#===================================================
#
#  Examples used for the paper:
#  Truth Table Invariant Cylindrical Algebraic Decomposition by Regular Chains
#  R. Bradford, C. Chen, J.H. Davenport, M.England, M. Moreno Maza and D. Wilson
#
#   Use the command:
#   > read(`PATH/examplebank.txt`):
#   to load the file (where PATH is the directory
#   the file is saved in).
#
#===================================================


#===================================================
# Code for RC-CAD and PL-CAD.


TTICADExamples:=proc(n) local L:


L:=[
#1: Intersection \dagger A
[[x*z+z*y-2*x,z^2-y,2*x^2-y^2-z^2],[z,y,x]],
#2: Intersection \dagger B
[[x*z+z*y-2*x,z^2-y,2*x^2-y^2-z^2],[z,x,y]],
#3: Random \dagger A
[[16*x^2+4*x*y^2-4*z+1,4*x+2*y^2*z+1,2*x^2*z-x-2*y^2],[z,y,x]],
#4: Random \dagger B
[[16*x^2+4*x*y^2-4*z+1,4*x+2*y^2*z+1,2*x^2*z-x-2*y^2],[z,x,y]],
#5: Ellipse \dagger A
[[x^2+y^2-1,b^2*x^2-2*b^2*x*c+b^2*c^2+a^2*y^2-a^2*b^2,a,a-1,b,b-1,c,c-1],[y,x,c,b,a]],
#6: Ellipse \dagger B
[[x^2+y^2-1,b^2*x^2-2*b^2*x*c+b^2*c^2+a^2*y^2-a^2*b^2,a,a-1,b,b-1,c,c-1],[x,y,c,b,a]],
#7: Solotareff \dagger A
[[3*x^2-2*x-a,x^3-x^2-a*x-2*b+a-2,4*a-1,4*a-7,x+1,x,3*y^2-2*y-a,y^3-y^2-a*y-a+2,4*b+3,4*b-3,y,y-1],[y,x,b,a]],
#8: Solotareff \dagger B
[[3*x^2-2*x-a,x^3-x^2-a*x-2*b+a-2,4*a-1,4*a-7,x+1,x,3*y^2-2*y-a,y^3-y^2-a*y-a+2,4*b+3,4*b-3,y,y-1],[y,x,a,b]],
#9: Collision \dagger A
[[x^2-2*x*t+t^2+4*y^2-80*y+396,t,x^2-2*x*a*t+5*a^2*t^2+4*y^2-8*y*a*t-4,a],[y,x,t,a]],
#10: Collision \dagger B
[[x^2-2*x*t+t^2+4*y^2-80*y+396,t,x^2-2*x*a*t+5*a^2*t^2+4*y^2-8*y*a*t-4,a],[t,x,y,a]],
#11: Kahan A
[[8*y^3*x+8*y*x^3+20*y^3+84*y*x^2+288*y*x+324*y,-225*x^2-324*x+63*y^2-4*x^4-52*x^3+12*y^2*x+4*y^4,2*y,2*x+9,8*y,8*x^2+56*x+8*y^2+96,y,x^2+7*x+y^2+12,8*y^3*x+8*y*x^3+20*y^3+84*y*x^2+288*y*x+324*y,-4*x^4-52*x^3-252*x^2+12*y^2*x-540*x+36*y^2+4*y^4-432,4*x^4+52*x^3+225*x^2-12*y^2*x+324*x-63*y^2-4*y^4,2*y,-2*x-6,2*x,8*y,-8*x^2-56*x-8*y^2-96,2*x^2+8*x+2*y^2],[y,x]],
#12: Kahan B
[[8*y^3*x+8*y*x^3+20*y^3+84*y*x^2+288*y*x+324*y,-225*x^2-324*x+63*y^2-4*x^4-52*x^3+12*y^2*x+4*y^4,2*y,2*x+9,8*y,8*x^2+56*x+8*y^2+96,y,x^2+7*x+y^2+12,8*y^3*x+8*y*x^3+20*y^3+84*y*x^2+288*y*x+324*y,-4*x^4-52*x^3-252*x^2+12*y^2*x-540*x+36*y^2+4*y^4-432,4*x^4+52*x^3+225*x^2-12*y^2*x+324*x-63*y^2-4*y^4,2*y,-2*x-6,2*x,8*y,-8*x^2-56*x-8*y^2-96,2*x^2+8*x+2*y^2],[x,y]],
#13: ArcSin A
[[-2*x*y,y^2-x^2+1,16*y^3*x-16*y*x^3+8*y*x,1-4*x^2+4*y^2+4*x^4-24*x^2*y^2+4*y^4,y,1-x,y,x+1],[y,x]],
#14: ArcSin B
[[-2*x*y,y^2-x^2+1,16*y^3*x-16*y*x^3+8*y*x,1-4*x^2+4*y^2+4*x^4-24*x^2*y^2+4*y^4,y,1-x,y,x+1],[x,y]],
#15: 2D Example A
[[x^2+y^2-1,4*x*y-1,x^2-8*x+16+y^2-2*y,4*x*y-4*x-16*y+15],[y,x]],
#16: 2D Example B
[[x^2+y^2-1,4*x*y-1,x^2-8*x+16+y^2-2*y,4*x*y-4*x-16*y+15],[x,y]],
#17: 3D Example A
[[x^2+y^2+z^2-1,4*x*y*z-1,x^2-8*x+y^2-2*y+z^2-4*z+20,4*y*x*z-8*y*x-4*x*z+8*x-16*y*z+32*y+16*z-33],[z,y,x]],
#18: 3D Example B
[[x^2+y^2+z^2-1,4*x*y*z-1,x^2-8*x+y^2-2*y+z^2-4*z+20,4*y*x*z-8*y*x-4*x*z+8*x-16*y*z+32*y+16*z-33],[z,x,y]],
#19: Sqrt Branch Cuts
[[y,x,v,u,y*u+x*v,x*u-y*v],[y,x,u,v]],
#20: Arctan Branch Cuts
[[x,1- y,x, y +1, u, 1 - v,u, v+1,-u^2*x-u*x^2-u*y^2-v^2*x+u+x, u^2*x^2+u^2*y^2+v^2*x^2+v^2*y^2-2*x*u+2*y*v+1 -( u^2*y+v^2*y+v*x^2+v*y^2+v+y),-u^2*x-u*x^2-u*y^2-v^2*x+u+x , u^2*y+v^2*y+v*x^2+v*y^2+v+y -( -u^2*x^2-u^2*y^2-v^2*x^2-v^2*y^2+2*x*u-2*y*v-1)],[y,v,x,u]],
#21: Arctanh Branch Cuts
[[y, 1 - x, y, x +1, v, 1 - u, v, u +1, -u^2*y-v^2*y-v*x^2-v*y^2+v+y , u^2*x^2+u^2*y^2+v^2*x^2+v^2*y^2+2*x*u-2*y*v+1 -( u^2*x+u*x^2+u*y^2+v^2*x+u+x), -u^2*y-v^2*y-v*x^2-v*y^2+v+y, u^2*x+u*x^2+u*y^2+v^2*x+u+x -( -u^2*x^2-u^2*y^2-v^2*x^2-v^2*y^2-2*x*u+2*y*v-1)],[x,u,y,v]],
#22: Phisanbut25 Branch Cuts
[[x , 1- y, x, y +1,v , u - 1, 2*u*x*y+v*x^2-v*y^2-2*x*y+v , u*x^2-u*y^2-2*v*x*y-x^2+y^2+u - 1],[v,x,y,u]],
#23: Phisanbut26 Branch Cuts
[[x , 1 - y, x, y +1, v , -1 - u, u - 1, 2*u^2*x*y+2*u*v*x^2-2*u*v*y^2-2*v^2*x*y+2*u*v-2*x*y , u^2*x^2-u^2*y^2-4*u*v*x*y-v^2*x^2+v^2*y^2+u^2-v^2-x^2+y^2 - 1],[x,y,u,v]],
#24: Phisanbut27 Branch Cuts
[[-2*v*u+3*u*y+3*v*x-4*y*x+v-5*y , -u^2+3*x*u+v^2-3*v*y-2*x^2+2*y^2+u-5*x +12, y-v , x-u +4, v-2*y , u-2*x +3],[y,v,x,u]],
#25: Phisanbut28 Branch Cuts
[[2*u*y*x+v*x^2-v*y^2-3*y*x^2+y^3-2*v*u+2*u*y+2*v*x+2*y*x-v+y , u*x^2-u*y^2-2*v*y*x-x^3+3*x*y^2-u^2+2*x*u+v^2-2*v*y+x^2-y^2-u+x +2,2*y*x-v+y, x^2-y^2-u+x +1, -y+v , -x+u +2],[v,u,y,x]],
#26: Intersection A
[[x^2-(1/2)*(y^2)-(1/2)*z^2,x*z+z*y-2*x,z^2-y],[z,y,x]],
#27: Intersection B
[[x^2-(1/2)*(y^2)-(1/2)*z^2,x*z+z*y-2*x,z^2-y],[z,x,y]],
#28: Random A
[[4*x^2+x*y^2-z+(1/4),2*x+y^2*z+(1/2),x^2*z-(1/2)*x-y^2],[z,y,x]],
#29: Random B
[[4*x^2+x*y^2-z+(1/4),2*x+y^2*z+(1/2),x^2*z-(1/2)*x-y^2],[x,y,z]],
#30: Psi(JSC) A
[[x^2+y^2-1,x*y-1/4,(x-4)^2+(y-1)^2-1,(x-4)*(y-1)-1/4],[y,x]],
#31: Psi(JSC) B
[[x^2+y^2-1,x*y-1/4,(x-4)^2+(y-1)^2-1,(x-4)*(y-1)-1/4],[x,y]],
#32: Random 1 (JSC)
[[-55*x-94*y+87*z-56, -62*y+97*z-73,-4*x-83*y-10*z+62,-75-10*x^2-7*x*y-40*x*z+42*y*z-50*z^2],[x,y,z]],
#33: Random 2 (JSC)
[[-81*x-6*y-51*z-29,-14*x-48*y+97*z-12,83*x-24*y-8*z+47,60+46*y-31*x^2-91*x*y+98*x*z+2*y^2],[x,y,z]],
#34: Random 3 (JSC)
[[-77*x+38*y+42*z+8,-6*x+23*y+76,-11*x+79*y+49*z-40,-51-4*y+29*z-44*x*y+65*x*z+56*y^2],[x,y,z]],
#35: Random 4 (JSC)
[[27*x-95*y+84*z+48,14*x+64*y-88*z+18,56*x+96*y+77*z+54,-94+90*x^2+85*x*y-72*x*z-2*y^2+32*z^2],[x,y,z]],
#36: Random 5 (JSC)
[[5*x-5*y-43*z+51,-45*x+30*y+21*z-12,82*x+23*y+63*z-67,48-90*y-14*z-75*x*y+77*x*z+38*y^2],[x,y,z]],
#37: Solotareff \dagger \dagger A
[[3*x^2-2*x-a,x^3-x^2-a*x-2*b+a-2,4*a-1,4*a-7,x+1,x,3*y^2-2*y-a,y^3-y^2-a*y-a+2,4*b+3,4*b-3,y,y-1],[y,x,b,a]],
#38: Solotareff \dagger \dagger B
[[3*x^2-2*x-a,x^3-x^2-a*x-2*b+a-2,4*a-1,4*a-7,x+1,x,3*y^2-2*y-a,y^3-y^2-a*y-a+2,4*b+3,4*b-3,y,y-1],[y,x,a,b]],
#39: Collision \dagger \dagger A
[[x^2-2*x*t+t^2+4*y^2-80*y+396,t,x^2-2*x*a*t+5*a^2*t^2+4*y^2-8*y*a*t-4,a],[y,x,t,a]],
#40: Collision \dagger \dagger B
[[x^2-2*x*t+t^2+4*y^2-80*y+396,t,x^2-2*x*a*t+5*a^2*t^2+4*y^2-8*y*a*t-4,a],[t,x,y,a]],
#41: blood-coagulation-2
[[1/200*x*s*(1 - 1/400*x) + y*s*(1 - 1/400*x) - 35/2*x, 250*x*s*(1 - 1/600*y )*(z + 3/250) - 55/2*y,500*(y + 1/20*x)*(1 - 1/700*z) - 5*z],[z,y,x,s]],
#42: Rose
[[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],[z,y,x]],
#43: MontesS10
[[r-c1+l*(s1*s2-c1*c2), z-s1-l*(s1*c2+s2*c1), s1^2+c1^2-1, s2^2+c2^2-1],[s1, c1, s2, c2, r, z, l]],
#44: Wang93
[[(x-u)^2+(y-v)^2-1, v^2-u^3, 2*v*(x-u)+3*u^2*(y-v), 2*w*v-1],[w,v,u,y,x]],
#45: genLinSyst-3-2
[[a*x+b*y-c, d*x+e*y-f, g*x+h*x-i],[x, y, a, b, c, d, e, f, g, h, i]],
#46: blood-coagulation-2 \dagger
[[1/200*x*s*(1 - 1/400*x) + y*s*(1 - 1/400*x) - 35/2*x, 250*x*s*(1 - 1/600*y )*(z + 3/250) - 55/2*y,500*(y + 1/20*x)*(1 - 1/700*z) - 5*z],[z,y,x,s]],
#47: Rose \dagger
[[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],[z,y,x]],
#48: MontesS10 \dagger
[[r-c1+l*(s1*s2-c1*c2), z-s1-l*(s1*c2+s2*c1), s1^2+c1^2-1, s2^2+c2^2-1],[s1, c1, s2, c2, r, z, l]],
#49: Wang93 \dagger
[[(x-u)^2+(y-v)^2-1, v^2-u^3, 2*v*(x-u)+3*u^2*(y-v), 2*w*v-1],[w,v,u,y,x]],
#50: genLinSyst-3-2 \dagger
[[a*x+b*y-c, d*x+e*y-f, g*x+h*x-i],[x, y, a, b, c, d, e, f, g, h, i]],
#51: MontesS10 \dagger \dagger
[[r-c1+l*(s1*s2-c1*c2), z-s1-l*(s1*c2+s2*c1), s1^2+c1^2-1, s2^2+c2^2-1],[s1, c1, s2, c2, r, z, l]],
#52: Wang93 \dagger \dagger
[[(x-u)^2+(y-v)^2-1, v^2-u^3, 2*v*(x-u)+3*u^2*(y-v), 2*w*v-1],[w,v,u,y,x]],
#53: MontesS10 half-\dagger 1
[[r-c1+l*(s1*s2-c1*c2), z-s1-l*(s1*c2+s2*c1), s1^2+c1^2-1, s2^2+c2^2-1],[s1, c1, s2, c2, r, z, l]],
#54: MontesS10 half-\dagger 2
[[r-c1+l*(s1*s2-c1*c2), z-s1-l*(s1*c2+s2*c1), s1^2+c1^2-1, s2^2+c2^2-1],[s1, c1, s2, c2, r, z, l]],
#55: Wang93 half-\dagger 1
[[(x-u)^2+(y-v)^2-1, v^2-u^3, 2*v*(x-u)+3*u^2*(y-v), 2*w*v-1],[w,v,u,y,x]],
#56: Wang93 half-\dagger 2
[[(x-u)^2+(y-v)^2-1, v^2-u^3, 2*v*(x-u)+3*u^2*(y-v), 2*w*v-1],[w,v,u,y,x]]
]:


if n<=0 or n>nops(L) then
  ERROR("Out of range"):
fi:


RETURN(op(L[n])):

end:


#===================================================
# Code for RC-TTICAD (as sourced from literature)


TTICADTCADExamples:=proc(n) local L:


L:=[
#1: Intersection \dagger A
[[[x*z+z*y-2*x=0],[z^2-y=0,2*x^2-y^2-z^2<0]],[z,y,x]],
#2: Intersection \dagger B
[[[x*z+z*y-2*x=0],[z^2-y=0,2*x^2-y^2-z^2<0]],[z,x,y]],
#3: Random \dagger A
[[[16*x^2+4*x*y^2-4*z+1=0],[4*x+2*y^2*z+1=0,2*x^2*z-x-2*y^2<0]],[z,y,x]],
#4: Random \dagger B
[[[16*x^2+4*x*y^2-4*z+1=0],[4*x+2*y^2*z+1=0,2*x^2*z-x-2*y^2<0]],[z,x,y]],
#5: Ellipse \dagger A
[[[x^2+y^2-1=0],[b^2*x^2-2*b^2*x*c+b^2*c^2+a^2*y^2-a^2*b^2=0,-a<0,a-1<0,-b<0,b-1<0,-c<0,c-1<0]],[y,x,c,b,a]],
#6: Ellipse \dagger B
[[[x^2+y^2-1=0],[b^2*x^2-2*b^2*x*c+b^2*c^2+a^2*y^2-a^2*b^2=0,-a<0,a-1<0,-b<0,b-1<0,-c<0,c-1<0]],[x,y,c,b,a]],
#7: Solotareff \dagger A
[[[3*x^2-2*x-a=0,-(x^3-x^2-a*x-2*b+a-2)<0,-(4*a-1)<0,4*a-7<0,-(x+1)<0,x<0],[3*y^2-2*y-a=0,-(y^3-y^2-a*y-a+2)<0,-(4*b+3)<0,4*b-3<0,-y<0,y-1<0]],[y,x,b,a]],
#8: Solotareff \dagger B
[[[3*x^2-2*x-a=0,-(x^3-x^2-a*x-2*b+a-2)<0,-(4*a-1)<0,4*a-7<0,-(x+1)<0,x<0],[3*y^2-2*y-a=0,-(y^3-y^2-a*y-a+2)<0,-(4*b+3)<0,4*b-3<0,-y<0,y-1<0]],[y,x,a,b]],
#9: Collision \dagger A
[[[x^2-2*x*t+t^2+4*y^2-80*y+396=0,-t<0],[x^2-2*x*a*t+5*a^2*t^2+4*y^2-8*y*a*t-4=0,-a<0]],[y,x,t,a]],
#10: Collision \dagger B
[[[x^2-2*x*t+t^2+4*y^2-80*y+396=0,-t<0],[x^2-2*x*a*t+5*a^2*t^2+4*y^2-8*y*a*t-4=0,-a<0]],[t,x,y,a]],
#11: Kahan A
[[[8*y^3*x+8*y*x^3+20*y^3+84*y*x^2+288*y*x+324*y=0,-225*x^2-324*x+63*y^2-4*x^4-52*x^3+12*y^2*x+4*y^4<0],[2*y=0,2*x+9<0],[8*y=0,8*x^2+56*x+8*y^2+96<0],[y=0,x^2+7*x+y^2+12<0],[8*y^3*x+8*y*x^3+20*y^3+84*y*x^2+288*y*x+324*y=0,-4*x^4-52*x^3-252*x^2+12*y^2*x-540*x+36*y^2+4*y^4-432<0,4*x^4+52*x^3+225*x^2-12*y^2*x+324*x-63*y^2-4*y^4<0],[2*y=0,-2*x-6<0,2*x<0],[8*y=0,-8*x^2-56*x-8*y^2-96<0,2*x^2+8*x+2*y^2<0]],[y,x]],
#12: Kahan B
[[[8*y^3*x+8*y*x^3+20*y^3+84*y*x^2+288*y*x+324*y=0,-225*x^2-324*x+63*y^2-4*x^4-52*x^3+12*y^2*x+4*y^4<0],[2*y=0,2*x+9<0],[8*y=0,8*x^2+56*x+8*y^2+96<0],[y=0,x^2+7*x+y^2+12<0],[8*y^3*x+8*y*x^3+20*y^3+84*y*x^2+288*y*x+324*y=0,-4*x^4-52*x^3-252*x^2+12*y^2*x-540*x+36*y^2+4*y^4-432<0,4*x^4+52*x^3+225*x^2-12*y^2*x+324*x-63*y^2-4*y^4<0],[2*y=0,-2*x-6<0,2*x<0],[8*y=0,-8*x^2-56*x-8*y^2-96<0,2*x^2+8*x+2*y^2<0]],[x,y]],
#13: ArcSin A
[[[-2*x*y=0,y^2-x^2+1<0],[16*y^3*x-16*y*x^3+8*y*x=0,1-4*x^2+4*y^2+4*x^4-24*x^2*y^2+4*y^4<0],[y=0,1-x<0],[y=0,x+1<0]],[y,x]],
#14: ArcSin B
[[[-2*x*y=0,y^2-x^2+1<0],[16*y^3*x-16*y*x^3+8*y*x=0,1-4*x^2+4*y^2+4*x^4-24*x^2*y^2+4*y^4<0],[y=0,1-x<0],[y=0,x+1<0]],[x,y]],
#15: 2D Example A
[[[x^2+y^2-1=0,4*x*y-1<0],[x^2-8*x+16+y^2-2*y=0,4*x*y-4*x-16*y+15<0]],[y,x]],
#16: 2D Example B
[[[x^2+y^2-1=0,4*x*y-1<0],[x^2-8*x+16+y^2-2*y=0,4*x*y-4*x-16*y+15<0]],[x,y]],
#17: 3D Example A
[[[x^2+y^2+z^2-1=0,4*x*y*z-1<0],[x^2-8*x+y^2-2*y+z^2-4*z+20=0,4*y*x*z-8*y*x-4*x*z+8*x-16*y*z+32*y+16*z-33<0]],[z,y,x]],
#18: 3D Example B
[[[x^2+y^2+z^2-1=0,4*x*y*z-1<0],[x^2-8*x+y^2-2*y+z^2-4*z+20=0,4*y*x*z-8*y*x-4*x*z+8*x-16*y*z+32*y+16*z-33<0]],[z,x,y]],
#19: Sqrt Branch Cuts
[[[y = 0, x < 0], [v = 0, u < 0], [y*u+x*v = 0, x*u-y*v < 0]],[y,x,u,v]],
#20: Arctan Branch Cuts
[[[x = 0, 1 < y], [x = 0, y < -1], [u = 0, 1 < v], [u = 0, v < -1], [-u^2*x-u*x^2-u*y^2-v^2*x+u+x = 0, u^2*x^2+u^2*y^2+v^2*x^2+v^2*y^2-2*x*u+2*y*v+1 < u^2*y+v^2*y+v*x^2+v*y^2+v+y], [-u^2*x-u*x^2-u*y^2-v^2*x+u+x = 0, u^2*y+v^2*y+v*x^2+v*y^2+v+y < -u^2*x^2-u^2*y^2-v^2*x^2-v^2*y^2+2*x*u-2*y*v-1]],[y,v,x,u]],
#21: Arctanh Branch Cuts
[[[y = 0, 1 <= x], [y = 0, x <= -1], [v = 0, 1 <= u], [v = 0, u <= -1], [-u^2*y-v^2*y-v*x^2-v*y^2+v+y = 0, u^2*x^2+u^2*y^2+v^2*x^2+v^2*y^2+2*x*u-2*y*v+1 <= u^2*x+u*x^2+u*y^2+v^2*x+u+x], [-u^2*y-v^2*y-v*x^2-v*y^2+v+y = 0, u^2*x+u*x^2+u*y^2+v^2*x+u+x <= -u^2*x^2-u^2*y^2-v^2*x^2-v^2*y^2-2*x*u+2*y*v-1]],[x,u,y,v]],
#22: Phisanbut25 Branch Cuts
[[[x = 0, 1 < y], [x = 0, y < -1], [v = 0, u < 1], [2*u*x*y+v*x^2-v*y^2-2*x*y+v = 0, u*x^2-u*y^2-2*v*x*y-x^2+y^2+u < 1]],[v,x,y,u]],
#23: Phisanbut26 Branch Cuts
[[[x = 0, 1 < y], [x = 0, y < -1], [v = 0, -1 < u, u < 1], [2*u^2*x*y+2*u*v*x^2-2*u*v*y^2-2*v^2*x*y+2*u*v-2*x*y = 0, u^2*x^2-u^2*y^2-4*u*v*x*y-v^2*x^2+v^2*y^2+u^2-v^2-x^2+y^2 < 1]],[x,y,u,v]],
#24: Phisanbut27 Branch Cuts
[[[-2*v*u+3*u*y+3*v*x-4*y*x+v-5*y = 0, -u^2+3*x*u+v^2-3*v*y-2*x^2+2*y^2+u-5*x < -12], [y-v = 0, x-u < -4], [v-2*y = 0, u-2*x < -3]],[y,v,x,u]],
#25: Phisanbut28 Branch Cuts
