1#auto_ri_4-body-homog.tst
variables:=[p,s,phi];
sys:={-2*p^3+2*p^3*phi^3-4*phi^3*s*p^2+5*phi^3*s^3*p-phi^3*s^5,
-2*s*p^3-2*phi^3*s^2+phi^3*s^4-3*phi^3*s^2*p+2*phi^3*p,
-2*s^2+s^4-4*s^2*p+phi^2+1+4*p};

2#auto_ri_Arnborg-Lazard.tst
variables:=[x,y,z];
sys:={x^2*y*z + x*y^2*z + x*y*z^2 + x*y*z + x*y + x*z + y*z,
x^2*y^2*z + x*y^2*z^2 + x^2*y*z + x*y*z + y*z + x + z,
x^2*y^2*z^2 + x^2*y^2*z + x*y^2*z + x*y*z + x*z + z + 1};

3#auto_ri_Arnborg-Lazard-rev.tst
variables:=[z,y,x];
sys:={x^2*y*z + x*y^2*z + x*y*z^2 + x*y*z + x*y + x*z + y*z,
x^2*y^2*z + x*y^2*z^2 + x^2*y*z + x*y*z + y*z + x + z,
x^2*y^2*z ^2 + x^2*y^2*z + x*y^2*z + x*y*z + x*z + z + 1};

4#auto_ri_Barry.tst
variables:=[x,y,z];
sys:={-x^5+y^5-3*y-1,
5*y^4-3,
-20*x+y-z};

5#auto_ri_Caprasse.tst
variables:=[x,y,z,t];
sys:={y^2*z+2*x*y*t-2*x-z,
-x^3*z+4*x*y^2*z+4*x^2*y*t+2*y^3*t+4*x^2-10*y^2+4*x*z-10*y*t+2,
2*y*z*t+x*t^2-x-2*z,
-x*z^3+4*y*z^2*t+4*x*z*t^2+2*y*t^3+4*x*z+4*z^2-10*y*t-10*t^2+2};

6#auto_ri_Caprasse-Li.tst
variables:=[t,z,y,x];
sys:={y^2*z+2*x*y*t-2*x-z,
-x^3*z+4*x*y^2*z+4*x^2*y*t+2*y^3*t+4*x^2-10*y^2+4*x*z-10*y*t+2,
2*y*z*t+x*t^2-x-2*z,
-x*z^3+4*y*z^2*t+4*x*z*t^2+2*y*t^3+4*x*z+4*z^2-10*y*t-10*t^2+2};

7#auto_ri_chemical-reaction.tst
variables:=[ x4, x3 , x2 , x1 ];
sys:={
2 - 7*x1 + x1^2*x2 - 1/2*(x3 - x1 ), 
6*x1 - x1^2*x2 - 5*(x4 - x2 ),
2 - 7*x3 + x3^2*x4 - 1/2*(x1 - x3 ),
6*x3 - x3^2*x4 + 1 + 1/2*(x2 - x4 )
};

8#auto_ri_circles.tst
variables := [y,x];
p1 :=  product( (x-'i'), 'i'=1..10) +1/100;
p2 :=  product ( (x-'i')^2+(y-'i')^2-2, 'i'=1..5)+1/1000;
sys := [ p1, p2];

9#auto_ri_cyclic-5.tst
variables:=[a,b,c,d,e];
sys:={a + b + c + d + e,
a*b + b*c + c*d + d*e + e*a,
a*b*c + b*c*d + c*d*e + d*e*a + e*a*b,
a*b*c*d + b*c*d*e + c*d*e*a + d*e*a*b  + e*a*b*c,
a*b*c*d*e - 1};

10#auto_ri_Czapor-Geddes-Wang.16.tst
variables:=[q,c,p,d,b];
sys:={b-2,
c*c*q*q-2*d*c*q*q+d*d*q*q-2*c*c*q+2*d*p*c*q+2*b*p*c*q+2*d*c*q-2*d*d*p*q+2*b*p*q-2*p*q-2*b*d*d*q-2*b*q+2*q+c*c-2*d*p*c-2*b*d*c+b*b*d*d*p*p-2*b*d*d*p*p+d*d*p*p+2*b*b*p*p+2*p*p-2*b*b*d*d*p+4*b*d*d*p-4*b*b*p+4*b*p+b*b*d*d+2*b*b-4*b+2,
-b*p*c*q-p*c*q+b*c*q-2*c*q+2*d*p*q+d*q+p*c+b*b*c-b*c+2*c+b*b*d*p*p+b*d*p*p-2*d*p*p-2*b*b*d*p+b*d*p-d*p+b*b*d-2*b*d,
-2*p*q-2*q-b*b*p*p+2*p*p+2*b*b*p-b*b+2,
3*c*c*q*q-3*d*d*q*q-4*q*q-6*c*c*q+6*b*d*p*c*q+6*b*d*c*q+6*d*d*p*q+3*c*c+6*b*d*p*c-6*b*d*c+3*b*b*d*d*p*p-3*d*d*p*p+b*b*p*p-6*b*b*d*d*p-2*b*b*p+4*p+3*b*b*d*d+b*b};

