$ echo 'card [P, Q, R] -> { [i3, i4, P - 2i3 - i4, i6, Q - i4 - 2i6, i8] : 2i8 = -P - Q + R + 2i3 + 2i4 + 2i6 and i3 >= 0 and i4 >= 0 and i4 <= P - 2i3 and i6 >= 0 and 2i6 <= Q - i4 and 2i6 >= P + Q - R - 2i3 - 2i4 };' | ./iscc 
[P, Q, R] -> { ((((((1 + 1/2 * P - 1/8 * P^2 - 1/16 * P^3) + (-11/24 + 1/8 * P + 1/16 * P^2) * Q + -1/16 * P * Q^2 + 1/48 * Q^3) + ((-1/6 + 1/8 * P + 1/16 * P^2) + (3/8 + 1/8 * P) * Q - 1/16 * Q^2) * R + ((-1/4 - 1/16 * P) + 1/16 * Q) * R^2 - 1/48 * R^3) + (((3/4 + 1/4 * P) - 1/4 * Q) - 1/2 * R) * [(Q)/2]) + (((1/2 + 1/4 * P) - 1/4 * Q) + 1/2 * [(Q)/2]) * [(R)/2]) + (((1/2 - 1/4 * Q) + 1/4 * R) + 1/2 * [(Q)/2]) * [(Q + R)/2]) : exists (e0 = [(-P - Q + R)/2]: 2e0 = -P - Q + R and R >= -P + Q and R >= P and R <= -1 + Q); ((((((1 + 1/3 * P - 1/8 * P^2 - 1/48 * P^3) + (-11/24 + 1/4 * P + 1/16 * P^2) * Q + -1/16 * P * Q^2 + 1/48 * Q^3) + ((1/8 * P - 1/16 * P^2) + (1/4 + 1/8 * P) * Q - 1/16 * Q^2) * R + ((-1/4 + 1/16 * P) + 1/16 * Q) * R^2 - 1/16 * R^3) + ((3/4 - 1/4 * Q) - 1/4 * R) * [(Q)/2]) + (((1/2 + 1/4 * P) - 1/4 * Q) + 1/2 * [(Q)/2]) * [(R)/2]) + (((1/2 - 1/4 * Q) + 1/4 * R) + 1/2 * [(Q)/2]) * [(Q + R)/2]) : exists (e0 = [(-P - Q + R)/2]: 2e0 = -P - Q + R and R >= -P + Q and R <= -1 + P and Q >= 1 + P); ((((((1 + 1/6 * P - 1/8 * P^2 + 1/48 * P^3) + (-7/24 + 1/4 * P - 1/16 * P^2) * Q + 1/16 * P * Q^2 - 1/48 * Q^3) + ((1/4 * P - 1/16 * P^2) + (1/8 + 1/8 * P) * Q - 1/16 * Q^2) * R + ((-1/4 + 1/16 * P) + 1/16 * Q) * R^2 - 1/16 * R^3) + ((3/4 - 1/4 * Q) - 1/4 * R) * [(Q)/2]) + (1/2 + 1/2 * [(Q)/2]) * [(R)/2]) + (((1/2 - 1/4 * Q) + 1/4 * R) + 1/2 * [(Q)/2]) * [(Q + R)/2]) : exists (e0 = [(-P - Q + R)/2]: 2e0 = -P - Q + R and Q <= P and R >= P - Q and R <= -1 + Q); (((((1 - 1/8 * Q + 1/8 * Q^2) + (1/6 + 3/8 * Q) * R + (-1/8 + 1/8 * Q) * R^2 - 1/24 * R^3) + ((3/4 - 1/4 * Q) - 1/4 * R) * [(Q)/2]) + (1/2 + 1/2 * [(Q)/2]) * [(R)/2]) + (((1/2 - 1/4 * Q) + 1/4 * R) + 1/2 * [(Q)/2]) * [(Q + R)/2]) : exists (e0 = [(-P - Q + R)/2]: 2e0 = -P - Q + R and R <= -2 + P - Q and R <= -1 + Q and R >= 0); (((((1 + 1/24 * Q - 1/24 * Q^3) + (3/8 * Q + 1/8 * Q^2) * R) + ((3/4 - 1/4 * Q) - 1/4 * R) * [(Q)/2]) + (1/2 + 1/2 * [(Q)/2]) * [(R)/2]) + (1/2 + 1/2 * [(Q)/2]) * [(Q + R)/2]) : exists (e0 = [(-P - Q + R)/2]: 2e0 = -P - Q + R and R <= -2 + P - Q and Q >= 0 and R >= Q); ((((((1 + 1/2 * P) + (1/24 + 3/8 * P) * Q + 1/8 * P * Q^2 - 1/24 * Q^3) - 1/2 * R) + (((3/4 + 1/4 * P) - 1/4 * Q) - 1/2 * R) * [(Q)/2]) + (1/2 + 1/2 * [(Q)/2]) * [(R)/2]) + (1/2 + 1/2 * [(Q)/2]) * [(Q + R)/2]) : exists (e0 = [(-P - Q + R)/2]: 2e0 = -P - Q + R and Q <= P and R >= 2 + P + Q and Q >= 0); ((((((1 + 1/3 * P - 1/8 * P^2 - 1/48 * P^3) + (-1/8 + 1/8 * P - 1/16 * P^2) * Q + (-1/8 + 1/16 * P) * Q^2 - 1/16 * Q^3) + ((-1/3 + 1/4 * P + 1/16 * P^2) + (1/4 + 1/8 * P) * Q + 1/16 * Q^2) * R + ((-1/8 - 1/16 * P) - 1/16 * Q) * R^2 + 1/48 * R^3) + (((3/4 + 1/4 * P) - 1/4 * Q) - 1/2 * R) * [(Q)/2]) + (1/2 + 1/2 * [(Q)/2]) * [(R)/2]) + (1/2 + 1/2 * [(Q)/2]) * [(Q + R)/2]) : exists (e0 = [(-P - Q + R)/2]: 2e0 = -P - Q + R and R <= P + Q and Q <= P and R >= P); ((((((1 + 1/6 * P - 1/8 * P^2 + 1/48 * P^3) + (-1/8 + 1/4 * P - 1/16 * P^2) * Q + (-1/8 + 1/16 * P) * Q^2 - 1/16 * Q^3) + ((-1/6 + 1/4 * P - 1/16 * P^2) + (1/8 + 1/8 * P) * Q + 1/16 * Q^2) * R + ((-1/8 + 1/16 * P) - 1/16 * Q) * R^2 - 1/48 * R^3) + ((3/4 - 1/4 * Q) - 1/4 * R) * [(Q)/2]) + (1/2 + 1/2 * [(Q)/2]) * [(R)/2]) + (1/2 + 1/2 * [(Q)/2]) * [(Q + R)/2]) : exists (e0 = [(-P - Q + R)/2]: 2e0 = -P - Q + R and R <= -1 + P and R >= P - Q and R >= Q); ((((((1 + 2/3 * P - 1/24 * P^3) + (-5/8 - 1/8 * P) * Q + 1/8 * Q^2) + ((3/8 * P + 1/8 * P^2) + 1/8 * Q) * R - 1/8 * R^2) + (((3/4 + 1/4 * P) - 1/4 * Q) - 1/2 * R) * [(Q)/2]) + (((1/2 + 1/4 * P) - 1/4 * Q) + 1/2 * [(Q)/2]) * [(R)/2]) + (((1/2 - 1/4 * Q) + 1/4 * R) + 1/2 * [(Q)/2]) * [(Q + R)/2]) : exists (e0 = [(-P - Q + R)/2]: 2e0 = -P - Q + R and P >= 0 and R <= -2 - P + Q and R >= P); ((((((1 + 1/2 * P) - 5/8 * Q + 1/8 * Q^2) + (1/6 + 3/8 * P) * R + (-1/8 + 1/8 * P) * R^2 - 1/24 * R^3) + ((3/4 - 1/4 * Q) - 1/4 * R) * [(Q)/2]) + (((1/2 + 1/4 * P) - 1/4 * Q) + 1/2 * [(Q)/2]) * [(R)/2]) + (((1/2 - 1/4 * Q) + 1/4 * R) + 1/2 * [(Q)/2]) * [(Q + R)/2]) : exists (e0 = [(-P - Q + R)/2]: 2e0 = -P - Q + R and R <= -1 + P and R <= -2 - P + Q and R >= 0); ((((((1 + 2/3 * P - 1/24 * P^3) + (-1/8 + 3/8 * P + 1/8 * P^2) * Q) + ((-1/2 - 1/8 * P) + 1/8 * Q) * R) + (((3/4 + 1/4 * P) - 1/4 * Q) - 1/2 * R) * [(Q)/2]) + (((1/2 + 1/4 * P) - 1/4 * Q) + 1/2 * [(Q)/2]) * [(R)/2]) + (1/2 + 1/2 * [(Q)/2]) * [(Q + R)/2]) : exists (e0 = [(-P - Q + R)/2]: 2e0 = -P - Q + R and P >= 0 and Q >= 1 + P and R >= 2 + P + Q); ((((((1 + 1/2 * P - 1/8 * P^2 - 1/16 * P^3) + (-7/24 + 1/8 * P + 1/16 * P^2) * Q + (-1/8 - 1/16 * P) * Q^2 - 1/48 * Q^3) + ((-1/3 + 1/8 * P + 1/16 * P^2) + (3/8 + 1/8 * P) * Q + 1/16 * Q^2) * R + ((-1/8 - 1/16 * P) - 1/16 * Q) * R^2 + 1/48 * R^3) + (((3/4 + 1/4 * P) - 1/4 * Q) - 1/2 * R) * [(Q)/2]) + (((1/2 + 1/4 * P) - 1/4 * Q) + 1/2 * [(Q)/2]) * [(R)/2]) + (1/2 + 1/2 * [(Q)/2]) * [(Q + R)/2]) : exists (e0 = [(-P - Q + R)/2]: 2e0 = -P - Q + R and R <= P + Q and Q >= 1 + P and R >= Q) }

