Author 
Comment/Response 
Fadoua

11/28/05 8:25pm
Hello,
I have started to use Mathematica some months ago.
I want to use CylindricalDecomposition[{ineqs}, {x1, x2, … }] function of mathematica to solve a system of inequalities and equalities.
I included the two equalities a==b and b==c to the set ineqs. And I got a strange result: Whenever I change the order of equalities elements, I et a different result.
This is a part of my code :
a = BC = Sqrt[(z  y)^2 + 1])
b = AC = Sqrt[(1 + x)^2 + z^2]
c = AB = Sqrt[x^2 + y^2]
Case 1 : a == b && b == c
cons = CylindricalDecomposition[{0 ≤ x ≤ 1, 0 ≤ y ≤ 1, 0 ≤ z ≤
1, (a == b), (b == c)}, {x, y, z}]
Result is :
x == 1 + Sqrt[3] && y ==1 + Sqrt[3] && z == 1
Case 2 : a == c && c == b
cons = CylindricalDecomposition[{0 ≤ x ≤ 1, 0 ≤ y ≤ 1, 0 ≤ z ≤
1, (a == c), (c == b)}, {x, y, z}]
Result is a logic combination of inequalities. The solution given by the first case is included in this combination.
Case 3: b == a && a == c
cons = CylindricalDecomposition[{0 ≤ x ≤ 1, 0 ≤ y ≤ 1, 0 ≤ z ≤
1, (b == a), (a == c)}, {x, y, z}]
Result is : False !!!
Why does CylindricalDecomposition depend on equalities order ?
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