11#auto_ri_d2v10.tst
nb_vars := 10;
even_d := 2; # must be even
variables := [ x||1 ];
sys := [ x||1^even_d-2 ];
for i from 2 to nb_vars do
    variables := [ x||i, op(variables) ];
    sys := [ x||i^even_d + x||i^(even_d/2)- x||(i-1), op(sys)];
od;

12#auto_ri_d2v15.tst
nb_vars := 15;
even_d := 2; # must be even
variables := [ x||1 ];
sys := [ x||1^even_d-2 ];
for i from 2 to nb_vars do
    variables := [ x||i, op(variables) ];
    sys := [ x||i^even_d + x||i^(even_d/2)- x||(i-1), op(sys)];
od;

13#auto_ri_d4v5.tst
nb_vars := 5;
even_d := 4; # must be even
variables := [ x||1 ];
sys := [ x||1^even_d-2 ];
for i from 2 to nb_vars do
    variables := [ x||i, op(variables) ];
    sys := [ x||i^even_d + x||i^(even_d/2)- x||(i-1), op(sys)];
od;

14#auto_ri_d4v10.tst
nb_vars := 10;
even_d := 4; # must be even
variables := [ x||1 ];
sys := [ x||1^even_d-2 ];
for i from 2 to nb_vars do
    variables := [ x||i, op(variables) ];
    sys := [ x||i^even_d + x||i^(even_d/2)- x||(i-1), op(sys)];
od;

15#auto_ri_easy1.tst
variables := [y,x];
sys := [
  x-1,
  y-x
];

16#auto_ri_easy2.tst
variables := [y,x];
sys := [
  (x-1)*(x-2),
  x*y-1
];

17#auto_ri_easy3.tst
variables := [y,x];
sys := [2*x-1, 3*y-2];

18#auto_ri_easy4.tst
variables := [y,x];
sys := [x, y];

19#auto_ri_easy5.tst
variables := [y,x];
sys := [(x^3+x+1)*(x-1), x*y-1];

20#auto_ri_easy6.tst
variables := [z,y,x];
sys := [(x^3-3)*(x^2-2), x*y-1,(z-x)*z];

21#auto_ri_easy7.tst
variables := [y,x];
sys := [ (x^2-2)*(x^2-3), (y-x)*(y-x-1) ];

22#auto_ri_easy8.tst
variables := [y,x];
sys := [ x^2-2, y^4-y^2-x ];

23#auto_ri_easy9.tst
variables := [y,x];
sys := [  (x-1)*(x^2-2),
    (y-2)*(y-x) ];

24#auto_ri_fabfaux.tst
variables:=[x,y,z];
sys:={30752*x^3 + 46128*y*x^2 - 216256*x + 46128*x*y^2 + 141980 + 30752*y^3- 216256*y,
30752*x^3 + 46128*z*x^2 - 216256*x + 46128*x*z^2 + 141980 + 30752*z^3+ 216256*z,
46128*y^3 + 46128*x*y^2 + 46128*z*y^2 + 46128*y*x^2 - 432512*y +46128*x*z*y + 46128*z^2*y + 46128*x^3 - 432512*x + 425940 +46128*z*x^2 - 432512*z + 46128*x*z^2 + 46128*z^3};

25#auto_ri_geometric-constraints.tst
variables:=[ c, b, s ];
sys:={
1/100 - 4*s*(s - 1)*(s - b)*(s - c),
1/5 - b*c, 
2*s - 1 - b - c
};

26#auto_ri_GonzalezGonzalez.tst
variables:=[x,y,z];
sys:={x^3 + y*x^2 + x + z,
x^2*y +3*x +2,
x^2-y*x+z};

27#auto_ri_Katsura-4.tst
variables:=[x,y,z,t,u];
sys:={
2*x^2 + 2*y^2 + 2*z^2 + 2*t^2 + u^2 - u ,
2*x*y + 2*y*z + 2*z*t + 2*t*u - t ,
2*x*z + 2*y*t + t^2 + 2*z*u - z ,
2*x*t + 2*z*t + 2*y*u - y ,
2*x + 2*y + 2*z + 2*t + u - 1};

28#auto_ri_l-3.tst
variables:=[x,y,z,t];
sys:={x^3 + y + z + t- 1,
x + y^3 + z + t -1,
x + y + z^3 + t-1,
x + y + z + t^3 -1};

29#auto_ri_lllp1.tst
variables := [z,y,x];
sys := [
    2*x^7+2-3*x^2-x^4,
    x^2+2*y^2-5,
    x*z-1
];