# below is the same in the old interface
bash-3.00$ cat sturmfels 
9 11
0 2 1 1 0 0 0 -1 0 0 0
0 0 1 0 2 1 0 0 -1 0 0
0 0 0 1 0 1 2 0 0 -1 0
1 1 0 0 0 0 0 0 0 0 0
1 0 1 0 0 0 0 0 0 0 0
1 0 0 1 0 0 0 0 0 0 0
1 0 0 0 1 0 0 0 0 0 0
1 0 0 0 0 1 0 0 0 0 0
1 0 0 0 0 0 1 0 0 0 0

0 5
bash-3.00$ ~/obj/barvinok/barvinok_enumerate < sturmfels
POLYHEDRON Dimension:9
           Constraints:10  Equations:3  Rays:7  Lines:0
Constraints 10 11
Equality:   [   2   0   0  -2  -2  -2  -1   1   1   0 ]
Equality:   [   0   1   0   2   1   0   0  -1   0   0 ]
Equality:   [   0   0   1   0   1   2   0   0  -1   0 ]
Inequality: [   0   0   0   2   2   2   1  -1  -1   0 ]
Inequality: [   0   0   0  -2  -1   0   0   1   0   0 ]
Inequality: [   0   0   0   0  -1  -2   0   0   1   0 ]
Inequality: [   0   0   0   1   0   0   0   0   0   0 ]
Inequality: [   0   0   0   0   1   0   0   0   0   0 ]
Inequality: [   0   0   0   0   0   1   0   0   0   0 ]
Inequality: [   0   0   0   0   0   0   0   0   0   1 ]
Rays 7 11
Ray:    [   0   0   0   0   0   1   0   0   2 ]
Ray:    [   0   0   0   0   1   0   0   1   1 ]
Ray:    [   0   0   0   1   0   0   0   2   0 ]
Ray:    [   0   0   1   0   0   0   1   0   1 ]
Ray:    [   0   1   0   0   0   0   1   1   0 ]
Ray:    [   1   0   0   0   0   0   2   0   0 ]
Vertex: [   0   0   0   0   0   0   0   0   0 ]/1
POLYHEDRON Dimension:3
           Constraints:1  Equations:0  Rays:4  Lines:3
Constraints 1 5
Inequality: [   0   0   0   1 ]
Rays 4 5
Line:   [   1   0   0 ]
Line:   [   0   1   0 ]
Line:   [   0   0   1 ]
Vertex: [   0   0   0 ]/1
         Q  >= 0
         P - Q  -1 >= 0
         - P - Q + R  -1 >= 0
          1 >= 0