[[[2*u*y*x+v*x^2-v*y^2-3*y*x^2+y^3-2*v*u+2*u*y+2*v*x+2*y*x-v+y = 0, u*x^2-u*y^2-2*v*y*x-x^3+3*x*y^2-u^2+2*x*u+v^2-2*v*y+x^2-y^2-u+x < -2], [2*y*x-v+y = 0, x^2-y^2-u+x < -1], [-y+v = 0, -x+u < -2]],[v,u,y,x]],
#26: Intersection A
[[[x^2-(1/2)*(y^2)-(1/2)*z^2=0,x*z+z*y-2*x=0,z^2-y=0]],[z,y,x]],
#27: Intersection B
[[[x^2-(1/2)*(y^2)-(1/2)*z^2=0,x*z+z*y-2*x=0,z^2-y=0]],[z,x,y]],
#28: Random A
[[[4*x^2+x*y^2-z+(1/4)=0,2*x+y^2*z+(1/2)=0,x^2*z-(1/2)*x-y^2=0]],[z,y,x]],
#29: Random B
[[[4*x^2+x*y^2-z+(1/4)=0,2*x+y^2*z+(1/2)=0,x^2*z-(1/2)*x-y^2=0]],[x,y,z]],
#30: Psi(JSC) A
[[[x^2+y^2-1=0,x*y-1/4<0],[(x-4)^2+(y-1)^2-1<0,(x-4)*(y-1)-1/4<0]],[y,x]],
#31: Psi(JSC) B
[[[x^2+y^2-1=0,x*y-1/4<0],[(x-4)^2+(y-1)^2-1<0,(x-4)*(y-1)-1/4<0]],[x,y]],
#32: Random 1 (JSC)
[[[-55*x-94*y+87*z-56=0, -62*y+97*z-73<0],[-4*x-83*y-10*z+62<0,-75-10*x^2-7*x*y-40*x*z+42*y*z-50*z^2<0]],[x,y,z]],
#33: Random 2 (JSC)
[[[-81*x-6*y-51*z-29=0,-14*x-48*y+97*z-12<0],[83*x-24*y-8*z+47<0,60+46*y-31*x^2-91*x*y+98*x*z+2*y^2<0]],[x,y,z]],
#34: Random 3 (JSC)
[[[-77*x+38*y+42*z+8=0,-6*x+23*y+76<0],[-11*x+79*y+49*z-40<0,-51-4*y+29*z-44*x*y+65*x*z+56*y^2<0]],[x,y,z]],
#35: Random 4 (JSC)
[[[27*x-95*y+84*z+48=0,14*x+64*y-88*z+18<0],[56*x+96*y+77*z+54<0,-94+90*x^2+85*x*y-72*x*z-2*y^2+32*z^2<0]],[x,y,z]],
#36: Random 5 (JSC)
[[[5*x-5*y-43*z+51=0,-45*x+30*y+21*z-12<0],[82*x+23*y+63*z-67<0,48-90*y-14*z-75*x*y+77*x*z+38*y^2<0]],[x,y,z]],
#37: Solotareff \dagger \dagger A
[[[3*x^2-2*x-a=0,-(x^3-x^2-a*x-2*b+a-2)<0,-(4*a-1)<0,4*a-7<0,-(x+1)<0,x<0],[3*y^2-2*y-a<0,-(y^3-y^2-a*y-a+2)<0,-(4*b+3)<0,4*b-3<0,-y<0,y-1<0]],[y,x,b,a]],
#38: Solotareff \dagger \dagger B
[[[3*x^2-2*x-a=0,-(x^3-x^2-a*x-2*b+a-2)<0,-(4*a-1)<0,4*a-7<0,-(x+1)<0,x<0],[3*y^2-2*y-a<0,-(y^3-y^2-a*y-a+2)<0,-(4*b+3)<0,4*b-3<0,-y<0,y-1<0]],[y,x,a,b]],
#39: Collision \dagger \dagger A
[[[x^2-2*x*t+t^2+4*y^2-80*y+396=0,-t<0],[x^2-2*x*a*t+5*a^2*t^2+4*y^2-8*y*a*t-4<0,-a<0]],[y,x,t,a]],
#40: Collision \dagger \dagger B
[[[x^2-2*x*t+t^2+4*y^2-80*y+396=0,-t<0],[x^2-2*x*a*t+5*a^2*t^2+4*y^2-8*y*a*t-4<0,-a<0]],[t,x,y,a]],
#41: blood-coagulation-2
[[[1/200*x*s*(1 - 1/400*x) + y*s*(1 - 1/400*x) - 35/2*x=0, 250*x*s*(1 - 1/600*y )*(z + 3/250) - 55/2*y=0,500*(y + 1/20*x)*(1 - 1/700*z) - 5*z=0]],[z,y,x,s]],
#42: Rose
[[[7*y^4 - 20*x^2=0,2160*x*x*z^4+1512*x*z^4+315*z^4-4000*x*x-2800*x-490=0, -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=0]],[z,y,x]],
#43: MontesS10
[[[r-c1+l*(s1*s2-c1*c2)=0, z-s1-l*(s1*c2+s2*c1)=0, s1^2+c1^2-1=0, s2^2+c2^2-1=0]],[s1, c1, s2, c2, r, z, l]],
#44: Wang93
[[[(x-u)^2+(y-v)^2-1=0, v^2-u^3=0, 2*v*(x-u)+3*u^2*(y-v)=0, 2*w*v-1=0]],[w,v,u,y,x]],
#45: genLinSyst-3-2
[[[a*x+b*y-c=0, d*x+e*y-f=0, g*x+h*x-i=0]],[x, y, a, b, c, d, e, f, g, h, i]],
#46: blood-coagulation-2 \dagger
[[[1/200*x*s*(1 - 1/400*x) + y*s*(1 - 1/400*x) - 35/2*x=0],[ 250*x*s*(1 - 1/600*y )*(z + 3/250) - 55/2*y=0,500*(y + 1/20*x)*(1 - 1/700*z) - 5*z<0]],[z,y,x,s]],
#47: Rose \dagger
[[[7*y^4 - 20*x^2=0],[2160*x*x*z^4+1512*x*z^4+315*z^4-4000*x*x-2800*x-490=0, -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<0]],[z,y,x]],
#48: MontesS10 \dagger
#[[[r-c1+l*(s1*s2-c1*c2)=0, z-s1-l*(s1*c2+s2*c1)<0], [s1^2+c1^2-1=0, s2^2+c2^2-1<0]],[s1, c1, s2, c2, r, z, l]],
[[[r-c1+l*(s1*s2-c1*c2)=0, z-s1-l*(s1*c2+s2*c1)=0], [s1^2+c1^2-1=0, s2^2+c2^2-1<0]],[s1, c1, s2, c2, r, z, l]],
#49: Wang93 \dagger
#[[[(x-u)^2+(y-v)^2-1=0, v^2-u^3<0], [2*v*(x-u)+3*u^2*(y-v)=0, 2*w*v-1<0]],[w,v,u,y,x]],
[[[(x-u)^2+(y-v)^2-1=0, v^2-u^3=0], [2*v*(x-u)+3*u^2*(y-v)=0, 2*w*v-1<0]],[w,v,u,y,x]],
#50: genLinSyst-3-2 \dagger
[[[a*x+b*y-c=0], [d*x+e*y-f=0, g*x+h*x-i<0]],[x, y, a, b, c, d, e, f, g, h, i]],
#51: MontesS10 \dagger \dagger
[[[r-c1+l*(s1*s2-c1*c2)=0, z-s1-l*(s1*c2+s2*c1)<0], [s1^2+c1^2-1<0, s2^2+c2^2-1<0]],[s1, c1, s2, c2, r, z, l]],
#52: Wang93 \dagger \dagger
[[[(x-u)^2+(y-v)^2-1=0, v^2-u^3<0], [2*v*(x-u)+3*u^2*(y-v)<0, 2*w*v-1<0]],[w,v,u,y,x]],
#53: MontesS10 half-\dagger 1
[[[r-c1+l*(s1*s2-c1*c2)=0, z-s1-l*(s1*c2+s2*c1)=0], [s1^2+c1^2-1=0, s2^2+c2^2-1<0]],[s1, c1, s2, c2, r, z, l]],
#54: MontesS10 half-\dagger 2
[[[r-c1+l*(s1*s2-c1*c2)=0, z-s1-l*(s1*c2+s2*c1)<0], [s1^2+c1^2-1=0, s2^2+c2^2-1=0]],[s1, c1, s2, c2, r, z, l]],
#55: Wang93 half-\dagger 1
[[[(x-u)^2+(y-v)^2-1=0, v^2-u^3=0], [2*v*(x-u)+3*u^2*(y-v)=0, 2*w*v-1<0]],[w,v,u,y,x]],
#56: Wang93 half-\dagger 2
[[[(x-u)^2+(y-v)^2-1=0, v^2-u^3<0], [2*v*(x-u)+3*u^2*(y-v)=0, 2*w*v-1=0]],[w,v,u,y,x]]
]:


if n<=0 or n>nops(L) then
  ERROR("Out of range"):
fi:


RETURN(op(L[n])):

end:

#===================================================
# Code for PL-TTICAD


TTICADPCADExamples:=proc(n) local L:


L:=[
#1: Intersection \dagger A
[[[x*z+z*y-2*x,[]],[z^2-y,[2*x^2-y^2-z^2]]],[z,y,x]],
#2: Intersection \dagger B
[[[x*z+z*y-2*x,[]],[z^2-y,[2*x^2-y^2-z^2]]],[z,x,y]],
#3: Random \dagger A
[[[16*x^2+4*x*y^2-4*z+1,[]],[4*x+2*y^2*z+1,[2*x^2*z-x-2*y^2]]],[z,y,x]],
#4: Random \dagger B
[[[16*x^2+4*x*y^2-4*z+1,[]],[4*x+2*y^2*z+1,[2*x^2*z-x-2*y^2]]],[z,x,y]],
#5: Ellipse \dagger A
[[[x^2+y^2-1,[]],[b^2*x^2-2*b^2*x*c+b^2*c^2+a^2*y^2-a^2*b^2,[-a,a-1,-b,b-1,-c,c-1]]],[y,x,c,b,a]],
#6: Ellipse \dagger B
[[[x^2+y^2-1,[]],[b^2*x^2-2*b^2*x*c+b^2*c^2+a^2*y^2-a^2*b^2,[-a,a-1,-b,b-1,-c,c-1]]],[x,y,c,b,a]],
#7: Solotareff \dagger A
[[[3*x^2-2*x-a,[-(x^3-x^2-a*x-2*b+a-2),-(4*a-1),4*a-7,-(x+1),x]],[3*y^2-2*y-a,[-(y^3-y^2-a*y-a+2),-(4*b+3),4*b-3,-y,y-1]]],[y,x,b,a]],
#8: Solotareff \dagger B
[[[3*x^2-2*x-a,[-(x^3-x^2-a*x-2*b+a-2),-(4*a-1),4*a-7,-(x+1),x]],[3*y^2-2*y-a,[-(y^3-y^2-a*y-a+2),-(4*b+3),4*b-3,-y,y-1]]],[y,x,a,b]],
#9: Collision \dagger A
[[[x^2-2*x*t+t^2+4*y^2-80*y+396,[-t]],[x^2-2*x*a*t+5*a^2*t^2+4*y^2-8*y*a*t-4,[-a]]],[y,x,t,a]],
#10: Collision \dagger B
[[[x^2-2*x*t+t^2+4*y^2-80*y+396,[-t]],[x^2-2*x*a*t+5*a^2*t^2+4*y^2-8*y*a*t-4,[-a]]],[t,x,y,a]],
#11: Kahan A
[[[8*y^3*x+8*y*x^3+20*y^3+84*y*x^2+288*y*x+324*y,[-225*x^2-324*x+63*y^2-4*x^4-52*x^3+12*y^2*x+4*y^4]],[2*y,[2*x+9]],[8*y,[8*x^2+56*x+8*y^2+96]],[y,[x^2+7*x+y^2+12]],[8*y^3*x+8*y*x^3+20*y^3+84*y*x^2+288*y*x+324*y,[-4*x^4-52*x^3-252*x^2+12*y^2*x-540*x+36*y^2+4*y^4-432,4*x^4+52*x^3+225*x^2-12*y^2*x+324*x-63*y^2-4*y^4]],[2*y,[-2*x-6,2*x]],[8*y,[-8*x^2-56*x-8*y^2-96,2*x^2+8*x+2*y^2]]],[y,x]],
#12: Kahan B
[[[8*y^3*x+8*y*x^3+20*y^3+84*y*x^2+288*y*x+324*y,[-225*x^2-324*x+63*y^2-4*x^4-52*x^3+12*y^2*x+4*y^4]],[2*y,[2*x+9]],[8*y,[8*x^2+56*x+8*y^2+96]],[y,[x^2+7*x+y^2+12]],[8*y^3*x+8*y*x^3+20*y^3+84*y*x^2+288*y*x+324*y,[-4*x^4-52*x^3-252*x^2+12*y^2*x-540*x+36*y^2+4*y^4-432,4*x^4+52*x^3+225*x^2-12*y^2*x+324*x-63*y^2-4*y^4]],[2*y,[-2*x-6,2*x]],[8*y,[-8*x^2-56*x-8*y^2-96,2*x^2+8*x+2*y^2]]],[x,y]],
#13: ArcSin A
[[[-2*x*y,[y^2-x^2+1]],[16*y^3*x-16*y*x^3+8*y*x,[1-4*x^2+4*y^2+4*x^4-24*x^2*y^2+4*y^4]],[y,[1-x]],[y,[x+1]]],[y,x]],
#14: ArcSin B
[[[-2*x*y,[y^2-x^2+1]],[16*y^3*x-16*y*x^3+8*y*x,[1-4*x^2+4*y^2+4*x^4-24*x^2*y^2+4*y^4]],[y,[1-x]],[y,[x+1]]],[x,y]],
#15: 2D Example A
[[[x^2+y^2-1,[4*x*y-1]],[x^2-8*x+16+y^2-2*y,[4*x*y-4*x-16*y+15]]],[y,x]],
#16: 2D Example B
[[[x^2+y^2-1,[4*x*y-1]],[x^2-8*x+16+y^2-2*y,[4*x*y-4*x-16*y+15]]],[x,y]],
#17: 3D Example A
[[[x^2+y^2+z^2-1,[4*x*y*z-1]],[x^2-8*x+y^2-2*y+z^2-4*z+20,[4*y*x*z-8*y*x-4*x*z+8*x-16*y*z+32*y+16*z-33]]],[z,y,x]],
#18: 3D Example B
[[[x^2+y^2+z^2-1,[4*x*y*z-1]],[x^2-8*x+y^2-2*y+z^2-4*z+20,[4*y*x*z-8*y*x-4*x*z+8*x-16*y*z+32*y+16*z-33]]],[z,x,y]],
#19: Sqrt Branch Cuts
[[[y , [x]], [v,[ u]], [y*u+x*v ,[ x*u-y*v ]]],[y,x,u,v]],
#20: Arctan Branch Cuts
[[[x,[ 1- y]], [x,[ y +1]], [u ,[ 1 - v]], [u,[ v +1]], [-u^2*x-u*x^2-u*y^2-v^2*x+u+x , [u^2*x^2+u^2*y^2+v^2*x^2+v^2*y^2-2*x*u+2*y*v+1 -( u^2*y+v^2*y+v*x^2+v*y^2+v+y)]], [-u^2*x-u*x^2-u*y^2-v^2*x+u+x ,[ u^2*y+v^2*y+v*x^2+v*y^2+v+y -( -u^2*x^2-u^2*y^2-v^2*x^2-v^2*y^2+2*x*u-2*y*v-1)]]],[y,v,x,u]],
#21: Arctanh Branch Cuts
[[[y ,[ 1 - x]], [y ,[ x +1]], [v , [1 - u]], [v , [u +1]], [-u^2*y-v^2*y-v*x^2-v*y^2+v+y ,[ u^2*x^2+u^2*y^2+v^2*x^2+v^2*y^2+2*x*u-2*y*v+1 -( u^2*x+u*x^2+u*y^2+v^2*x+u+x)]], [-u^2*y-v^2*y-v*x^2-v*y^2+v+y , [u^2*x+u*x^2+u*y^2+v^2*x+u+x -( -u^2*x^2-u^2*y^2-v^2*x^2-v^2*y^2-2*x*u+2*y*v-1)]]],[x,u,y,v]],
#22: Phisanbut25 Branch Cuts
[[[x , [1 - y]], [x ,[ y +1]], [v , [u - 1]], [2*u*x*y+v*x^2-v*y^2-2*x*y+v , [u*x^2-u*y^2-2*v*x*y-x^2+y^2+u - 1]]],[v,x,y,u]],
#23: Phisanbut26 Branch Cuts
[[[x ,[ 1 - y]], [x , [y +1]], [v , [-1 - u, u - 1]], [2*u^2*x*y+2*u*v*x^2-2*u*v*y^2-2*v^2*x*y+2*u*v-2*x*y , [u^2*x^2-u^2*y^2-4*u*v*x*y-v^2*x^2+v^2*y^2+u^2-v^2-x^2+y^2 - 1]]],[x,y,u,v]],
#24: Phisanbut27 Branch Cuts
[[[-2*v*u+3*u*y+3*v*x-4*y*x+v-5*y , [-u^2+3*x*u+v^2-3*v*y-2*x^2+2*y^2+u-5*x +12]], [y-v , [x-u +4]], [v-2*y , [u-2*x +3]]],[y,v,x,u]],
#25: Phisanbut28 Branch Cuts
[[[2*u*y*x+v*x^2-v*y^2-3*y*x^2+y^3-2*v*u+2*u*y+2*v*x+2*y*x-v+y , [u*x^2-u*y^2-2*v*y*x-x^3+3*x*y^2-u^2+2*x*u+v^2-2*v*y+x^2-y^2-u+x +2]], [2*y*x-v+y , [x^2-y^2-u+x +1]], [-y+v , [-x+u +2]]],[v,u,y,x]],
#26: Intersection A
[[[[x^2-(1/2)*(y^2)-(1/2)*z^2,x*z+z*y-2*x,z^2-y],[]]],[z,y,x]],
#27: Intersection B
[[[[x^2-(1/2)*(y^2)-(1/2)*z^2,x*z+z*y-2*x,z^2-y],[]]],[z,x,y]],
#28: Random A
[[[[4*x^2+x*y^2-z+(1/4),2*x+y^2*z+(1/2),x^2*z-(1/2)*x-y^2],[]]],[z,y,x]],
#29: Random B
[[[[4*x^2+x*y^2-z+(1/4),2*x+y^2*z+(1/2),x^2*z-(1/2)*x-y^2],[]]],[x,y,z]],
#30: Psi(JSC) A
[[[x^2+y^2-1,[x*y-1/4]],[[],[(x-4)^2+(y-1)^2-1,(x-4)*(y-1)-1/4]]],[y,x]],
#31: Psi(JSC) B
[[[x^2+y^2-1,[x*y-1/4]],[[],[(x-4)^2+(y-1)^2-1,(x-4)*(y-1)-1/4]]],[x,y]],
#32: Random 1 (JSC)
[[[-55*x-94*y+87*z-56,[ -62*y+97*z-73]],[[],[-4*x-83*y-10*z+62,-75-10*x^2-7*x*y-40*x*z+42*y*z-50*z^2]]],[x,y,z]],
#33: Random 2 (JSC)
[[[-81*x-6*y-51*z-29,[-14*x-48*y+97*z-12]],[[],[83*x-24*y-8*z+47,60+46*y-31*x^2-91*x*y+98*x*z+2*y^2]]],[x,y,z]],
#34: Random 3 (JSC)
[[[-77*x+38*y+42*z+8,[-6*x+23*y+76]],[[],[-11*x+79*y+49*z-40,-51-4*y+29*z-44*x*y+65*x*z+56*y^2]]],[x,y,z]],
#35: Random 4 (JSC)
[[[27*x-95*y+84*z+48,[14*x+64*y-88*z+18]],[[],[56*x+96*y+77*z+54,-94+90*x^2+85*x*y-72*x*z-2*y^2+32*z^2]]],[x,y,z]],
#36: Random 5 (JSC)
[[[5*x-5*y-43*z+51,[-45*x+30*y+21*z-12]],[[],[82*x+23*y+63*z-67,48-90*y-14*z-75*x*y+77*x*z+38*y^2]]],[x,y,z]],
#37: Solotareff \dagger \dagger A
[[[3*x^2-2*x-a,[-(x^3-x^2-a*x-2*b+a-2),-(4*a-1),4*a-7,-(x+1),x]],[[],[3*y^2-2*y-a,-(y^3-y^2-a*y-a+2),-(4*b+3),4*b-3,-y,y-1]]],[y,x,b,a]],
#38: Solotareff \dagger \dagger B
[[[3*x^2-2*x-a,[-(x^3-x^2-a*x-2*b+a-2),-(4*a-1),4*a-7,-(x+1),x]],[[],[3*y^2-2*y-a,-(y^3-y^2-a*y-a+2),-(4*b+3),4*b-3,-y,y-1]]],[y,x,a,b]],
#39: Collision \dagger \dagger A
[[[x^2-2*x*t+t^2+4*y^2-80*y+396,[-t]],[[],[x^2-2*x*a*t+5*a^2*t^2+4*y^2-8*y*a*t-4,-a]]],[y,x,t,a]],
#40: Collision \dagger \dagger B
[[[x^2-2*x*t+t^2+4*y^2-80*y+396,[-t]],[[],[x^2-2*x*a*t+5*a^2*t^2+4*y^2-8*y*a*t-4,-a]]],[t,x,y,a]],
#41: blood-coagulation-2
[[[[1/200*x*s*(1 - 1/400*x) + y*s*(1 - 1/400*x) - 35/2*x, 250*x*s*(1 - 1/600*y )*(z + 3/250) - 55/2*y,500*(y + 1/20*x)*(1 - 1/700*z) - 5*z],[]]],[z,y,x,s]],
#42: Rose
[[[[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],[]]],[z,y,x]],
#43: MontesS10
[[[[r-c1+l*(s1*s2-c1*c2), z-s1-l*(s1*c2+s2*c1), s1^2+c1^2-1, s2^2+c2^2-1],[]]],[s1, c1, s2, c2, r, z, l]],
#44: Wang93
[[[[(x-u)^2+(y-v)^2-1, v^2-u^3, 2*v*(x-u)+3*u^2*(y-v), 2*w*v-1],[]]],[w,v,u,y,x]],
#45: genLinSyst-3-2
[[[[a*x+b*y-c, d*x+e*y-f, g*x+h*x-i],[]]],[x, y, a, b, c, d, e, f, g, h, i]],
#46: blood-coagulation-2 \dagger
[[[1/200*x*s*(1 - 1/400*x) + y*s*(1 - 1/400*x) - 35/2*x,[]],[ 250*x*s*(1 - 1/600*y )*(z + 3/250) - 55/2*y,[500*(y + 1/20*x)*(1 - 1/700*z) - 5*z]]],[z,y,x,s]],
#47: Rose \dagger
[[[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]]],[z,y,x]],
#48: MontesS10 \dagger
[[[r-c1+l*(s1*s2-c1*c2), [z-s1-l*(s1*c2+s2*c1)]], [s1^2+c1^2-1, [s2^2+c2^2-1]]],[s1, c1, s2, c2, r, z, l]],
#49: Wang93 \dagger
[[[(x-u)^2+(y-v)^2-1, [v^2-u^3]], [2*v*(x-u)+3*u^2*(y-v), [2*w*v-1]]],[w,v,u,y,x]],
#50: genLinSyst-3-2 \dagger
[[[a*x+b*y-c,[]], [d*x+e*y-f, [g*x+h*x-i]]],[x, y, a, b, c, d, e, f, g, h, i]],
#51: MontesS10 \dagger \dagger
[[[r-c1+l*(s1*s2-c1*c2), [z-s1-l*(s1*c2+s2*c1)]], [[],[s1^2+c1^2-1, s2^2+c2^2-1]]],[s1, c1, s2, c2, r, z, l]],
#52: Wang93 \dagger \dagger
[[[(x-u)^2+(y-v)^2-1, [v^2-u^3]], [[],[2*v*(x-u)+3*u^2*(y-v), 2*w*v-1]]],[w,v,u,y,x]],
#53: MontesS10 half-\dagger 1
[[[[r-c1+l*(s1*s2-c1*c2),z-s1-l*(s1*c2+s2*c1)],[]], [s1^2+c1^2-1, [s2^2+c2^2-1]]],[s1, c1, s2, c2, r, z, l]],
#54: MontesS10 half-\dagger 2
[[[r-c1+l*(s1*s2-c1*c2), [z-s1-l*(s1*c2+s2*c1)]], [[s1^2+c1^2-1, s2^2+c2^2-1],[]]],[s1, c1, s2, c2, r, z, l]],
#55: Wang93 half-\dagger 1
[[[[(x-u)^2+(y-v)^2-1, v^2-u^3],[]], [2*v*(x-u)+3*u^2*(y-v), [2*w*v-1]]],[w,v,u,y,x]],
#56: Wang93 half-\dagger 2
[[[(x-u)^2+(y-v)^2-1, [v^2-u^3]], [[2*v*(x-u)+3*u^2*(y-v), 2*w*v-1],[]]],[w,v,u,y,x]]
]:


if n<=0 or n>nops(L) then
  ERROR("Out of range"):
fi:


RETURN(op(L[n])):

end:


#===================================================
# Code for RC-TTICAD (when all inequalities non-strict --- not in paper)

TTICADTCADExamples2:=proc(n) local L:


L:=[
#1: Intersection \dagger A
[[[x*z+z*y-2*x=0],[z^2-y=0,2*x^2-y^2-z^2<=0]],[z,y,x]],
#2: Intersection \dagger B
[[[x*z+z*y-2*x=0],[z^2-y=0,2*x^2-y^2-z^2<=0]],[z,x,y]],
#3: Random \dagger A
[[[16*x^2+4*x*y^2-4*z+1=0],[4*x+2*y^2*z+1=0,2*x^2*z-x-2*y^2<=0]],[z,y,x]],
#4: Random \dagger B
[[[16*x^2+4*x*y^2-4*z+1=0],[4*x+2*y^2*z+1=0,2*x^2*z-x-2*y^2<=0]],[z,x,y]],
#5: Ellipse \dagger A
[[[x^2+y^2-1=0],[b^2*x^2-2*b^2*x*c+b^2*c^2+a^2*y^2-a^2*b^2=0,-a<=0,a-1<=0,-b<=0,b-1<=0,-c<=0,c-1<=0]],[y,x,c,b,a]],
#6: Ellipse \dagger B
[[[x^2+y^2-1=0],[b^2*x^2-2*b^2*x*c+b^2*c^2+a^2*y^2-a^2*b^2=0,-a<=0,a-1<=0,-b<=0,b-1<=0,-c<=0,c-1<=0]],[x,y,c,b,a]],
#7: Solotareff \dagger A
[[[3*x^2-2*x-a=0,-(x^3-x^2-a*x-2*b+a-2)<=0,-(4*a-1)<=0,4*a-7<=0,-(x+1)<=0,x<=0],[3*y^2-2*y-a=0,-(y^3-y^2-a*y-a+2)<=0,-(4*b+3)<=0,4*b-3<=0,-y<=0,y-1<=0]],[y,x,b,a]],
#8: Solotareff \dagger B
[[[3*x^2-2*x-a=0,-(x^3-x^2-a*x-2*b+a-2)<=0,-(4*a-1)<=0,4*a-7<=0,-(x+1)<=0,x<=0],[3*y^2-2*y-a=0,-(y^3-y^2-a*y-a+2)<=0,-(4*b+3)<=0,4*b-3<=0,-y<=0,y-1<=0]],[y,x,a,b]],
#9: Collision \dagger A
[[[x^2-2*x*t+t^2+4*y^2-80*y+396=0,-t<=0],[x^2-2*x*a*t+5*a^2*t^2+4*y^2-8*y*a*t-4=0,-a<=0]],[y,x,t,a]],
#10: Collision \dagger B
[[[x^2-2*x*t+t^2+4*y^2-80*y+396=0,-t<=0],[x^2-2*x*a*t+5*a^2*t^2+4*y^2-8*y*a*t-4=0,-a<=0]],[t,x,y,a]],
#11: Kahan A
[[[8*y^3*x+8*y*x^3+20*y^3+84*y*x^2+288*y*x+324*y=0,-225*x^2-324*x+63*y^2-4*x^4-52*x^3+12*y^2*x+4*y^4<=0],[2*y=0,2*x+9<=0],[8*y=0,8*x^2+56*x+8*y^2+96<=0],[y=0,x^2+7*x+y^2+12<=0],[8*y^3*x+8*y*x^3+20*y^3+84*y*x^2+288*y*x+324*y=0,-4*x^4-52*x^3-252*x^2+12*y^2*x-540*x+36*y^2+4*y^4-432<=0,4*x^4+52*x^3+225*x^2-12*y^2*x+324*x-63*y^2-4*y^4<=0],[2*y=0,-2*x-6<=0,2*x<=0],[8*y=0,-8*x^2-56*x-8*y^2-96<=0,2*x^2+8*x+2*y^2<=0]],[y,x]],
#12: Kahan B
[[[8*y^3*x+8*y*x^3+20*y^3+84*y*x^2+288*y*x+324*y=0,-225*x^2-324*x+63*y^2-4*x^4-52*x^3+12*y^2*x+4*y^4<=0],[2*y=0,2*x+9<=0],[8*y=0,8*x^2+56*x+8*y^2+96<=0],[y=0,x^2+7*x+y^2+12<=0],[8*y^3*x+8*y*x^3+20*y^3+84*y*x^2+288*y*x+324*y=0,-4*x^4-52*x^3-252*x^2+12*y^2*x-540*x+36*y^2+4*y^4-432<=0,4*x^4+52*x^3+225*x^2-12*y^2*x+324*x-63*y^2-4*y^4<=0],[2*y=0,-2*x-6<0,2*x<=0],[8*y=0,-8*x^2-56*x-8*y^2-96<=0,2*x^2+8*x+2*y^2<=0]],[x,y]],
#13: ArcSin A
[[[-2*x*y=0,y^2-x^2+1<=0],[16*y^3*x-16*y*x^3+8*y*x=0,1-4*x^2+4*y^2+4*x^4-24*x^2*y^2+4*y^4<=0],[y=0,1-x<=0],[y=0,x+1<=0]],[y,x]],
#14: ArcSin B
[[[-2*x*y=0,y^2-x^2+1<=0],[16*y^3*x-16*y*x^3+8*y*x=0,1-4*x^2+4*y^2+4*x^4-24*x^2*y^2+4*y^4<=0],[y=0,1-x<=0],[y=0,x+1<=0]],[x,y]],
#15: 2D Example A
[[[x^2+y^2-1=0,4*x*y-1<=0],[x^2-8*x+16+y^2-2*y=0,4*x*y-4*x-16*y+15<=0]],[y,x]],
#16: 2D Example B
[[[x^2+y^2-1=0,4*x*y-1<=0],[x^2-8*x+16+y^2-2*y=0,4*x*y-4*x-16*y+15<=0]],[x,y]],
#17: 3D Example A
[[[x^2+y^2+z^2-1=0,4*x*y*z-1<=0],[x^2-8*x+y^2-2*y+z^2-4*z+20=0,4*y*x*z-8*y*x-4*x*z+8*x-16*y*z+32*y+16*z-33<=0]],[z,y,x]],
#18: 3D Example B
[[[x^2+y^2+z^2-1=0,4*x*y*z-1<=0],[x^2-8*x+y^2-2*y+z^2-4*z+20=0,4*y*x*z-8*y*x-4*x*z+8*x-16*y*z+32*y+16*z-33<=0]],[z,x,y]],
#19: Sqrt Branch Cuts
[[[y = 0, x < 0], [v = 0, u < 0], [y*u+x*v = 0, x*u-y*v < 0]],[y,x,u,v]],
#20: Arctan Branch Cuts
[[[x = 0, 1 < y], [x = 0, y < -1], [u = 0, 1 < v], [u = 0, v < -1], [-u^2*x-u*x^2-u*y^2-v^2*x+u+x =
 0, u^2*x^2+u^2*y^2+v^2*x^2+v^2*y^2-2*x*u+2*y*v+1 < u^2*y+v^2*y+v*x^2+v*y^2+v+y], [-u^2*x-u*x^2-u*y^2-
v^2*x+u+x = 0, u^2*y+v^2*y+v*x^2+v*y^2+v+y < -u^2*x^2-u^2*y^2-v^2*x^2-v^2*y^2+2*x*u-2*y*v-1]],[y,v,x,u
]],
#21: Arctanh Branch Cuts
[[[y = 0, 1 <= x], [y = 0, x <= -1], [v = 0, 1 <= u], [v = 0, u <= -1], [-u^2*y-v^2*y-v*x^2-v*y^2+v+y =
 0, u^2*x^2+u^2*y^2+v^2*x^2+v^2*y^2+2*x*u-2*y*v+1 <= u^2*x+u*x^2+u*y^2+v^2*x+u+x], [-u^2*y-v^2*y-v*x^2-
v*y^2+v+y = 0, u^2*x+u*x^2+u*y^2+v^2*x+u+x <= -u^2*x^2-u^2*y^2-v^2*x^2-v^2*y^2-2*x*u+2*y*v-1]],[x,u,y,v
]],
#22: Phisanbut25 Branch Cuts
[[[x = 0, 1 < y], [x = 0, y < -1], [v = 0, u < 1], [2*u*x*y+v*x^2-v*y^2-2*x*y+v = 0, u*x^2-u*y^2-2*v*x*
y-x^2+y^2+u < 1]],[v,x,y,u]],
#23: Phisanbut26 Branch Cuts
[[[x = 0, 1 < y], [x = 0, y < -1], [v = 0, -1 < u, u < 1], [2*u^2*x*y+2*u*v*x^2-2*u*v*y^2-2*v^2*x*y+2*u
*v-2*x*y = 0, u^2*x^2-u^2*y^2-4*u*v*x*y-v^2*x^2+v^2*y^2+u^2-v^2-x^2+y^2 < 1]],[x,y,u,v]],
#24: Phisanbut27 Branch Cuts
