=======================================================
                Quantifier Elimination                 
                          in                           
            Elementary Algebra and Geometry            
                          by                           
      Partial Cylindrical Algebraic Decomposition      
                                                       
               Version B 1.69, 16 Mar 2012
                                                       
                          by                           
                       Hoon Hong                       
                  (hhong@math.ncsu.edu)                
                                                       
With contributions by: Christopher W. Brown, George E. 
Collins, Mark J. Encarnacion, Jeremy R. Johnson        
Werner Krandick, Richard Liska, Scott McCallum,        
Nicolas Robidoux, and Stanly Steinberg                 
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Enter an informal description  between '[' and ']':

[]Enter a variable list:
(x,y,z)Enter the number of free variables:
3
Enter a prenex formula:
[ [x + y^2 + z = 0] /\ [x - y^2 + z = 0] /\ [x^2 + y^2 + z^2 -1 >= 0] ].

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Before Normalization >
prop-eqn-const

Before Normalization >
full-cad

Before Normalization >
go

Before Projection (z) >
d-proj-factors


A_3,1  = input
       = z + y^2 + x

A_3,2  = input
       = z - y^2 + x

A_3,3  = input
       = z^2 + y^2 + x^2 - 1



Before Projection (z) >
eqn-const-list (A_3,1)
Before Projection (z) >
eqn-const-list (A_3,2)
Before Projection (z) >
go

Before Choice >
go

Before Solution >
d-fpc-stat
          propagation    trial-eval     total
true          0              4              4
false         0            129            129
total         0            133            133

Length of the projection-based formula :24

Before Solution >
go 
An equivalent quantifier-free formula:

2 x^2 - 1 >= 0 /\ y = 0 /\ z + y^2 + x = 0


=====================  The End  =======================

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249753414 Cells in AVAIL, 250000000 Cells in SPACE.

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System time after the initialization: 1596 milliseconds.
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