[ ( 1 * {( 1/2 * P + ( 1/2 * Q + ( 1/2 * R + 0 )
 )
 )
} + 0 )
= 0 ] * 
( ( 1/8 * Q^2 + 1/2 * Q + ( -1/4 * {( 1/2 * Q + 0 )
} + 1/2 )
 )
 * P + ( -1/24 * Q^3 + 0 * Q^2 + ( -1/4 * {( 1/2 * Q + ( 1/2 * R + 0 )
 )
} + ( -1/4 * {( 1/2 * R + 0 )
} + 2/3 )
 )
 * Q + ( ( 1/2 * {( 1/2 * Q + ( 1/2 * R + 0 )
 )
} + -1/2 )
 * {( 1/2 * Q + 0 )
} + ( ( 1/2 * {( 1/2 * R + 0 )
} + -3/4 )
 * {( 1/2 * Q + ( 1/2 * R + 0 )
 )
} + ( -1/2 * {( 1/2 * R + 0 )
} + 1 )
 )
 )
 )
 )
         P + Q - R  >= 0
         P - Q  -1 >= 0
         - P + R  -1 >= 0
          1 >= 0

[ ( 1 * {( 1/2 * P + ( 1/2 * Q + ( 1/2 * R + 0 )
 )
 )
} + 0 )
= 0 ] * 
( -1/48 * P^3 + ( -1/16 * Q + ( 1/16 * R + -1/8 )
 )
 * P^2 + ( 1/16 * Q^2 + ( 1/8 * R + 1/4 )
 * Q + ( -1/16 * R^2 + 1/4 * R + ( -1/4 * {( 1/2 * Q + 0 )
} + 1/3 )
 )
 )
 * P + ( -1/16 * Q^3 + ( 1/16 * R + -1/8 )
 * Q^2 + ( -1/16 * R^2 + 1/4 * R + ( -1/4 * {( 1/2 * Q + ( 1/2 * R + 0 )
 )
} + ( -1/4 * {( 1/2 * R + 0 )
} + 1/2 )
 )
 )
 * Q + ( 1/48 * R^3 + -1/8 * R^2 + 1/6 * R + ( ( 1/2 * {( 1/2 * Q + ( 1/2 * R + 0 )
 )
} + -1/2 )
 * {( 1/2 * Q + 0 )
} + ( ( 1/2 * {( 1/2 * R + 0 )
} + -3/4 )
 * {( 1/2 * Q + ( 1/2 * R + 0 )
 )
} + ( -1/2 * {( 1/2 * R + 0 )
} + 1 )
 )
 )
 )
 )
 )
         P - R  >= 0
         - Q + R  -1 >= 0
         - P + Q + R  -1 >= 0
          1 >= 0

[ ( 1 * {( 1/2 * P + ( 1/2 * Q + ( 1/2 * R + 0 )
 )
 )
} + 0 )
= 0 ] * 
( 1/48 * P^3 + ( -1/16 * Q + ( -1/16 * R + -1/8 )
 )
 * P^2 + ( 1/16 * Q^2 + ( 1/8 * R + 1/4 )
 * Q + ( 1/16 * R^2 + 1/4 * R + 1/6 )
 )
 * P + ( -1/16 * Q^3 + ( 1/16 * R + -1/8 )
 * Q^2 + ( -1/16 * R^2 + 1/4 * R + ( -1/4 * {( 1/2 * Q + ( 1/2 * R + 0 )
 )
} + ( -1/4 * {( 1/2 * R + 0 )
} + 1/2 )
 )
 )
 * Q + ( -1/48 * R^3 + -1/8 * R^2 + ( -1/4 * {( 1/2 * Q + 0 )
} + 1/3 )
 * R + ( ( 1/2 * {( 1/2 * Q + ( 1/2 * R + 0 )
 )
} + -1/2 )
 * {( 1/2 * Q + 0 )
} + ( ( 1/2 * {( 1/2 * R + 0 )
} + -3/4 )
 * {( 1/2 * Q + ( 1/2 * R + 0 )
 )
} + ( -1/2 * {( 1/2 * R + 0 )
} + 1 )
 )
 )
 )
 )
 )
         - P + Q  >= 0
         P  >= 0
         - P - Q + R  -1 >= 0
          1 >= 0