[[[-2*v*u+3*u*y+3*v*x-4*y*x+v-5*y = 0, -u^2+3*x*u+v^2-3*v*y-2*x^2+2*y^2+u-5*x < -12], [y-v = 0, x-u < -
4], [v-2*y = 0, u-2*x < -3]],[y,v,x,u]],
#25: Phisanbut28 Branch Cuts
[[[2*u*y*x+v*x^2-v*y^2-3*y*x^2+y^3-2*v*u+2*u*y+2*v*x+2*y*x-v+y = 0, u*x^2-u*y^2-2*v*y*x-x^3+3*x*y^2-u^2+2*x*u+v^2-2*v*y+x^2-y^2-u+x < -2], [2*y*x-v+y = 0, x^2-y^2-u+x < -1], [-y+v = 0, -x+u < -2]],[v,u,y,x]],
#26: Intersection A
[[[x^2-(1/2)*(y^2)-(1/2)*z^2=0,x*z+z*y-2*x=0,z^2-y=0]],[z,y,x]],
#27: Intersection B
[[[x^2-(1/2)*(y^2)-(1/2)*z^2=0,x*z+z*y-2*x=0,z^2-y=0]],[z,x,y]],
#28: Random A
[[[4*x^2+x*y^2-z+(1/4)=0,2*x+y^2*z+(1/2)=0,x^2*z-(1/2)*x-y^2=0]],[z,y,x]],
#29: Random B
[[[4*x^2+x*y^2-z+(1/4)=0,2*x+y^2*z+(1/2)=0,x^2*z-(1/2)*x-y^2=0]],[x,y,z]],
#30: Psi(JSC) A
[[[x^2+y^2-1=0,x*y-1/4<=0],[(x-4)^2+(y-1)^2-1<=0,(x-4)*(y-1)-1/4<=0]],[y,x]],
#31: Psi(JSC) B
[[[x^2+y^2-1=0,x*y-1/4<=0],[(x-4)^2+(y-1)^2-1<=0,(x-4)*(y-1)-1/4<=0]],[x,y]],
#32: Random 1 (JSC)
[[[-55*x-94*y+87*z-56=0, -62*y+97*z-73<=0],[-4*x-83*y-10*z+62<=0,-75-10*x^2-7*x*y-40*x*z+42*y*z-50*z^2<=0]],[x,y,z]],
#33: Random 2 (JSC)
[[[-81*x-6*y-51*z-29=0,-14*x-48*y+97*z-12<=0],[83*x-24*y-8*z+47<=0,60+46*y-31*x^2-91*x*y+98*x*z+2*y^2<=0]],[x,y,z]],
#34: Random 3 (JSC)
[[[-77*x+38*y+42*z+8=0,-6*x+23*y+76<=0],[-11*x+79*y+49*z-40<=0,-51-4*y+29*z-44*x*y+65*x*z+56*y^2<=0]],[x,y,z]],
#35: Random 4 (JSC)
[[[27*x-95*y+84*z+48=0,14*x+64*y-88*z+18<=0],[56*x+96*y+77*z+54<=0,-94+90*x^2+85*x*y-72*x*z-2*y^2+32*z^2<=0]],[x,y,z]],
#36: Random 5 (JSC)
[[[5*x-5*y-43*z+51=0,-45*x+30*y+21*z-12<=0],[82*x+23*y+63*z-67<=0,48-90*y-14*z-75*x*y+77*x*z+38*y^2<=0]],[x,y,z]],
#37: Solotareff \dagger \dagger A
[[[3*x^2-2*x-a=0,-(x^3-x^2-a*x-2*b+a-2)<=0,-(4*a-1)<=0,4*a-7<=0,-(x+1)<=0,x<=0],[3*y^2-2*y-a<=0,-(y^3-y^2-a*y-a+2)<=0,-(4*b+3)<=0,4*b-3<=0,-y<=0,y-1<=0]],[y,x,b,a]],
#38: Solotareff \dagger \dagger B
[[[3*x^2-2*x-a=0,-(x^3-x^2-a*x-2*b+a-2)<=0,-(4*a-1)<=0,4*a-7<=0,-(x+1)<=0,x<=0],[3*y^2-2*y-a<=0,-(y^3-y^2-a*y-a+2)<=0,-(4*b+3)<=0,4*b-3<=0,-y<=0,y-1<=0]],[y,x,a,b]],
#39: Collision \dagger \dagger A
[[[x^2-2*x*t+t^2+4*y^2-80*y+396=0,-t<=0],[x^2-2*x*a*t+5*a^2*t^2+4*y^2-8*y*a*t-4<=0,-a<=0]],[y,x,t,a]],
#40: Collision \dagger \dagger B
[[[x^2-2*x*t+t^2+4*y^2-80*y+396=0,-t<=0],[x^2-2*x*a*t+5*a^2*t^2+4*y^2-8*y*a*t-4<=0,-a<=0]],[t,x,y,a]],
#41: blood-coagulation-2
[[[1/200*x*s*(1 - 1/400*x) + y*s*(1 - 1/400*x) - 35/2*x=0, 250*x*s*(1 - 1/600*y )*(z + 3/250) - 55/2*y=0,500*(y + 1/20*x)*(1 - 1/700*z) - 5*z=0]],[z,y,x,s]],
#42: Rose
[[[7*y^4 - 20*x^2=0,2160*x*x*z^4+1512*x*z^4+315*z^4-4000*x*x-2800*x-490=0, -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=0]],[z,y,x]],
#43: MontesS10
[[[r-c1+l*(s1*s2-c1*c2)=0, z-s1-l*(s1*c2+s2*c1)=0, s1^2+c1^2-1=0, s2^2+c2^2-1=0]],[s1, c1, s2, c2, r, z, l]],
#44: Wang93
[[[(x-u)^2+(y-v)^2-1=0, v^2-u^3=0, 2*v*(x-u)+3*u^2*(y-v)=0, 2*w*v-1=0]],[w,v,u,y,x]],
#45: genLinSyst-3-2
[[[a*x+b*y-c=0, d*x+e*y-f=0, g*x+h*x-i=0]],[x, y, a, b, c, d, e, f, g, h, i]],
#46: blood-coagulation-2 \dagger
[[[1/200*x*s*(1 - 1/400*x) + y*s*(1 - 1/400*x) - 35/2*x=0],[ 250*x*s*(1 - 1/600*y )*(z + 3/250) - 55/2*y=0,500*(y + 1/20*x)*(1 - 1/700*z) - 5*z<=0]],[z,y,x,s]],
#47: Rose \dagger
[[[7*y^4 - 20*x^2=0],[2160*x*x*z^4+1512*x*z^4+315*z^4-4000*x*x-2800*x-490=0, -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<=0]],[z,y,x]],
#48: MontesS10 \dagger
[[[r-c1+l*(s1*s2-c1*c2)=0, z-s1-l*(s1*c2+s2*c1)<=0], [s1^2+c1^2-1=0, s2^2+c2^2-1<=0]],[s1, c1, s2, c2, r, z, l]],
#49: Wang93 \dagger
[[[(x-u)^2+(y-v)^2-1=0, v^2-u^3<=0], [2*v*(x-u)+3*u^2*(y-v)=0, 2*w*v-1<=0]],[w,v,u,y,x]],
#50: genLinSyst-3-2 \dagger
[[[a*x+b*y-c=0], [d*x+e*y-f=0, g*x+h*x-i<=0]],[x, y, a, b, c, d, e, f, g, h, i]],
#51: MontesS10 \dagger \dagger
[[[r-c1+l*(s1*s2-c1*c2)=0, z-s1-l*(s1*c2+s2*c1)<=0], [s1^2+c1^2-1<=0, s2^2+c2^2-1<=0]],[s1, c1, s2, c2, r, z, l]],
#52: Wang93 \dagger \dagger
[[[(x-u)^2+(y-v)^2-1=0, v^2-u^3<=0], [2*v*(x-u)+3*u^2*(y-v)<=0, 2*w*v-1<=0]],[w,v,u,y,x]],
#53: MontesS10 half-\dagger 1
[[[r-c1+l*(s1*s2-c1*c2)=0, z-s1-l*(s1*c2+s2*c1)=0], [s1^2+c1^2-1=0, s2^2+c2^2-1<=0]],[s1, c1, s2, c2, r, z, l]],
#54: MontesS10 half-\dagger 2
[[[r-c1+l*(s1*s2-c1*c2)=0, z-s1-l*(s1*c2+s2*c1)<=0], [s1^2+c1^2-1=0, s2^2+c2^2-1=0]],[s1, c1, s2, c2, r, z, l]],
#55: Wang93 half-\dagger 1
[[[(x-u)^2+(y-v)^2-1=0, v^2-u^3=0], [2*v*(x-u)+3*u^2*(y-v)=0, 2*w*v-1<=0]],[w,v,u,y,x]],
#56: Wang93 half-\dagger 2
[[[(x-u)^2+(y-v)^2-1=0, v^2-u^3<=0], [2*v*(x-u)+3*u^2*(y-v)=0, 2*w*v-1=0]],[w,v,u,y,x]]
]:


