E-02 2.92357825283939E-01
y : 6.25290402357416E-02 -2.92856254019975E-01
x : 4.67889490684533E-01 -3.90288499946593E-01
== err : 2.046E-13 = rco : 7.565E-03 = res : 3.926E-18 ==
solution 30 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
bx : 1.11256875354288E-01 7.35865844321100E-01
by : 1.16247295058443E-01 3.66309789144710E-01
y : 4.15766144217166E-02 -9.41891746850768E-02
x : -2.51207564750123E-01 2.25329652796194E-01
== err : 3.862E-14 = rco : 1.441E-02 = res : 3.469E-18 ==
solution 31 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
bx : 5.81051048294493E-01 2.71102828840326E-01
by : 1.44652288859636E-01 2.67024928868184E-01
y : 1.34373580768017E-01 -2.59259706384782E-01
x : 4.87403732141584E-01 -1.68688910021554E-01
== err : 3.876E-13 = rco : 2.500E-03 = res : 3.185E-18 ==
solution 32 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
bx : 4.10128328342863E-01 3.83183749554116E-01
by : 5.33809408978672E-02 3.00741174670326E-01
y : 5.24290008999879E-02 -2.98380116830571E-01
x : 4.10643844279420E-01 -3.80097858680438E-01
== err : 2.724E-13 = rco : 6.839E-04 = res : 2.800E-18 ==
solution 33 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
bx : 4.22897870112592E-01 3.59147292155787E-01
by : 1.30151402978544E-01 3.38695015590421E-01
y : 8.46054145410420E-02 -2.21230007269954E-01
x : 4.46198075780421E-02 -3.66755463488274E-01
== err : 2.408E-14 = rco : 1.349E-02 = res : 1.260E-18 ==
solution 34 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
bx : 2.43134627508985E-02 3.19180931825398E-01
by : 7.32532369536361E-02 1.75269267542269E-01
y : 1.22819657745345E-01 -2.94837409933799E-01
x : 4.33564833462992E-01 -3.27856655510230E-01
== err : 1.328E-14 = rco : 3.325E-02 = res : 1.411E-18 ==
solution 35 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
bx : -9.27794256887926E-04 5.90051132524505E-05
by : 2.76331602391193E-02 -8.68452347612911E-02
y : 4.12749367461024E-02 -5.72686811005432E-02
x : 3.34803931333403E-01 -1.60553319642052E-01
== err : 8.093E-16 = rco : 1.125E-02 = res : 9.133E-20 ==
solution 36 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
bx : 2.45198947851124E-01 6.65270362439399E-01
by : 2.19375120413216E-01 6.11788889109240E-01
y : -1.42177193321315E-01 7.31524928134001E-02
x : 6.54269902031460E-02 -3.28326558145374E-01
== err : 2.431E-14 = rco : 1.909E-02 = res : 3.496E-18 ==