[ ( 1 * {( 1/2 * P + ( 1/2 * Q + ( 1/2 * R + 0 )
 )
 )
} + 0 )
= 0 ] * 
( -1/24 * P^3 + ( 1/8 * Q + 0 )
 * P^2 + ( 1/2 * Q + ( -1/4 * {( 1/2 * Q + 0 )
} + ( -1/4 * {( 1/2 * R + 0 )
} + 2/3 )
 )
 )
 * P + ( ( -1/4 * {( 1/2 * Q + ( 1/2 * R + 0 )
 )
} + 1/2 )
 * Q + ( ( 1/2 * {( 1/2 * Q + ( 1/2 * R + 0 )
 )
} + -1/2 )
 * {( 1/2 * Q + 0 )
} + ( ( 1/2 * {( 1/2 * R + 0 )
} + -3/4 )
 * {( 1/2 * Q + ( 1/2 * R + 0 )
 )
} + ( -1/2 * {( 1/2 * R + 0 )
} + 1 )
 )
 )
 )
 )
         - P + Q  >= 0
         P + Q - R  >= 0
         - Q + R  -1 >= 0
          1 >= 0

[ ( 1 * {( 1/2 * P + ( 1/2 * Q + ( 1/2 * R + 0 )
 )
 )
} + 0 )
= 0 ] * 
( -1/16 * P^3 + ( 1/16 * Q + ( 1/16 * R + -1/8 )
 )
 * P^2 + ( -1/16 * Q^2 + ( 1/8 * R + 1/4 )
 * Q + ( -1/16 * R^2 + 1/4 * R + ( -1/4 * {( 1/2 * Q + 0 )
} + ( -1/4 * {( 1/2 * R + 0 )
} + 1/2 )
 )
 )
 )
 * P + ( -1/48 * Q^3 + ( 1/16 * R + -1/8 )
 * Q^2 + ( -1/16 * R^2 + 1/4 * R + ( -1/4 * {( 1/2 * Q + ( 1/2 * R + 0 )
 )
} + 1/3 )
 )
 * Q + ( 1/48 * R^3 + -1/8 * R^2 + 1/6 * R + ( ( 1/2 * {( 1/2 * Q + ( 1/2 * R + 0 )
 )
} + -1/2 )
 * {( 1/2 * Q + 0 )
} + ( ( 1/2 * {( 1/2 * R + 0 )
} + -3/4 )
 * {( 1/2 * Q + ( 1/2 * R + 0 )
 )
} + ( -1/2 * {( 1/2 * R + 0 )
} + 1 )
 )
 )
 )
 )
 )
         Q - R  >= 0
         P - Q + R  -1 >= 0
         - P + R  -1 >= 0
          1 >= 0

[ ( 1 * {( 1/2 * P + ( 1/2 * Q + ( 1/2 * R + 0 )
 )
 )
} + 0 )
= 0 ] * 
( -1/16 * P^3 + ( 1/16 * Q + ( 1/16 * R + -1/8 )
 )
 * P^2 + ( -1/16 * Q^2 + ( 1/8 * R + 1/4 )
 * Q + ( -1/16 * R^2 + 1/4 * R + ( -1/4 * {( 1/2 * Q + 0 )
} + ( -1/4 * {( 1/2 * R + 0 )
} + 1/2 )
 )
 )
 )
 * P + ( 1/48 * Q^3 + ( -1/16 * R + -1/8 )
 * Q^2 + ( 1/16 * R^2 + 1/4 * R + 1/6 )
 * Q + ( -1/48 * R^3 + -1/8 * R^2 + ( -1/4 * {( 1/2 * Q + ( 1/2 * R + 0 )
 )
} + 1/3 )
 * R + ( ( 1/2 * {( 1/2 * Q + ( 1/2 * R + 0 )
 )
} + -1/2 )
 * {( 1/2 * Q + 0 )
} + ( ( 1/2 * {( 1/2 * R + 0 )
} + -3/4 )
 * {( 1/2 * Q + ( 1/2 * R + 0 )
 )
} + ( -1/2 * {( 1/2 * R + 0 )
} + 1 )
 )
 )
 )
 )
 )
         P - R  >= 0
         - P + Q  -1 >= 0
         P - Q + R  -1 >= 0
          1 >= 0

