var x;
var y;

subject to

cons1:  -270*x^4*y^3 - 314*x*y^4 - 689*x*y^3 + 1428 = 0;
cons2: 36*x^7 + 417*x^6*y - 422*x^5*y^2 - 270*x^4*y^3 + 1428*x^3*y^4
- 1475*x^2*y^5 + 510*x*y^6 - 200*x^6 - 174*x^5*y - 966*x^4*y^2
+ 529*x^3*y^3 + 269*x^2*y^4 + 49*x*y^5 - 267*y^6 + 529*x^4*y
+ 1303*x^2*y^3 - 314*x*y^4 + 262*y^5 + 36*x^4 - 788*x^2*y^2 
- 689*x*y^3 + 177*y^4 = 0;

solve;
display x, y;

# TITLE : the system sendra of the PoSSo test suite

# ROOT COUNTS :

# total degree : 49
# 1-homogeneous Bezout number : 49
#   with partition : {x y }
# generalized Bezout number : 46
#   based on the set structure :
#      {x }{x y }{x }{x }{y }{y }{y }
#      {x }{x y }{x y }{x y }{x y }{x y }{x y }
# mixed volume : 46

# REFERENCES :

# See the PoSSo test suite.

# THE SOLUTIONS :

# 46 2
# ===========================================================
# solution 1 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x :  5.00256943517446E-01   1.64883944206886E+00
#  y :  1.21327895854065E+00   2.87654469209477E+00
# == err :  3.601E-15 = rco :  2.113E-01 = res :  6.390E-10 ==
# solution 2 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x :  1.13454109131018E+00   8.46486298862573E-01
#  y : -1.12000443752762E+00  -4.10152267830658E-01
# == err :  3.576E-15 = rco :  9.935E-02 = res :  2.344E-12 ==
# solution 3 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x :  3.05462631140359E+00   2.25008959973218E+00
#  y :  1.99918990299544E-01  -2.18877338106381E-01
# == err :  5.019E-15 = rco :  9.764E-04 = res :  5.610E-11 ==
# solution 4 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x :  8.80799397446810E-02   1.46629762922461E+00
#  y : -3.45488305816064E-01   1.08482122947928E+00
# == err :  3.690E-15 = rco :  1.820E-01 = res :  4.617E-12 ==
# solution 5 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x :  8.36234971456537E-01   1.60473100152749E+00
#  y :  2.84786498764032E+00   5.56229841356002E-01
# == err :  4.495E-15 = rco :  2.113E-01 = res :  3.425E-10 ==
# solution 6 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x :  5.38593631773821E-01   1.58274820140551E+00
#  y : -8.18274273436525E-01   6.12881380901085E-01
# == err :  3.909E-15 = rco :  1.192E-01 = res :  3.582E-12 ==
# solution 7 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x :  8.36234971456537E-01  -1.60473100152749E+00
#  y :  2.84786498764032E+00  -5.56229841356002E-01
# == err :  4.495E-15 = rco :  2.113E-01 = res :  3.425E-10 ==
# solution 8 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x :  3.05462631140359E+00  -2.25008959973218E+00
#  y :  1.99918990299544E-01   2.18877338106381E-01
# == err :  5.019E-15 = rco :  9.764E-04 = res :  5.610E-11 ==
# solution 9 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x :  4.56253327336965E-01   2.99627286700301E-94
#  y : -2.75343151310694E+00   2.39701829360241E-94
# == err :  3.413E-16 = rco :  1.001E-02 = res :  2.910E-11 ==
# solution 10 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x : -7.51672368346469E-01  -7.20346274884387E-01
#  y : -1.40695386330471E+00   1.90591935488604E-01
# == err :  5.495E-16 = rco :  1.654E-01 = res :  1.875E-12 ==
# solution 11 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x :  1.13454109131018E+00  -8.46486298862573E-01
#  y : -1.12000443752762E+00   4.10152267830658E-01
# == err :  3.576E-15 = rco :  9.935E-02 = res :  2.344E-12 ==
# solution 12 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x :  8.80799397446810E-02  -1.46629762922461E+00
#  y : -3.45488305816064E-01  -1.08482122947928E+00
# == err :  3.690E-15 = rco :  1.820E-01 = res :  4.617E-12 ==
# solution 13 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x :  5.00256943517446E-01  -1.64883944206886E+00
#  y :  1.21327895854065E+00  -2.87654469209477E+00
# == err :  3.601E-15 = rco :  2.113E-01 = res :  6.390E-10 ==
# solution 14 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x :  8.26164354430881E-01  -1.37108304270387E+00
#  y :  6.10856021873192E-01  -1.08561674720917E+00
# == err :  3.674E-15 = rco :  2.995E-01 = res :  4.547E-12 ==
# solution 15 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x :  2.80043582269256E-01   1.61079629330082E-90
#  y :  1.61833529321431E+00  -3.28295625491786E-90
# == err :  2.597E-15 = rco :  1.911E-01 = res :  3.411E-13 ==
# solution 16 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x :  5.38593631773821E-01  -1.58274820140551E+00
#  y : -8.18274273436525E-01  -6.12881380901085E-01
# == err :  3.909E-15 = rco :  1.192E-01 = res :  3.582E-12 ==
# solution 17 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x : -8.48165107974402E-01  -2.24030915414134E+00
#  y :  4.46102447359539E-01   2.47287644148072E-01
# == err :  4.383E-15 = rco :  1.984E-02 = res :  4.023E-12 ==
# solution 18 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x : -9.68236894272083E-01  -3.96367806857604E-01
#  y :  6.42313169885967E-01  -9.23194680778619E-01
# == err :  5.563E-16 = rco :  2.405E-01 = res :  1.137E-12 ==
# solution 19 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x : -6.33132195886447E-02  -5.67925804740317E-01
#  y :  2.66976366758431E-01  -1.39070349071201E+00
# == err :  2.954E-15 = rco :  2.462E-01 = res :  1.833E-12 ==
# solution 20 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x :  8.26164354430881E-01   1.37108304270387E+00
#  y :  6.10856021873192E-01   1.08561674720917E+00
# == err :  3.674E-15 = rco :  2.995E-01 = res :  4.547E-12 ==
# solution 21 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x : -9.68236894272083E-01   3.96367806857604E-01
#  y :  6.42313169885967E-01   9.23194680778619E-01
# == err :  5.563E-16 = rco :  2.405E-01 = res :  1.137E-12 ==
# solution 22 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x : -1.01254521520691E+00  -8.19870499227230E-02
#  y : -1.45493055265200E+00   1.01034133848404E+00
# == err :  3.490E-15 = rco :  8.253E-02 = res :  1.467E-11 ==
# solution 23 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x : -7.51672368346469E-01   7.20346274884387E-01
#  y : -1.40695386330471E+00  -1.90591935488604E-01
# == err :  5.495E-16 = rco :  1.654E-01 = res :  1.875E-12 ==
# solution 24 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x : -1.89978757148561E+00   3.45170634278746E-92
#  y :  9.55236081598879E-01   1.67791280552168E-93
# == err :  4.137E-15 = rco :  1.262E-01 = res :  1.876E-12 ==
# solution 25 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x : -8.40431029278377E-01   1.14784417624630E+00
#  y : -9.23146742199925E-01  -2.48883428983917E-01
# == err :  1.011E-15 = rco :  2.518E-01 = res :  2.334E-12 ==
# solution 26 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x :  1.02753696406242E+00   7.14311451493517E-92
#  y :  1.02177486045526E+00  -3.78728890389180E-92
# == err :  2.435E-15 = rco :  7.988E-02 = res :  5.969E-13 ==
# solution 27 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x :  5.81559822561863E-01   2.08084369485503E-01
#  y :  1.26497468734055E+00  -1.48550681438031E-01
# == err :  1.309E-15 = rco :  1.143E-01 = res :  4.583E-13 ==
# solution 28 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x : -1.19279497489775E+00   1.20926259078661E+00
#  y :  4.63962555330766E-01  -5.99192326200071E-01
# == err :  5.162E-15 = rco :  1.814E-01 = res :  2.967E-12 ==
# solution 29 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x : -8.48165107974402E-01   2.24030915414134E+00
#  y :  4.46102447359539E-01  -2.47287644148072E-01
# == err :  4.383E-15 = rco :  1.984E-02 = res :  4.023E-12 ==
# solution 30 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x : -1.19279497489775E+00  -1.20926259078661E+00
#  y :  4.63962555330766E-01   5.99192326200071E-01
# == err :  5.162E-15 = rco :  1.814E-01 = res :  2.967E-12 ==
# solution 31 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x :  5.81559822561863E-01  -2.08084369485503E-01
#  y :  1.26497468734055E+00   1.48550681438031E-01
# == err :  1.309E-15 = rco :  1.143E-01 = res :  4.583E-13 ==
# solution 32 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x :  1.88528164922380E+00   3.37500175739219E-90
#  y :  6.54332695427371E-01  -1.20426199070585E-90
# == err :  4.141E-15 = rco :  5.074E-01 = res :  9.592E-13 ==
# solution 33 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x :  1.99238556575678E-01  -1.56398860569596E+00
#  y : -4.50302565574240E-01   7.80629193065677E-01
# == err :  1.339E-15 = rco :  1.074E-01 = res :  3.354E-12 ==
# solution 34 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x : -1.58356999883061E+00  -2.90573248640199E-01
#  y : -3.74948227743026E-01   1.20298458924881E+00
# == err :  4.580E-15 = rco :  9.451E-02 = res :  3.865E-12 ==
# solution 35 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x :  4.43108440444656E-01  -9.62506249347813E-02
#  y : -5.69165342083820E-01   1.54272841971098E+00
# == err :  2.739E-15 = rco :  8.401E-02 = res :  2.034E-12 ==
# solution 36 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x : -2.56801356362087E+00  -3.35582561104337E-93
#  y :  5.30867479356297E-01   3.59552744040361E-93
# == err :  1.480E-15 = rco :  2.269E-02 = res :  4.320E-12 ==
# solution 37 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x : -6.33132195886447E-02   5.67925804740317E-01
#  y :  2.66976366758431E-01   1.39070349071201E+00
# == err :  2.954E-15 = rco :  2.462E-01 = res :  1.833E-12 ==
# solution 38 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x :  6.59691610790567E+00  -1.17161010420904E+00
#  y : -9.44606746555161E-02   1.00085945288797E-01
# == err :  4.846E-15 = rco :  8.417E-05 = res :  1.744E-09 ==
# solution 39 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x :  1.46584948259295E+00   8.89026370110391E-01
#  y :  4.67566315567595E-02   7.84212255731813E-01
# == err :  1.141E-15 = rco :  2.489E-01 = res :  2.734E-12 ==
# solution 40 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x :  1.46584948259295E+00  -8.89026370110391E-01
#  y :  4.67566315567595E-02  -7.84212255731813E-01
# == err :  1.141E-15 = rco :  2.489E-01 = res :  2.734E-12 ==
# solution 41 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x :  6.59691610790567E+00   1.17161010420904E+00
#  y : -9.44606746555161E-02  -1.00085945288797E-01
# == err :  4.846E-15 = rco :  8.417E-05 = res :  1.744E-09 ==
# solution 42 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x :  1.99238556575678E-01   1.56398860569596E+00
#  y : -4.50302565574240E-01  -7.80629193065677E-01
# == err :  1.339E-15 = rco :  1.074E-01 = res :  3.354E-12 ==
# solution 43 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x :  4.43108440444656E-01   9.62506249347813E-02
#  y : -5.69165342083820E-01  -1.54272841971098E+00
# == err :  2.739E-15 = rco :  8.401E-02 = res :  2.034E-12 ==
# solution 44 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x : -1.58356999883061E+00   2.90573248640199E-01
#  y : -3.74948227743026E-01  -1.20298458924881E+00
# == err :  4.580E-15 = rco :  9.451E-02 = res :  3.865E-12 ==
# solution 45 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x : -8.40431029278377E-01  -1.14784417624630E+00
#  y : -9.23146742199925E-01   2.48883428983917E-01
# == err :  1.011E-15 = rco :  2.518E-01 = res :  2.334E-12 ==
# solution 46 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x : -1.01254521520691E+00   8.19870499227230E-02
#  y : -1.45493055265200E+00  -1.01034133848404E+00
# == err :  3.490E-15 = rco :  8.253E-02 = res :  1.467E-11 ==