# Makes a global table `CADExamples` full of pure CAD examples (unquantified)
:-`CADExamples` := table([
#2.4:
'`Sphere and Catastrophe`' = [ z^2+y^2+x^2-1 = 0, z^3+x*z+y = 0 ],
#2.6:
'`Arnon-84-2`' = [ 144*y^2+96*x^2*y+9*x^4+105*x^2+70*x-98 = 0,
                   x*y^2+6*x*y+x^3+9*x = 0 ],
#2.17:
'`McCallum Trivariate Random Polynomial`' = ( (y-1)*z^4+x*z^3+x*(1-y)*z^2+
                                              (y-x-1)*z+y = 0 ),
#6.2:
'`Concentric Circles`' = [ x^2+y^2-9 = 0, x^2+y^2-1 = 0 ],
#6.3:
'`Non-Concentric Circles`' = [ x^2+y^2-9 = 0, x^2+(y-1)^2-1 = 0 ],
#2.5:
'`Arnon-84`' = ( y^4-2*y^3+y^2-3*x^2*y+2*x^4 = 0 ),
#5.1:
'`Piano Movers Problem (Davenport) (Original)`' =
    ':-Or'( ':-And'((x-a)^2+(y-b)^2-9 = 0, y*b >= 0),
            ':-And'(x*(y-b)^2+y*(a-x)*(y-b) >= 0, (y-1)*(b-1) >= 0),
            ':-And'((x+1)*(y-b)^2+(y-1)*(a-x)*(y-b) >= 0, x*a >= 0),
            ':-And'(y*(x-a)^2+x*(b-y)*(x-a) >= 0,(x+1)*(a+1) >= 0),
            (y-1)*(x-a)^2+(x+1)*(b-y)*(x-a) >= 0
          ),
### 8: TTICAD Examples
#8.1:
'`Intersection`' =
    ':-Or'( x*z+z*y-2*x = 0, ':-And'( z^2-y = 0, 2*x^2-y^2-z^2 < 0 ) ),
#8.2: Intersection B
# different variable ordering for above - z > x > y rather than z > y > x
#8.3:
'`Random`' =
    ':-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) ),
#8.4: Random B
# different variable ordering for above - z > x > y rather than z > y > x
#8.5:
'`Ellipse`' = 
    ':-And'(':-Or'(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),
#8.6: Ellipse B
# different variable ordering for above - x > y > c > b > a rather than 
# y > x > c > b > a
#8.7:
'`Solotareff`' = 
    ':-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) ),
#8.8: Solotareff B
# different variable ordering for above - y > x > a> b rather than y > x > b > a
#8.9:
'`Collision`' =
    ':-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) ),
#8.10: Collision B
# different variable ordering for above - t > x > y > a rather than 
# y > x > t > a
#8.11:
'`Kahan`' =
    ':-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, 8*y = 0, 
                   -8*x^2-56*x-8*y^2-96 < 0, 2*x^2+8*x+2*y^2 <= 0) 
          ),
#8.12: Kahan B
# different variable ordering for above - x > y rather than y > x
#8.13:
'`ArcSin`' = 
    ':-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)
           ),
#8.14: ArcSin B
# different variable ordering for above - x > y rather than y > x
#8.15:
'`2D Example`' =
    ':-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-17 < 0) ),
#8.16: 2D Example B
# different variable ordering for above - x > y rather than y > x
#8.17:
'`3D Example`' =
    ':-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) ),
'`3D Sphere`' = ':-And'( z - x - 1 < 0, z - y - 1 < 0,
                                             x^2 + y^2 - 1 = 0 ),
#8.18: 3D Example B
# different variable ordering for above - z > y > x rather than z > x > y
'`ProjectionCAD 1`' = ':-Or'(
    ':-And'( y^2 + x^2 - 1 = 0, y*x - 1/4 < 0 ),
    ':-And'( (x-4)^2 + (y-1)^2 - 1 = 0, (x-4)*(y-1) - 1/4 < 0 ) ),
'`ProjectionCAD 2`' = ':-Or'(
    ':-And'( y^2 + x^2 - 1 = 0, x^3 + y^3 - 1 = 0, y*x - 1/4 < 0 ),
    ':-And'( (x-4)^2 + (y-1)^2 - 1 = 0, (x-4)^3 + (y-1)^3 -1 = 0,
             (x-4)*(y-1) - 1/4 < 0 ) )
]): # end table