# 
# Auto-calibration of a camera. 
# 
# Characteristics:
#      Overconstrained system. Generically, one solution. 
# 
# Ref: D. Bini and B. Mourrain. Polynomial test suite. 1996.
# 



# Domains
var x1 >= -1.0e4, <= 1.0e4;
var x2 >= -1.0e4, <= 1.0e4;
var x3 >= -1.0e4, <= 1.0e4;
var x4 >= -1.0e4, <= 1.0e4;
var x5 >= -1.0e4, <= 1.0e4;



subject to

cons1 : x3*(.57446030378411210500e-6 +.2878669609051599434800e-9*x5 -.1413879606430073317000e-6*x2 +.2260715598278493751000e-6*x1 -.7611538299225383794000e-9*x4) +x1*(.790810468123839913500e-1 +.576239877677818343400e-6*x5 -.436641385104830185600e-3*x2 -.6151155671580043684100e-4*x1 +.2115114651153454255600e-6*x4) +x2*(.4196244389653656099100e-1 -.3793171623177442676000e-7*x5 +.1807977610453753238700e-4*x2 +.850811727332718313800e-6*x4) -x4*(.1751613950359005401700e-3 +.679218657484954924800e-9*x5 +.1484781695906232749900e-10*x4) +x5*(.2282679824198712676900e-11*x5 -.665943977391716185500e-4)= 6.9769247755906706053;


cons2 : x5*(.2110060214660143967700e-5 -.2719534201040163893200e-7*x1 -.1702623115659556670500e-11*x3 +.2680086049409404086500e-9*x2 +.8760864140509743994200e-10*x4) -x1*(.2140331089638663771600e-1 +.3446099368558527309900e-6*x3 -.140622165312776746000e-4*x2 +.2590133019090686504200e-6*x4 -.1305462899815279601400e-3*x1) +x3*(.4144285953595159155600e-4 -.1625848844223454788000e-9*x3 +.4520633740597296727900e-7*x2 +.304870430133298478900e-9*x4) -x2*(.3467463041748386549300e-2 +.3087420810097024967200e-5*x2 -.839472055445605435900e-7*x4) +x4*(.1576026908829047847300e-9*x4 -.54394552730618051300e-5)= -1.1826782050651733260;


cons3 : x3*(.1625848844223454788000e-9*x5 -.83143756564905307600e-7 -.7361898024912568609700e-7*x2 +.1069425676286599803300e-6*x1 -.3396959730689738740600e-9*x4) +x5*(.4826964540794779731400e-6*x1 -.2038492830775620589500e-7*x2 -.5512071046488164152300e-4 -.626570189478976739800e-9*x4 +.1702623115659556670500e-11*x5) +x4*(.546904606080249513600e-6*x2 +.8883888149326932971700e-7*x1 -.957036922257151281200e-4 -.6399491108284453574900e-11*x4) +x2*(.3051426422684597984200e-1 +.8881273513268696911800e-5*x2 -.3014241254786833377300e-3*x1) +x1*(.4686170555882289551700e-1 -.2733386318298371620200e-4*x1)= 4.4014472669284116425;
 

cons4 : x5*(.3207696067928841112300e-5 -.4376017581335482685400e-7*x1 -.2282679824198712676900e-11*x3 +.3389912578490747337300e-9*x2 +.1492222688503745521800e-9*x4) +x3*(.487371291653174919400e-4 -.2878669609051599434800e-9*x3 +.7956048280753772387500e-7*x2 -.404587350244953551000e-6*x1 +.339304230142815885200e-9*x4) +x4*(.44796228846808710100e-5 +.104006712183549433500e-6*x2 -.487305302729242293000e-6*x1 +.3670883734196991159000e-9*x4) +x2*(.156849356143918522500e-4*x1 -.404932285692824059400e-2 -.5466582902191680761100e-5*x2) +x1*(.2043225074084700103000e-3*x1 -.336358923748597430700e-1)= -1.8076594872821129902;


cons5 : x3*(.4402988563609430296600e-8*x2 +.5488123987758462276800e-9*x1 -.4457806485092739330300e-6 -.1238847876744372048600e-11*x4 -.1258853259393682361600e-10*x5) +x5*(.1530449695126830728600e-5 -.609097372823032230000e-8*x1 +.3112699969451913220500e-8*x2 -.82383344534135310800e-12*x4 +.4798265714190216903300e-12*x5) +x4*(.1942974533178491052600e-7*x2 +.3608724108147413946000e-9*x1 -.4471368125552494678500e-5 -.4601063463831239553400e-14*x4) +x2*(.509308631271440496400e-3 -.1147402523972623816600e-5*x2 -.634938152177819890200e-5*x1) +x1*(.1800887517012775260100e-2 -.1589643272453758478900e-6*x1)= .17177290969169927671;


cons6 : x5*(.2917641023893891547000e-6 -.2718337974873329238800e-8*x1 -.4798265714190216903300e-12*x3 +.1062821257557842011900e-9*x2 +.6325589727025528857800e-11*x4) +x3*(.1258853259393682361600e-10*x3 -.6068899144792232719100e-8*x2 +.7757028881892643658900e-7*x1 -.9188332647086083948900e-5 -.1654976899960615756700e-9*x4) +x4*(.3808014658443819642300e-7*x2 +.3890768116462328262900e-7*x1 -.9491915829641256767100e-5 -.6163566382078377514700e-12*x4) +x2*(.2085940028260375922400e-2 +.7266399813916554957300e-6*x2 -.1772588602045364626700e-4*x1) +x1*(.6609292840561707240900e-2 -.1824424946063856304500e-4*x1)= .52449706997795274452;

# 
# ORIGINAL SYSTEM:
# 
# -.665943977391716185500e-4*x5+.57446030378411210500e-6*x3
# -.1751613950359005401700e-3*x4+.4196244389653656099100e-1*x2
# +.790810468123839913500e-1*x1+.576239877677818343400e-6*x5*x1
# +.2878669609051599434800e-9*x5*x3-.3793171623177442676000e-7*x5*x2
# -.1413879606430073317000e-6*x3*x2+.2260715598278493751000e-6*x3*
# x1+.1807977610453753238700e-4*x2^2-.436641385104830185600e-3*x2*
# x1-.7611538299225383794000e-9*x4*x3+.850811727332718313800e-6*x4
# *x2+.2115114651153454255600e-6*x4*x1-.6151155671580043684100e-4*
# x1^2-.679218657484954924800e-9*x4*x5-.1484781695906232749900e-10
# *x4^2+.2282679824198712676900e-11*x5^2-6.9769247755906706053 = 0,
#  
#  .2110060214660143967700e-5*x5+.4144285953595159155600e-4*x3
# -.54394552730618051300e-5*x4-.3467463041748386549300e-2*x2
# -.2140331089638663771600e-1*x1-.2719534201040163893200e-7*x5*x1
# -.1702623115659556670500e-11*x5*x3+.2680086049409404086500e-9*x5*x2
# -.1625848844223454788000e-9*x3^2+.4520633740597296727900e-7*x3*x2
# -.3446099368558527309900e-6*x3*x1-.3087420810097024967200e-5*x2^2
# +.140622165312776746000e-4*x2*x1+.304870430133298478900e-9*x4*x3
# +.839472055445605435900e-7*x4*x2-.2590133019090686504200e-6*x4*x1
# +.1305462899815279601400e-3*x1^2+.8760864140509743994200e-10*x4*x5
# +.1576026908829047847300e-9*x4^2+1.1826782050651733260 = 0, 
# 
# -.5512071046488164152300e-4*x5-.83143756564905307600e-7*x3
# -.957036922257151281200e-4*x4+.3051426422684597984200e-1*x2
# +.4686170555882289551700e-1*x1+.4826964540794779731400e-6*x5*x1
# +.1625848844223454788000e-9*x5*x3-.2038492830775620589500e-7*x5*x2
# -.7361898024912568609700e-7*x3*x2+.1069425676286599803300e-6*x3*x1
# +.8881273513268696911800e-5*x2^2-.3014241254786833377300e-3*x2*x1
# -.3396959730689738740600e-9*x4*x3+.546904606080249513600e-6*x4*x2
# +.8883888149326932971700e-7*x4*x1-.2733386318298371620200e-4*x1^2
# -.626570189478976739800e-9*x4*x5-.6399491108284453574900e-11*x4^2
# +.1702623115659556670500e-11*x5^2-4.4014472669284116425 = 0,
#  
#  .3207696067928841112300e-5*x5+.487371291653174919400e-4*x3
# +.44796228846808710100e-5*x4-.404932285692824059400e-2*x2
# -.336358923748597430700e-1*x1-.4376017581335482685400e-7*x5*x1
# -.2282679824198712676900e-11*x5*x3+.3389912578490747337300e-9*x5*x2
# -.2878669609051599434800e-9*x3^2+.7956048280753772387500e-7*x3*x2
# -.404587350244953551000e-6*x3*x1-.5466582902191680761100e-5*x2^2
# +.156849356143918522500e-4*x2*x1+.339304230142815885200e-9*x4*x3
# +.104006712183549433500e-6*x4*x2-.487305302729242293000e-6*x4*x1
# +.2043225074084700103000e-3*x1^2+.1492222688503745521800e-9*x4*x5
# +.3670883734196991159000e-9*x4^2+1.8076594872821129902 = 0, 
# 
# .1530449695126830728600e-5*x5-.4457806485092739330300e-6*x3
# -.4471368125552494678500e-5*x4+.509308631271440496400e-3*x2
# +.1800887517012775260100e-2*x1-.609097372823032230000e-8*x5*x1
# -.1258853259393682361600e-10*x5*x3+.3112699969451913220500e-8*x5*x2
# +.4402988563609430296600e-8*x3*x2+.5488123987758462276800e-9*x3*x1
# -.1147402523972623816600e-5*x2^2-.634938152177819890200e-5*x2*x1
# -.1238847876744372048600e-11*x4*x3+.1942974533178491052600e-7*x4*x2
# +.3608724108147413946000e-9*x4*x1-.1589643272453758478900e-6*x1^2
# -.82383344534135310800e-12*x4*x5-.4601063463831239553400e-14*x4^2
# +.4798265714190216903300e-12*x5^2-.17177290969169927671 = 0, 
# 
# .2917641023893891547000e-6*x5-.9188332647086083948900e-5*x3
# -.9491915829641256767100e-5*x4+.2085940028260375922400e-2*x2
# +.6609292840561707240900e-2*x1-.2718337974873329238800e-8*x5*x1
# -.4798265714190216903300e-12*x5*x3+.1062821257557842011900e-9*x5*x2
# +.1258853259393682361600e-10*x3^2-.6068899144792232719100e-8*x3*x2
# +.7757028881892643658900e-7*x3*x1+.7266399813916554957300e-6*x2^2
# -.1772588602045364626700e-4*x2*x1-.1654976899960615756700e-9*x4*x3
# +.3808014658443819642300e-7*x4*x2+.3890768116462328262900e-7*x4*x1
# -.1824424946063856304500e-4*x1^2+.6325589727025528857800e-11*x4*x5
# -.6163566382078377514700e-12*x4^2-.52449706997795274452 = 0
# 



solve;
display x1, x2, x3, x4, x5;