var d1;
var d2;
var d3;
var q1;
var q2;
var q3;

subject to


cons1:  - d1*q1 - d2*q2 - d3*q3 + 1 = 0;

cons2:  - 3.6*d1*q1 + 4.1*d1*q2 + 2.0*d1*q3 + 0.1*d1 + 4.1*d2*q1 + 1.8*d2*q2
 + 3.7*d2*q3 - 0.2*d2 + 2.0*d3*q1 + 3.7*d3*q2 - 4.0*d3*q3 + 0.3*d3 + 
0.1*q1 - 0.2*q2 + 0.3*q3 + 5.8 = 0;

cons3:  - 2.140796*d1*q1 - 3.998792*d1*q2 + 3.715992*d1*q3 - 0.2828*d1 - 
3.998792*d2*q1 - 1.575196*d2*q2 - 3.998792*d2*q3 + 3.715992*d3*q1 - 
3.998792*d3*q2 - 2.140796*d3*q3 + 0.2828*d3 - 0.2828*q1 + 0.2828*q3 + 5.856788 = 0;

cons4: 0.3464*d1*q1 + 0.1732*d1*q2 - 5.999648*d1*q3 - 0.1732*d1 + 0.1732*d2*
q1 - 5.999648*d2*q2 - 0.1732*d2*q3 + 0.3464*d2 - 5.999648*d3*q1 - 
0.1732*d3*q2 - 0.3464*d3*q3 - 0.1732*d3 - 0.1732*q1 + 0.3464*q2 - 
0.1732*q3 + 5.999648 = 0;

cons5:  - 5701.3*d1*q1 - 2.9*d1*q2 + 3796.7*d1*q3 - 1902.7*d1 - 2.9*d2*q1 - 
5698.7*d2*q2 + 1897.3*d2*q3 + 3803.3*d2 + 3796.7*d3*q1 + 1897.3*d3*q2
 + 5703.1*d3*q3 + 0.7*d3 - 1902.7*q1 + 3803.3*q2 + 0.7*q3 + 5696.9 = 0;

cons6:  - 6.8*d1*q1 - 3.2*d1*q2 + 1.3*d1*q3 + 5.1*d1 - 3.2*d2*q1 - 4.8*d2*q2
 - 0.7*d2*q3 - 7.1*d2 + 1.3*d3*q1 - 0.7*d3*q2 + 9.0*d3*q3 - d3 + 5.1*q1
 - 7.1*q2 - q3 + 2.6 = 0;

solve;
display d1, d2, d3, q1, q2, q3;

# TITLE : camera displacement between two positions, scaled first frame.

# ROOT COUNTS :

# total degree : 64
# 2-homogeneous Bezout bound : 20
#  with partition : {{d1 d2 d3 }{q1 q2 q3 }}
# mixed volume : 20

# REFERENCES :

# Ioannis Z. Emiris:
# `Sparse Elimination and Application in Kinematics'
# PhD Thesis, Computer Science, University of California at Berkeley, 1994.

# Ioannis Z. Emiris:
# `A general Solver Based on Sparse Resultants:
#  Numerical Issues and Kinematic Applications',
# INRIA Rapport de Recherche no 3110, January 1997, 29 pages
# Available via anonymous ftp to ftp.inria.fr

# NOTE :

# This system models the displacement of a camera between two positions
# in a static environment, coordinates of matched points in first instance.
# The coordinates of the frames have been scaled, i.e., all components have
# been divided by 1000.

