=======================================================
                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 ']':

[EC24]Enter a variable list:
(v,u,x,y,z)Enter the number of free variables:
5
Enter a prenex formula:
[ [z^2 + x - y = 0] /\ [-u^2 + v^2 + z^2 - 1 = 0] /\ [z^2 + x + y = 0] /\ [u^2 - v^2 + z^2 - 1 = 0] /\ [0 <= x^2 - 1] /\ [0 <= z]].

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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
       = x + 1

A_3,2  = input
       = x - 1



A_5,1  = input
       = z^2 - y + x

A_5,2  = input
       = z^2 - u^2 + v^2 - 1

A_5,3  = input
       = z^2 + y + x

A_5,4  = input
       = z^2 + u^2 - v^2 - 1

A_5,5  = input
       = z



Before Projection (z) >
eqn-const-list (A_5,2)
Before Projection (z) >
eqn-const-list (A_5,4)
Before Projection (z) >
go

Before Choice >
go

Before Solution >
d-fpc-stat
          propagation    trial-eval     total
true          0              5              5
false         0           5628           5628
total         0           5633           5633

Length of the projection-based formula :75

Before Solution >
go