[ ( 1 * {( 1/2 * P + ( 1/2 * Q + ( 1/2 * R + 0 )
 )
 )
} + 0 )
= 0 ] * 
( -1/48 * P^3 + ( 1/16 * Q + ( -1/16 * R + -1/8 )
 )
 * P^2 + ( -1/16 * Q^2 + ( 1/8 * R + 1/4 )
 * Q + ( 1/16 * R^2 + 1/4 * R + ( -1/4 * {( 1/2 * R + 0 )
} + 1/3 )
 )
 )
 * P + ( 1/48 * Q^3 + ( -1/16 * R + -1/8 )
 * Q^2 + ( 1/16 * R^2 + 1/4 * R + 1/6 )
 * Q + ( -1/16 * R^3 + -1/8 * R^2 + ( -1/4 * {( 1/2 * Q + 0 )
} + ( -1/4 * {( 1/2 * Q + ( 1/2 * R + 0 )
 )
} + 1/2 )
 )
 * R + ( ( 1/2 * {( 1/2 * Q + ( 1/2 * R + 0 )
 )
} + -1/2 )
 * {( 1/2 * Q + 0 )
} + ( ( 1/2 * {( 1/2 * R + 0 )
} + -3/4 )
 * {( 1/2 * Q + ( 1/2 * R + 0 )
 )
} + ( -1/2 * {( 1/2 * R + 0 )
} + 1 )
 )
 )
 )
 )
 )
         - P + Q - R  >= 0
         P  >= 0
         - P + R  -1 >= 0
          1 >= 0

[ ( 1 * {( 1/2 * P + ( 1/2 * Q + ( 1/2 * R + 0 )
 )
 )
} + 0 )
= 0 ] * 
( -1/24 * P^3 + ( 1/8 * R + 0 )
 * P^2 + ( 1/2 * R + ( -1/4 * {( 1/2 * Q + 0 )
} + ( -1/4 * {( 1/2 * R + 0 )
} + 2/3 )
 )
 )
 * P + ( ( -1/4 * {( 1/2 * Q + ( 1/2 * R + 0 )
 )
} + 1/2 )
 * R + ( ( 1/2 * {( 1/2 * Q + ( 1/2 * R + 0 )
 )
} + -1/2 )
 * {( 1/2 * Q + 0 )
} + ( ( 1/2 * {( 1/2 * R + 0 )
} + -3/4 )
 * {( 1/2 * Q + ( 1/2 * R + 0 )
 )
} + ( -1/2 * {( 1/2 * R + 0 )
} + 1 )
 )
 )
 )
 )
         - P + Q - R  >= 0
         P - R  >= 0
         R  >= 0
          1 >= 0

[ ( 1 * {( 1/2 * P + ( 1/2 * Q + ( 1/2 * R + 0 )
 )
 )
} + 0 )
= 0 ] * 
( ( 1/8 * R^2 + 1/2 * R + ( -1/4 * {( 1/2 * R + 0 )
} + 1/2 )
 )
 * P + ( -1/24 * R^3 + 0 * R^2 + ( -1/4 * {( 1/2 * Q + 0 )
} + ( -1/4 * {( 1/2 * Q + ( 1/2 * R + 0 )
 )
} + 2/3 )
 )
 * R + ( ( 1/2 * {( 1/2 * Q + ( 1/2 * R + 0 )
 )
} + -1/2 )
 * {( 1/2 * Q + 0 )
} + ( ( 1/2 * {( 1/2 * R + 0 )
} + -3/4 )
 * {( 1/2 * Q + ( 1/2 * R + 0 )
 )
} + ( -1/2 * {( 1/2 * R + 0 )
} + 1 )
 )
 )
 )
 )
         P - Q - R  >= 0
         Q  >= 0
         - Q + R  -1 >= 0
          1 >= 0