30#auto_ri_lllp2.tst
variables := [z,y,x];
sys := [
    y*(320+1600*y^4-240*y^5-471*y^6+36*y^7-48*y^2+36*y^8),
    -40*y^2+3*y^3+6*y^4+8*x,
    -8*y*z-8-40*y^4+3*y^5+6*y^6
];

31#auto_ri_lllp3.tst
variables := [z,y,x];
sys := [
    2450*x^6-1241*x^4+196*x^2-49,
    86*x^2+35*y*x^2-77*y-14,
    175*x^4+70*x^2*z-76*x^2-154*z+21
];

32#auto_ri_lllp4.tst
variables := [y,x];
sys := [
     x^4+y^4-1,
    x^5*y^2-4*x^3*y^3+x^2*y^5-1
];

33#auto_ri_lllp5.tst
variables := [z,y,x];
f51 := -7*x*y*z+6*y*z-14*x*z+9*z-3*x*y-12*y-x+1;
f52 := 2*x*y*z-y*z+14*z+15*x*y+14*y-15*x;
f53 := -8*x*y*z+11*y*z-12*x*z-5*z+15*x*y+2*y+10*x-14;
sys := [f51,f52,f53];

34#auto_ri_lllp6.tst
variables := [x2,y2,x1,y1];
f1 := 2*x^2-x*y+4;
f2 := x*y-2*y^2+4;
sub := {x=x1+I*x2, y=y1+I*y2};
f1 := expand(subs( sub, f1));
f2 := expand(subs( sub, f2));
p1 := Re(f1) assuming real;
p2 := Im(f1) assuming real;
p3 := Re(f2) assuming real;
p4 := Im(f2) assuming real;
sys := [p1,p2,p3,p4];

35#auto_ri_neural-network.tst
variables := [x,y,c,z];
sys:={1 - c*x - x*y^2 - x*z^2,
1 - c*y - y*x^2 - y*z^2,
1 - c*z - z*x^2 - z*y^2, 
8*c^6 + 378*c^3 - 27
};

36#auto_ri_PlateForme2d-easy.tst
variables:=[x1,y1,x2,y2,x3,y3];
sys:={(x1+5)^2+ (y1-0)^2 - 1,
(x2-5)^2+ (y2-0)^2 - 1,
(x3)^2  + (y3-5)^2 - 1,
(x1-x2)^2 + (y1-y2)^2 - 3,
(x1-x3)^2 + (y1-y3)^2 - 3,
(x2-x3)^2 + (y2-y3)^2 - 3};

37#auto_ri_r-5.tst
variables:=[a,b,c,d,e];
sys:={a^2 + a,
a*b + b + a*b^2 +a,
b^2*c + c + b*c^3 + b,
c^3*d + d + c*d^4 + c,
d^4*e + e + d*e^5 + d};

38#auto_ri_r-6.tst
variables:=[a,b,c,d,e,f];
sys:={a^2 + a,
a*b + b + a*b^2 +a,
b^2*c + c + b*c^3 + b,
c^3*d + d + c*d^4 + c,
d^4*e + e + d*e^5 + d,
e^5*f + f + e*f^6 + e};

39#auto_ri_Rose.tst
variables:=[z,y,x];
sys:={7*y^4 - 20*x^2,
2160*x*x*z^4+1512*x*z^4+315*z^4-4000*x*x-2800*x-490,
-10080000*x^4*z^3-28224000*x^3*z^3-15288000*x*x*z^3-1978032*x*z^3-180075*z^3-23520000*x^4*y*z*z-41395200*x^3*y*z*z-26726560*x*x*y*z*z-7727104*x*y*z*z-852355*y*z*z+40320000*x^6*y*y*z+28800000*x^5*y*y*z+21168000*x^3*y*y*z+4939200*x*x*y*y*z+347508*x*y*y*z+67200000*x^5*y^3+94080000*x^4*y^3+40924800*x^3*y^3+2634240*x*x*y^3-2300844*x*y^3-432180*y^3};

40#auto_ri_Takeuchi-Lu.tst
variables:=[ y2, y1, x2, x1 ];
sys:={
2*x1*(2 - x1 - y1 ) + x2 - x1,
2*x2*(2 - x2 - y2 ) + x1 - x2,
2*y1*(5 - x1 - 2*y1 ) + y2 - y1,
y2*(3 - 2*x2 - 4*y2 ) + y1 - y2
};

41#auto_ri_Trinks-difficult.tst
variables:=[x,y,t,z,u,v];
sys:={45*y+35*u-165*v-36 ,
35*y+25*z+40*t-27*u ,
25*y*u-165*v^2+15*x-18*z+30*t ,
15*y*z+20*t*u-9*x ,
-11*v^3+x*y+2*z*t ,
-11*u*v+3*v^2+99*x};