if n<=0 or n>nops(L) then
  ERROR("Out of range"):
fi:


RETURN(op(L[n])):

end:




#===================================================
# Code for SyNRAC


SyNRACExamples:=proc(n) local L:


L:=[
#1: Intersection \dagger A
[Or(x*z+z*y-2*x=0,And(z^2-y=0,2*x^2-y^2-z^2<=0)),[x,y,z]],
#2: Intersection \dagger B
[Or(x*z+z*y-2*x=0,And(z^2-y=0,2*x^2-y^2-z^2<=0)),[y,x,z]],
#3: Random \dagger A
[Or(16*x^2+4*x*y^2-4*z+1=0,And(4*x+2*y^2*z+1=0,2*x^2*z-x-2*y^2<=0)),[x,y,z]],
#4: Random \dagger B
[Or(16*x^2+4*x*y^2-4*z+1=0,And(4*x+2*y^2*z+1=0,2*x^2*z-x-2*y^2<=0)),[y,x,z]],
#5: Ellipse \dagger A
[Or(x^2+y^2-1=0,And(b^2*x^2-2*b^2*x*c+b^2*c^2+a^2*y^2-a^2*b^2=0,-a<=0,a-1<=0,-b<=0,b-1<=0,-c<=0,c-1<=0)),[a,b,c,x,y]],
#6: Ellipse \dagger B
[Or(x^2+y^2-1=0,And(b^2*x^2-2*b^2*x*c+b^2*c^2+a^2*y^2-a^2*b^2=0,-a<=0,a-1<=0,-b<=0,b-1<=0,-c<=0,c-1<=0)),[a,b,c,y,x]],
#7: Solotareff \dagger A
[Or(And(3*x^2-2*x-a=0,-(x^3-x^2-a*x-2*b+a-2)<=0,-(4*a-1)<=0,4*a-7<=0,-(x+1)<=0,x<=0),And(3*y^2-2*y-a=0,-(y^3-y^2-a*y-a+2)<=0,-(4*b+3)<=0,4*b-3<=0,-y<=0,y-1<=0)),[a,b,x,y]],
#8: Solotareff \dagger B
[Or(And(3*x^2-2*x-a=0,-(x^3-x^2-a*x-2*b+a-2)<=0,-(4*a-1)<=0,4*a-7<=0,-(x+1)<=0,x<=0),And(3*y^2-2*y-a=0,-(y^3-y^2-a*y-a+2)<=0,-(4*b+3)<=0,4*b-3<=0,-y<=0,y-1<=0)),[b,a,x,y]],
#9: Collision \dagger A
[Or(And(x^2-2*x*t+t^2+4*y^2-80*y+396=0,-t<=0),And(x^2-2*x*a*t+5*a^2*t^2+4*y^2-8*y*a*t-4=0,-a<=0)),[a,t,x,y]],
#10: Collision \dagger B
[Or(And(x^2-2*x*t+t^2+4*y^2-80*y+396=0,-t<=0),And(x^2-2*x*a*t+5*a^2*t^2+4*y^2-8*y*a*t-4=0,-a<=0)),[a,y,x,t]],
#11: Kahan A
[Or(And(8*y^3*x+8*y*x^3+20*y^3+84*y*x^2+288*y*x+324*y=0,-225*x^2-324*x+63*y^2-4*x^4-52*x^3+12*y^2*x+4*y^4<=0),And(2*y=0,2*x+9<=0),And(8*y=0,8*x^2+56*x+8*y^2+96<=0),And(y=0,x^2+7*x+y^2+12<=0),And(8*y^3*x+8*y*x^3+20*y^3+84*y*x^2+288*y*x+324*y=0,-4*x^4-52*x^3-252*x^2+12*y^2*x-540*x+36*y^2+4*y^4-432<=0,4*x^4+52*x^3+225*x^2-12*y^2*x+324*x-63*y^2-4*y^4<=0),And(2*y=0,-2*x-6<=0,2*x<=0),And(8*y=0,-8*x^2-56*x-8*y^2-96<=0,2*x^2+8*x+2*y^2<=0)),[x,y]],
#12: Kahan B
[Or(And(8*y^3*x+8*y*x^3+20*y^3+84*y*x^2+288*y*x+324*y=0,-225*x^2-324*x+63*y^2-4*x^4-52*x^3+12*y^2*x+4*y^4<=0),And(2*y=0,2*x+9<=0),And(8*y=0,8*x^2+56*x+8*y^2+96<=0),And(y=0,x^2+7*x+y^2+12<=0),And(8*y^3*x+8*y*x^3+20*y^3+84*y*x^2+288*y*x+324*y=0,-4*x^4-52*x^3-252*x^2+12*y^2*x-540*x+36*y^2+4*y^4-432<=0,4*x^4+52*x^3+225*x^2-12*y^2*x+324*x-63*y^2-4*y^4<=0),And(2*y=0,-2*x-6<=0,2*x<=0),And(8*y=0,-8*x^2-56*x-8*y^2-96<=0,2*x^2+8*x+2*y^2<=0)),[y,x]],
#13: ArcSin A
[Or(And(-2*x*y=0,y^2-x^2+1<=0),And(16*y^3*x-16*y*x^3+8*y*x=0,1-4*x^2+4*y^2+4*x^4-24*x^2*y^2+4*y^4<=0),And(y=0,1-x<=0),And(y=0,x+1<=0)),[x,y]],
#14: ArcSin B
[Or(And(-2*x*y=0,y^2-x^2+1<=0),And(16*y^3*x-16*y*x^3+8*y*x=0,1-4*x^2+4*y^2+4*x^4-24*x^2*y^2+4*y^4<=0),And(y=0,1-x<=0),And(y=0,x+1<=0)),[y,x]],
#15: 2D Example A
[Or(And(x^2+y^2-1=0,4*x*y-1<=0),And(x^2-8*x+16+y^2-2*y=0,4*x*y-4*x-16*y+15<=0)),[x,y]],
#16: 2D Example B
[Or(And(x^2+y^2-1=0,4*x*y-1<=0),And(x^2-8*x+16+y^2-2*y=0,4*x*y-4*x-16*y+15<=0)),[y,x]],
#17: 3D Example A
[Or(And(x^2+y^2+z^2-1=0,4*x*y*z-1<=0),And(x^2-8*x+y^2-2*y+z^2-4*z+20=0,4*y*x*z-8*y*x-4*x*z+8*x-16*y*z+32*y+16*z-33<=0)),[x,y,z]],
#18: 3D Example B
[Or(And(x^2+y^2+z^2-1=0,4*x*y*z-1<=0),And(x^2-8*x+y^2-2*y+z^2-4*z+20=0,4*y*x*z-8*y*x-4*x*z+8*x-16*y*z+32*y+16*z-33<=0)),[y,x,z]],


