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Student Support Forum: 'CylindricalDecomposition gives different results' topicStudent Support Forum > General > "CylindricalDecomposition gives different results"

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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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