=======================================================
                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                 
=======================================================
Enter an informal description  between '[' and ']':
[CAD for Example 23 using EC]Enter a variable list:
(x,y)Enter the number of free variables:
2
Enter a prenex formula:
[ [x^2 + y^2 - 1 = 0 /\ x y - 1/4 < 0] ].

=======================================================

Before Normalization >
prop-eqn-const

Before Normalization >
go

Before Projection (y) >
eqn-const-list (A_2,1)
Before Projection (y) >
go

Before Choice >
go

Before Solution >
d-fpc-stat
          propagation    trial-eval     total
true          0             14             14
false         0             55             55
total         0             69             69

Length of the projection-based formula :70

Before Solution >
d-cell(1,1)---------- Information about the cell (1,1) ----------

Level                       : 2
Dimension                   : 2
Number of children          : 0
Truth value                 : F    by trial evaluation.
Degrees after substitution  : Not known yet or No polynomial.
Multiplicities              : ()
Signs of Projection Factors
Level 1  : (-,-,+)
Level 2  : (+,+)
----------   Sample point  ---------- 
The sample point is in a PRIMITIVE representation.

alpha = the unique root of x between 0 and 0
      = 0.0000000000

Coordinate 1 = -2
             = -2.0000000000
Coordinate 2 = -2
             = -2.0000000000


----------------------------------------------------

Before Solution >
d-cell(1,2)---------- Information about the cell (1,2) ----------

Level                       : 2
Dimension                   : 1
Number of children          : 0
Truth value                 : F    by trial evaluation.
Degrees after substitution  : Not known yet or No polynomial.
Multiplicities              : ((2,1))
Signs of Projection Factors
Level 1  : (-,-,+)
Level 2  : (+,0)
----------   Sample point  ---------- 
The sample point is in a PRIMITIVE representation.

alpha = the unique root of x between 0 and 0
      = 0.0000000000

Coordinate 1 = -2
             = -2.0000000000
Coordinate 2 = -1/8
             = -0.1250000000


----------------------------------------------------

Before Solution >
d-cell(1,3)---------- Information about the cell (1,3) ----------

Level                       : 2
Dimension                   : 2
Number of children          : 0
Truth value                 : F    by trial evaluation.
Degrees after substitution  : Not known yet or No polynomial.
Multiplicities              : ()
Signs of Projection Factors
Level 1  : (-,-,+)
Level 2  : (+,-)
----------   Sample point  ---------- 
The sample point is in a PRIMITIVE representation.

alpha = the unique root of x between 0 and 0
      = 0.0000000000

Coordinate 1 = -2
             = -2.0000000000
Coordinate 2 = 1
             = 1.0000000000


----------------------------------------------------

Before Solution >
go 
An equivalent quantifier-free formula:

4 x y - 1 < 0 /\ y^2 + x^2 - 1 = 0


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

-----------------------------------------------------------------------------
0 Garbage collections, 0 Cells and 0 Arrays reclaimed, in 0 milliseconds.
476038 Cells in AVAIL, 500000 Cells in SPACE.

System time: 10 milliseconds.
System time after the initialization: 6 milliseconds.
-----------------------------------------------------------------------------