# THE SOLUTIONS :

# 20 6
# ===========================================================
# solution 1 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  d1 : -1.00187746343441E+01  -1.02003169143904E-67
#  q1 :  2.16349900882507E+00  -2.81088278606781E-68
#  d2 :  5.27096688651916E+00   4.40468230394131E-68
#  q2 :  4.14807645389239E+00  -5.44789653382215E-68
#  d3 :  3.46044449033976E-01   3.18759903574700E-69
#  q3 :  2.34430970383515E+00  -3.44840259321721E-68
# == err :  3.403E-14 = rco :  1.837E-06 = res :  2.183E-11 ==
# solution 2 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  d1 : -4.00074964087066E-01   1.86690458335834E-60
#  q1 :  7.14374212666202E+01  -2.54894705781192E-57
#  d2 :  4.15805732418402E-01  -7.46761833343337E-60
#  q2 :  6.27398271488606E+01  -2.30998327114206E-57
#  d3 : -3.88155169000059E-01   5.60071375007503E-60
#  q3 : -8.99831883542215E+00   2.04114901113845E-58
# == err :  1.114E-13 = rco :  4.472E-08 = res :  2.910E-11 ==
# solution 3 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  d1 : -4.11362919961996E-03   6.34702729602409E-01
#  q1 :  1.07073370333179E+00  -5.28986736899611E+00
#  d2 :  2.97394007311655E-01  -3.71117214378002E+00
#  q2 :  7.08792243065625E-02   1.94181773315705E-01
#  d3 :  2.72180047596179E-02   5.59540380075883E-01
#  q3 : -1.15287061420216E+00   5.47490578453015E+00
# == err :  2.672E-15 = rco :  5.284E-06 = res :  3.750E-12 ==
# solution 4 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  d1 :  2.39689707893600E-02   2.03752779273601E-71
#  q1 : -1.85992426440753E+02  -3.33828553561868E-67
#  d2 : -1.86554926678331E-02  -2.32493948224955E-71
#  q2 : -1.07460371835044E+02  -2.22552369041245E-67
#  d3 : -2.54759702551365E-02  -4.75423151638402E-71
#  q3 : -1.35552083903577E+02  -1.94733322911090E-67
# == err :  2.907E-13 = rco :  2.823E-09 = res :  1.819E-11 ==
# solution 5 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  d1 : -2.56263047259548E+00   1.00151652128078E-60
#  q1 :  8.11735863421135E+00   2.17805534725140E-60
#  d2 :  1.35645958316042E+00  -1.25918824762972E-60
#  q2 :  1.57220206476798E+01   4.04495993060974E-60
#  d3 :  5.38269606136141E-02  -4.80095905225616E-62
#  q3 :  8.83395631861776E+00   2.17805534725140E-60
# == err :  4.462E-14 = rco :  4.721E-07 = res :  2.842E-14 ==
# solution 6 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  d1 : -4.11362919961983E-03  -6.34702729602409E-01
#  q1 :  1.07073370333179E+00   5.28986736899611E+00
#  d2 :  2.97394007311654E-01   3.71117214378002E+00
#  q2 :  7.08792243065624E-02  -1.94181773315705E-01
#  d3 :  2.72180047596180E-02  -5.59540380075882E-01
#  q3 : -1.15287061420216E+00  -5.47490578453015E+00
# == err :  3.759E-15 = rco :  5.284E-06 = res :  4.547E-12 ==
# solution 7 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  d1 :  4.31525045865282E-03   4.59858703221669E-73
#  q1 :  1.53964291762927E+01   1.26779507103574E-70
#  d2 :  1.57557671967738E-01  -4.10335458259335E-72
#  q2 :  1.19603230035780E+01   8.15011117094404E-71
#  d3 :  3.44291835195695E-02   0.00000000000000E+00
#  q3 : -2.76184329480271E+01   0.00000000000000E+00
# == err :  3.066E-14 = rco :  3.142E-07 = res :  4.775E-12 ==
# solution 8 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  d1 :  2.54964137276597E+01  -1.44890865261227E-70
#  q1 :  3.54809887556081E-01  -2.26391976970668E-72
#  d2 :  1.30967935950199E+01  -5.43340744729603E-71
#  q2 : -3.56996638737865E-01  -1.13195988485334E-72
#  d3 : -9.06123055507048E+00   9.05567907882671E-71
#  q3 :  3.72010001913294E-01   4.24484956820002E-72
# == err :  1.310E-14 = rco :  3.754E-07 = res :  1.455E-11 ==
# solution 9 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  d1 :  1.07073370333179E+00  -5.28986736899611E+00
#  q1 : -4.11362919961994E-03   6.34702729602409E-01
#  d2 :  7.08792243065625E-02   1.94181773315705E-01
#  q2 :  2.97394007311655E-01  -3.71117214378002E+00
#  d3 : -1.15287061420216E+00   5.47490578453015E+00
#  q3 :  2.72180047596179E-02   5.59540380075883E-01
# == err :  4.664E-15 = rco :  4.608E-06 = res :  1.095E-11 ==
# solution 10 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  d1 :  7.14374212666199E+01  -4.35611069450280E-59
#  q1 : -4.00074964087066E-01  -9.72346137165803E-63
#  d2 :  6.27398271488603E+01  -3.98272977783113E-59
#  q2 :  4.15805732418403E-01   1.40990189889042E-61
#  d3 : -8.99831883542212E+00   4.01862763508772E-60
#  q3 : -3.88155169000059E-01  -8.75111523449223E-62
# == err :  1.433E-13 = rco :  4.472E-08 = res :  1.455E-11 ==
# solution 11 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  d1 : -5.44504357673233E-02  -9.33452291679171E-61
#  q1 : -2.53902514663185E+01   8.96114200012004E-59
#  d2 : -1.30887818487475E-02  -2.91703841149741E-62
#  q2 : -1.35197609918457E+01   5.60071375007503E-59
#  d3 :  1.18597460143422E-02   1.26404997831554E-61
#  q3 : -4.71736458922360E+01  -1.19481893334934E-58
# == err :  3.343E-14 = rco :  1.800E-07 = res :  5.230E-12 ==
# solution 12 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  d1 :  1.52525122261781E+01   1.03234741498625E-69
#  q1 :  2.94025403132356E+00  -2.51861074379868E-71
#  d2 : -1.59650216570430E+01  -1.08668148945921E-69
#  q2 :  2.07407537095237E+00  -2.00922879561468E-71
#  d3 :  1.51939278512973E+01   1.03234741498625E-69
#  q3 : -7.06440260233406E-01  -3.50907564304535E-71
# == err :  1.971E-13 = rco :  4.927E-07 = res :  5.821E-11 ==
# solution 13 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  d1 :  2.16349900882506E+00  -3.41840438847353E-64
#  q1 : -1.00187746343442E+01  -1.51929083932157E-63
#  d2 :  4.14807645389238E+00  -7.21663148677745E-64
#  q2 :  5.27096688651919E+00   3.41840438847353E-64
#  d3 :  2.34430970383515E+00  -1.70920219423676E-64
#  q3 :  3.46044449033977E-01   3.32344871101593E-65
# == err :  9.576E-15 = rco :  1.830E-06 = res :  1.455E-11 ==
# solution 14 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  d1 :  2.94025403132356E+00  -1.11276184520623E-67
#  q1 :  1.52525122261781E+01  -3.17137125883775E-66
#  d2 :  2.07407537095237E+00  -4.40468230394131E-68
#  q2 : -1.59650216570430E+01   2.96736492054994E-66
#  d3 : -7.06440260233406E-01  -9.27301537671855E-69
#  q3 :  1.51939278512973E+01  -3.26410141260493E-66
# == err :  2.443E-14 = rco :  4.927E-07 = res :  4.366E-11 ==
# solution 15 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  d1 : -1.85992426440753E+02   4.07831529249908E-56
#  q1 :  2.39689707893600E-02   1.92913473613695E-59
#  d2 : -1.07460371835044E+02   2.03915764624954E-56
#  q2 : -1.86554926678331E-02   8.71222138900560E-60
#  d3 : -1.35552083903577E+02   1.01957882312477E-56
#  q3 : -2.54759702551365E-02  -8.82890292546549E-60
# == err :  2.534E-13 = rco :  2.823E-09 = res :  2.274E-13 ==
# solution 16 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  d1 :  1.07073370333179E+00   5.28986736899611E+00
#  q1 : -4.11362919961979E-03  -6.34702729602409E-01
#  d2 :  7.08792243065624E-02  -1.94181773315705E-01
#  q2 :  2.97394007311654E-01   3.71117214378002E+00
#  d3 : -1.15287061420216E+00  -5.47490578453015E+00
#  q3 :  2.72180047596180E-02  -5.59540380075883E-01
# == err :  4.058E-15 = rco :  4.608E-06 = res :  1.819E-12 ==
# solution 17 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  d1 :  3.54809887556081E-01  -5.11261178461591E-75
#  q1 :  2.54964137276597E+01   3.53737464016668E-74
#  d2 : -3.56996638737865E-01   2.76357393763022E-75
#  q2 :  1.30967935950199E+01   1.76868732008334E-74
#  d3 :  3.72010001913294E-01  -5.52714787526044E-76
#  q3 : -9.06123055507050E+00  -1.06121239205001E-73
# == err :  4.185E-14 = rco :  3.753E-07 = res :  7.276E-12 ==
# solution 18 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  d1 : -2.53902514663185E+01   5.11150998216783E-64
#  q1 : -5.44504357673233E-02  -2.04006338287808E-67
#  d2 : -1.35197609918457E+01   3.03858167864314E-64
#  q2 : -1.30887818487475E-02   0.00000000000000E+00
#  d3 : -4.71736458922361E+01   6.07716335728627E-64
#  q3 :  1.18597460143422E-02  -2.07715544438496E-66
# == err :  4.941E-14 = rco :  1.800E-07 = res :  7.276E-12 ==
# solution 19 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  d1 :  8.11735863421133E+00  -4.98062349335469E-71
#  q1 : -2.56263047259548E+00  -1.58474383879467E-71
#  d2 :  1.57220206476798E+01   1.81113581576534E-70
#  q2 :  1.35645958316043E+00  -1.01876389636801E-71
#  d3 :  8.83395631861774E+00  -4.52783953941336E-71
#  q3 :  5.38269606136141E-02  -3.11288968334668E-72
# == err :  2.370E-14 = rco :  4.722E-07 = res :  2.910E-11 ==
# solution 20 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  d1 :  1.53964291762927E+01   4.40468230394131E-68
#  q1 :  4.31525045865282E-03  -8.15011117094404E-71
#  d2 :  1.19603230035780E+01   2.46314470944087E-68
#  q2 :  1.57557671967738E-01  -3.62227163153069E-71
#  d3 : -2.76184329480271E+01   1.85460307534371E-68
#  q3 :  3.44291835195695E-02  -1.44890865261227E-70
# == err :  4.201E-14 = rco :  3.241E-07 = res :  2.842E-14 ==