42#auto_ri_trivial-5.tst
variables:=[x,y];
sys:={x^2 -1,
y^2 - 1,
(x-1)*(y-1)};

43#auto_ri_wilkinsonxy.tst
variables := [y,x];
sys := [
	mul( (x-i),i=1..5 )+1/100,
	mul( (y-x-i),i=1..5)
];

44#5-body-homog
variables := [p, s, phi]:
sys := [-9*phi^3*s^2*p - 5*phi^3*s^2 - 6*s*p^3 + 3*phi^3*s^4 + 5*phi^3*p,
-12*s^2*p-6*s^2+3*s^4+4*phi^2+3+12*p,
-6*p^3+4*p^3*phi^3+15*phi^3*s^3*p-3*phi^3*s^5-12*phi^3*s*p^2-3*phi^3*s*p+phi^3*s^3
]:

45#simple-nql-20-30
variables := [x20, x19, x18, x17, x16, x15, x14, 
x13, x12, x11, x10, x9, x8, x7, x6, x5, x4, x3, 
x2, x1]:
sys := [x20^30-x19, x19^30-x18, x18^30-x17, x17^30-x16, x16^30-x15,
x15^30-x14, x14^30-x13, x13^30-x12, x12^30-x11, x11^30-x10, x10^30-x9,
x9^30-x8, x8^30-x7, x7^30-x6, x6^30-x5, x5^30-x4, x4^30-x3, x3^30-x2,
x2^30-x1, x1^30-2]:

46#nld-9-3
variables := [x, y, z]:
sys := [x^9+y+z-1, x+y^9+z-1, x+y+z^9-1]:

47#nld-10-3
variables := [x, y, z]:
sys := [x^10+y+z-1, x+y^10+z-1, x+y+z^10-1]:

48#nql-10-4
variables := [x10, x9, x8, x7, x6, x5, x4, x3, x2,
x1]:
sys := [x10^4+x10^2-x9, x9^4+x9^2-x8, x8^4+x8^2-x7, x7^4+x7^2-x6,
x6^4+x6^2-x5, x5^4+x5^2-x4, x4^4+x4^2-x3, x3^4+x3^2-x2, x2^4+x2^2-x1, x1^4-2]:

49#nql-15-2
variables := [x15, x14, x13, x12, x11, x10, x9, x8
, x7, x6, x5, x4, x3, x2, x1]:
sys := [x15^2+x15-x14, x14^2+x14-x13, x13^2+x13-x12, x12^2+x12-x11,
x11^2+x11-x10, x10^2+x10-x9, x9^2+x9-x8, x8^2+x8-x7, x7^2+x7-x6, x6^2+x6-x5,
x5^2+x5-x4, x4^2+x4-x3, x3^2+x3-x2, x2^2+x2-x1, x1^2-2]:

50#13_sings_9

51#challenge_12

52#SA_2_4_eps

53#ten_circles

--------------------------------------------

#auto_ri_wilkinson20.tst	?? Univariate case
variables := [x];
sys := [
	mul( (x-i),i=0..20 )+1/100
];

#auto_ri_Reif.tst	? Not a regular chain
variables:=[x16,x15,x14,x13,x12,x11,x10,x9,x8,x7,x6,x5,x4,x3,x2,x1];
sys:={x4*x13+x5*x14+x6*(1-x13-x14),
x4*x15+x5*x16-x6*(x15+x16) ,
x7*x13+x8*x14+x9*(1-x13-x14) ,
x7*x15+x8*x16-x9*(x15+x16)-1 ,
x10*x13+x11*x14+x12*(1-x13-x14) ,
x10*x15+x11*x16-x12*(x15+x16) ,
x1*x13+x2*x14+x3*(1-x13-x14) ,
x1*x15+x2*x16-x3*(x15+x16) ,
x1*x4*x13+x2*x5*x14+x3*x6*(1-x13-x14)-1 ,
x1*x4*x15+x2*x5*x16-x3*x6*(x15+x16) ,
x1*x7*x13+x2*x8*x14+x3*x9*(1-x13-x14) ,
x1*x7*x15+x2*x8*x16-x3*x9*(x15+x16) ,
x1*x10*x13+x2*x11*x14+x3*x12*(1-x13-x14) ,
x1*x10*x15+x2*x11*x16-x3*x12*(x15+x16)-1};

#auto_ri_p3p-special.tst	?? More than 1 day
variables:=[ z, y, x, a, b ];
sys:={
x^2 + y^2 - x*y - 1,
y^2 + z^2 - y*z - a^2,
z^2 + x^2 - z*x - b^2,
a^2 - 1 + b - b^2,
3*b^6 + 56*b^4 - 122*b^3 + 56*b^2 + 3
};