[ ( 1 * {( 1/2 * P + ( 1/2 * Q + ( 1/2 * R + 0 )
 )
 )
} + 0 )
= 0 ] * 
( -1/24 * Q^3 + ( 1/8 * R + 0 )
 * Q^2 + ( 1/2 * R + ( -1/4 * {( 1/2 * Q + ( 1/2 * R + 0 )
 )
} + ( -1/4 * {( 1/2 * R + 0 )
} + 2/3 )
 )
 )
 * Q + ( ( -1/4 * {( 1/2 * Q + 0 )
} + 1/2 )
 * R + ( ( 1/2 * {( 1/2 * Q + ( 1/2 * R + 0 )
 )
} + -1/2 )
 * {( 1/2 * Q + 0 )
} + ( ( 1/2 * {( 1/2 * R + 0 )
} + -3/4 )
 * {( 1/2 * Q + ( 1/2 * R + 0 )
 )
} + ( -1/2 * {( 1/2 * R + 0 )
} + 1 )
 )
 )
 )
 )
         Q - R  >= 0
         P - Q  >= 0
         - P + Q + R  -1 >= 0
          1 >= 0

[ ( 1 * {( 1/2 * P + ( 1/2 * Q + ( 1/2 * R + 0 )
 )
 )
} + 0 )
= 0 ] * 
( 1/48 * P^3 + ( -1/16 * Q + ( -1/16 * R + -1/8 )
 )
 * P^2 + ( 1/16 * Q^2 + ( 1/8 * R + 1/4 )
 * Q + ( 1/16 * R^2 + 1/4 * R + 1/6 )
 )
 * P + ( -1/48 * Q^3 + ( -1/16 * R + -1/8 )
 * Q^2 + ( 1/16 * R^2 + 1/4 * R + ( -1/4 * {( 1/2 * R + 0 )
} + 1/3 )
 )
 * Q + ( -1/16 * R^3 + -1/8 * R^2 + ( -1/4 * {( 1/2 * Q + 0 )
} + ( -1/4 * {( 1/2 * Q + ( 1/2 * R + 0 )
 )
} + 1/2 )
 )
 * R + ( ( 1/2 * {( 1/2 * Q + ( 1/2 * R + 0 )
 )
} + -1/2 )
 * {( 1/2 * Q + 0 )
} + ( ( 1/2 * {( 1/2 * R + 0 )
} + -3/4 )
 * {( 1/2 * Q + ( 1/2 * R + 0 )
 )
} + ( -1/2 * {( 1/2 * R + 0 )
} + 1 )
 )
 )
 )
 )
 )
         Q - R  >= 0
         P - Q - R  >= 0
         R  >= 0
          1 >= 0

[ ( 1 * {( 1/2 * P + ( 1/2 * Q + ( 1/2 * R + 0 )
 )
 )
} + 0 )
= 0 ] * 
( ( 1/8 * R^2 + 1/2 * R + ( -1/4 * {( 1/2 * R + 0 )
} + 1/2 )
 )
 * Q + ( -1/24 * R^3 + 0 * R^2 + ( -1/4 * {( 1/2 * Q + 0 )
} + ( -1/4 * {( 1/2 * Q + ( 1/2 * R + 0 )
 )
} + 2/3 )
 )
 * R + ( ( 1/2 * {( 1/2 * Q + ( 1/2 * R + 0 )
 )
} + -1/2 )
 * {( 1/2 * Q + 0 )
} + ( ( 1/2 * {( 1/2 * R + 0 )
} + -3/4 )
 * {( 1/2 * Q + ( 1/2 * R + 0 )
 )
} + ( -1/2 * {( 1/2 * R + 0 )
} + 1 )
 )
 )
 )
 )