#19: Sqrt Branch Cuts
[Or(And(y = 0, x < 0), And(v = 0, u < 0), And(y*u+x*v = 0, x*u-y*v < 0)),[v,u,x,y]],
#20: Arctan Branch Cuts
[Or(And(x = 0, 1 < y), And(x = 0, y < -1), And(u = 0, 1 < v), And(u = 0, v < -1), And(-u^2*x-u*x^2-u*y^2-v^2*x+u+x = 0, u^2*x^2+u^2*y^2+v^2*x^2+v^2*y^2-2*x*u+2*y*v+1 < u^2*y+v^2*y+v*x^2+v*y^2+v+y), And(-u^2*x-u*x^2-u*y^2-v^2*x+u+x = 0, u^2*y+v^2*y+v*x^2+v*y^2+v+y < -u^2*x^2-u^2*y^2-v^2*x^2-v^2*y^2+2*x*u-2*y*v-1)),[u,x,v,y]],
#21: Arctanh Branch Cuts
[Or(And(y = 0, 1 <= x), And(y = 0, x <= -1), And(v = 0, 1 <= u), And(v = 0, u <= -1), And(-u^2*y-v^2*y-v*x^2-v*y^2+v+y = 0, u^2*x^2+u^2*y^2+v^2*x^2+v^2*y^2+2*x*u-2*y*v+1 <= u^2*x+u*x^2+u*y^2+v^2*x+u+x), And(-u^2*y-v^2*y-v*x^2-v*y^2+v+y = 0, u^2*x+u*x^2+u*y^2+v^2*x+u+x <= -u^2*x^2-u^2*y^2-v^2*x^2-v^2*y^2-2*x*u+2*y*v-1)),[v,y,u,x]],
#22: Phisanbut25 Branch Cuts
[Or(And(x = 0, 1 < y), And(x = 0, y < -1), And(v = 0, u < 1), And(2*u*x*y+v*x^2-v*y^2-2*x*y+v = 0, u*x^2-u*y^2-2*v*x*y-x^2+y^2+u < 1)),[u,y,x,v]],
#23: Phisanbut26 Branch Cuts
[Or(And(x = 0, 1 < y), And(x = 0, y < -1), And(v = 0, -1 < u, u < 1), And(2*u^2*x*y+2*u*v*x^2-2*u*v*y^2-2*v^2*x*y+2*u*v-2*x*y = 0, u^2*x^2-u^2*y^2-4*u*v*x*y-v^2*x^2+v^2*y^2+u^2-v^2-x^2+y^2 < 1)),[v,u,y,x]],
#24: Phisanbut27 Branch Cuts
[Or(And(-2*v*u+3*u*y+3*v*x-4*y*x+v-5*y = 0, -u^2+3*x*u+v^2-3*v*y-2*x^2+2*y^2+u-5*x < -12), And(y-v = 0, x-u < -4), And(v-2*y = 0, u-2*x < -3)),[u,x,v,y]],
#25: Phisanbut28 Branch Cuts
[Or(And(2*u*y*x+v*x^2-v*y^2-3*y*x^2+y^3-2*v*u+2*u*y+2*v*x+2*y*x-v+y = 0, u*x^2-u*y^2-2*v*y*x-x^3+3*x*y^2-u^2+2*x*u+v^2-2*v*y+x^2-y^2-u+x < -2), And(2*y*x-v+y = 0, x^2-y^2-u+x < -1), And(-y+v = 0, -x+u < -2)),[x,y,u,v]],
#26: Intersection A
[Or(And(x^2-(1/2)*(y^2)-(1/2)*z^2=0,x*z+z*y-2*x=0,z^2-y=0)),[x,y,z]],
#27: Intersection B
[Or(And(x^2-(1/2)*(y^2)-(1/2)*z^2=0,x*z+z*y-2*x=0,z^2-y=0)),[y,x,z]],
#28: Random A
[Or(And(4*x^2+x*y^2-z+(1/4)=0,2*x+y^2*z+(1/2)=0,x^2*z-(1/2)*x-y^2=0)),[x,y,z]],
#29: Random B
[Or(And(4*x^2+x*y^2-z+(1/4)=0,2*x+y^2*z+(1/2)=0,x^2*z-(1/2)*x-y^2=0)),[z,y,x]],
#30: Psi(JSC) A
[Or(And(x^2+y^2-1=0,x*y-1/4<=0),And((x-4)^2+(y-1)^2-1<=0,(x-4)*(y-1)-1/4<=0)),[x,y]],
#31: Psi(JSC) B
[Or(And(x^2+y^2-1=0,x*y-1/4<=0),And((x-4)^2+(y-1)^2-1<=0,(x-4)*(y-1)-1/4<=0)),[y,x]],
#32: Random 1 (JSC)
[Or(And(-55*x-94*y+87*z-56=0, -62*y+97*z-73<=0),And(-4*x-83*y-10*z+62<=0,-75-10*x^2-7*x*y-40*x*z+42*y*z-50*z^2<=0)),[z,y,x]],
#33: Random 2 (JSC)
[Or(And(-81*x-6*y-51*z-29=0,-14*x-48*y+97*z-12<=0),And(83*x-24*y-8*z+47<=0,60+46*y-31*x^2-91*x*y+98*x*z+2*y^2<=0)),[z,y,x]],
#34: Random 3 (JSC)
[Or(And(-77*x+38*y+42*z+8=0,-6*x+23*y+76<=0),And(-11*x+79*y+49*z-40<=0,-51-4*y+29*z-44*x*y+65*x*z+56*y^2<=0)),[z,y,x]],
#35: Random 4 (JSC)
[Or(And(27*x-95*y+84*z+48=0,14*x+64*y-88*z+18<=0),And(56*x+96*y+77*z+54<=0,-94+90*x^2+85*x*y-72*x*z-2*y^2+32*z^2<=0)),[z,y,x]],
#36: Random 5 (JSC)
[Or(And(5*x-5*y-43*z+51=0,-45*x+30*y+21*z-12<=0),And(82*x+23*y+63*z-67<=0,48-90*y-14*z-75*x*y+77*x*z+38*y^2<=0)),[z,y,x]],
#37: Solotareff \dagger \dagger A
[Or(And(3*x^2-2*x-a=0,-(x^3-x^2-a*x-2*b+a-2)<=0,-(4*a-1)<=0,4*a-7<=0,-(x+1)<=0,x<=0),And(3*y^2-2*y-a<=0,-(y^3-y^2-a*y-a+2)<=0,-(4*b+3)<=0,4*b-3<=0,-y<=0,y-1<=0)),[a,b,x,y]],
#38: Solotareff \dagger \dagger B
[Or(And(3*x^2-2*x-a=0,-(x^3-x^2-a*x-2*b+a-2)<=0,-(4*a-1)<=0,4*a-7<=0,-(x+1)<=0,x<=0),And(3*y^2-2*y-a<=0,-(y^3-y^2-a*y-a+2)<=0,-(4*b+3)<=0,4*b-3<=0,-y<=0,y-1<=0)),[b,a,x,y]],
#39: Collision \dagger \dagger A
[Or(And(x^2-2*x*t+t^2+4*y^2-80*y+396=0,-t<=0),And(x^2-2*x*a*t+5*a^2*t^2+4*y^2-8*y*a*t-4<=0,-a<=0)),[a,t,x,y]],
#40: Collision \dagger \dagger B
[Or(And(x^2-2*x*t+t^2+4*y^2-80*y+396=0,-t<=0),And(x^2-2*x*a*t+5*a^2*t^2+4*y^2-8*y*a*t-4<=0,-a<=0)),[a,y,x,t]],
#41: blood-coagulation-2
[Or(And(1/200*x*s*(1 - 1/400*x) + y*s*(1 - 1/400*x) - 35/2*x=0, 250*x*s*(1 - 1/600*y )*(z + 3/250) - 55/2*y=0,500*(y + 1/20*x)*(1 - 1/700*z) - 5*z=0)),[s,x,y,z]],
#42: Rose
[Or(And(7*y^4 - 20*x^2=0,2160*x*x*z^4+1512*x*z^4+315*z^4-4000*x*x-2800*x-490=0, -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=0)),[x,y,z]],
#43: MontesS10
[Or(And(r-c1+l*(s1*s2-c1*c2)=0, z-s1-l*(s1*c2+s2*c1)=0, s1^2+c1^2-1=0, s2^2+c2^2-1=0)),[l,z,r,c2,s2,c1,s1]],
#44: Wang93
[Or(And((x-u)^2+(y-v)^2-1=0, v^2-u^3=0, 2*v*(x-u)+3*u^2*(y-v)=0, 2*w*v-1=0)),[x,y,u,v,w]],
#45: genLinSyst-3-2
[Or(And(a*x+b*y-c=0, d*x+e*y-f=0, g*x+h*x-i=0)),[i,h,g,f,e,d,c,b,a,y,x]],
#46: blood-coagulation-2 \dagger
[Or(And(1/200*x*s*(1 - 1/400*x) + y*s*(1 - 1/400*x) - 35/2*x=0),And( 250*x*s*(1 - 1/600*y )*(z + 3/250) - 55/2*y=0,500*(y + 1/20*x)*(1 - 1/700*z) - 5*z<=0)),[s,x,y,z]],
#47: Rose \dagger
[Or(And(7*y^4 - 20*x^2=0),And(2160*x*x*z^4+1512*x*z^4+315*z^4-4000*x*x-2800*x-490=0, -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<=0)),[x,y,z]],
#48: MontesS10 \dagger
[Or(And(r-c1+l*(s1*s2-c1*c2)=0, z-s1-l*(s1*c2+s2*c1)<=0), And(s1^2+c1^2-1=0, s2^2+c2^2-1<=0)),[l,z,r,c2,s1,c1,s1]],
#49: Wang93 \dagger
[Or(And((x-u)^2+(y-v)^2-1=0, v^2-u^3<=0), And(2*v*(x-u)+3*u^2*(y-v)=0, 2*w*v-1<=0)),[x,y,u,v,w]],
#50: genLinSyst-3-2 \dagger
[Or(And(a*x+b*y-c=0), And(d*x+e*y-f=0, g*x+h*x-i<=0)),[i,h,g,f,e,d,c,b,a,y,x]],
#51: MontesS10 \dagger \dagger
[Or(And(r-c1+l*(s1*s2-c1*c2)=0, z-s1-l*(s1*c2+s2*c1)<=0), And(s1^2+c1^2-1<=0, s2^2+c2^2-1<=0)),[l,z,r,c2,s2,c1,s1]],
#52: Wang93 \dagger \dagger
[Or(And((x-u)^2+(y-v)^2-1=0, v^2-u^3<=0), And(2*v*(x-u)+3*u^2*(y-v)<=0, 2*w*v-1<=0)),[x,y,u,v,w]],
#53: MontesS10 half-\dagger 1
[Or(And(r-c1+l*(s1*s2-c1*c2)=0, z-s1-l*(s1*c2+s2*c1)=0), And(s1^2+c1^2-1=0, s2^2+c2^2-1<=0)),[l,z,r,c2,s2,c1,s1]],
#54: MontesS10 half-\dagger 2
[Or(And(r-c1+l*(s1*s2-c1*c2)=0, z-s1-l*(s1*c2+s2*c1)<=0), And(s1^2+c1^2-1=0, s2^2+c2^2-1=0)),[l,z,r,c2,s2,c1,s1]],
#55: Wang93 half-\dagger 3
[Or(And((x-u)^2+(y-v)^2-1=0, v^2-u^3=0), And(2*v*(x-u)+3*u^2*(y-v)=0, 2*w*v-1<=0)),[x,y,u,v,w]],
#56: Wang93 half-\dagger 4
[Or(And((x-u)^2+(y-v)^2-1=0, v^2-u^3<=0), And(2*v*(x-u)+3*u^2*(y-v)=0, 2*w*v-1=0)),[x,y,u,v,w]]
]:


if n<=0 or n>nops(L) then
  ERROR("Out of range"):
fi:


RETURN(op(L[n])):

end: