BEGINCAD
DIMENSION
3
INPUTVARIABLES
(X,Y,Z)
MINPOLYVARIABLE
(U)
FIELDELEMENTVARIABLE
(U)
INPUTPOLYNOMIALS
(
 Z**2 + Y**2 + X**2 - 1  $
)
BASIS
(
 Z**2 + Y**2 + X**2 - 1  $
)
CONTENTS
(
)
PROJECTION
(
 1  $ , 
 4 Y**2 + 4 X**2 - 4  $
)
 
CELLS
 
BEGINCELL
INDEX
(1,1,1)
INPUTSIGNATURE
(GT)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(- 3 )
(0)
(0)
)
DEFININGFORMULA
( ( (  X + 1 < 0 ) & ( 0= 0 ) ) & ( 0= 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(2,1,1)
INPUTSIGNATURE
(GT)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U + 1  $ , 
(-2 , -1)
POINT
(
(- 1 )
(- 1 )
(0)
)
DEFININGFORMULA
( ( (  X + 1 = 0 ) & (  Y < 0 ) ) & ( 0= 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(2,2,1)
INPUTSIGNATURE
(EQ)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U + 1  $ , 
(-2 , -1)
POINT
(
(- 1 )
(0)
(- 1 )
)
DEFININGFORMULA
( ( (  X + 1 = 0 ) & (  Y = 0 ) ) & (  Z < 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(2,2,2)
INPUTSIGNATURE
(GT)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U + 1  $ , 
(-2 , -1)
POINT
(
(- 1 )
(0)
(0)
)
DEFININGFORMULA
( ( (  X + 1 = 0 ) & (  Y = 0 ) ) & (  Z = 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(2,2,3)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U + 1  $ , 
(-2 , -1)
POINT
(
(- 1 )
(0)
( 2 )
)
DEFININGFORMULA
( ( (  X + 1 = 0 ) & (  Y = 0 ) ) & (  Z > 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(2,3,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U + 1  $ , 
(-2 , -1)
POINT
(
(- 1 )
( 2 )
(0)
)
DEFININGFORMULA
( ( (  X + 1 = 0 ) & (  Y > 0 ) ) & ( 0= 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,1,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(- 1/2 )
(- 1 )
(0)
)
DEFININGFORMULA
( ( ( (  X + 1 > 0 ) & (  X - 1 < 0 ) ) & ( (  Y < 0 ) & (  Y**2 + X**2 - 1 > 0 
) ) ) & ( 0= 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,2,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 4 U**2 - 3  $ , 
(-1 , -3/4)
POINT
(
(- 1/2 )
( U )
(- 1 )
)
DEFININGFORMULA
( ( ( (  X + 1 > 0 ) & (  X - 1 < 0 ) ) & ( (  Y < 0 ) & (  Y**2 + X**2 - 1 = 0 
) ) ) & (  Z < 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,2,2)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 4 U**2 - 3  $ , 
(-1 , -3/4)
POINT
(
(- 1/2 )
( U )
(0)
)
DEFININGFORMULA
( ( ( (  X + 1 > 0 ) & (  X - 1 < 0 ) ) & ( (  Y < 0 ) & (  Y**2 + X**2 - 1 = 0 
) ) ) & (  Z = 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,2,3)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 4 U**2 - 3  $ , 
(-1 , -3/4)
POINT
(
(- 1/2 )
( U )
( 2 )
)
DEFININGFORMULA
( ( ( (  X + 1 > 0 ) & (  X - 1 < 0 ) ) & ( (  Y < 0 ) & (  Y**2 + X**2 - 1 = 0 
) ) ) & (  Z > 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,3,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(- 1/2 )
(0)
(- 1 )
)
DEFININGFORMULA
( ( ( (  X + 1 > 0 ) & (  X - 1 < 0 ) ) & ( ( (  Y < 0 ) & (  Y**2 + X**2 - 1 < 
0 ) ) | (  Y = 0 ) | ( (  Y > 0 ) & (  Y**2 + X**2 - 1 < 0 ) ) ) ) & ( (  Z < 0 
) & (  Z**2 + Y**2 + X**2 - 1 > 0 ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,3,2)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 4 U**2 - 3  $ , 
(-1 , -3/4)
POINT
(
(- 1/2 )
(0)
( U )
)
DEFININGFORMULA
( ( ( (  X + 1 > 0 ) & (  X - 1 < 0 ) ) & ( ( (  Y < 0 ) & (  Y**2 + X**2 - 1 < 
0 ) ) | (  Y = 0 ) | ( (  Y > 0 ) & (  Y**2 + X**2 - 1 < 0 ) ) ) ) & ( (  Z < 0 
) & (  Z**2 + Y**2 + X**2 - 1 = 0 ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,3,3)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(- 1/2 )
(0)
(0)
)
DEFININGFORMULA
( ( ( (  X + 1 > 0 ) & (  X - 1 < 0 ) ) & ( ( (  Y < 0 ) & (  Y**2 + X**2 - 1 < 
0 ) ) | (  Y = 0 ) | ( (  Y > 0 ) & (  Y**2 + X**2 - 1 < 0 ) ) ) ) & ( ( (  Z < 
0 ) & (  Z**2 + Y**2 + X**2 - 1 < 0 ) ) | (  Z = 0 ) | ( (  Z > 0 ) & (  Z**2 + 
Y**2 + X**2 - 1 < 0 ) ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,3,4)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 4 U**2 - 3  $ , 
(0 , 1)
POINT
(
(- 1/2 )
(0)
( U )
)
DEFININGFORMULA
( ( ( (  X + 1 > 0 ) & (  X - 1 < 0 ) ) & ( ( (  Y < 0 ) & (  Y**2 + X**2 - 1 < 
0 ) ) | (  Y = 0 ) | ( (  Y > 0 ) & (  Y**2 + X**2 - 1 < 0 ) ) ) ) & ( (  Z > 0 
) & (  Z**2 + Y**2 + X**2 - 1 = 0 ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,3,5)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(- 1/2 )
(0)
( 3 )
)
DEFININGFORMULA
( ( ( (  X + 1 > 0 ) & (  X - 1 < 0 ) ) & ( ( (  Y < 0 ) & (  Y**2 + X**2 - 1 < 
0 ) ) | (  Y = 0 ) | ( (  Y > 0 ) & (  Y**2 + X**2 - 1 < 0 ) ) ) ) & ( (  Z > 0 
) & (  Z**2 + Y**2 + X**2 - 1 > 0 ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,4,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 4 U**2 - 3  $ , 
(0 , 1)
POINT
(
(- 1/2 )
( U )
(- 1 )
)
DEFININGFORMULA
( ( ( (  X + 1 > 0 ) & (  X - 1 < 0 ) ) & ( (  Y > 0 ) & (  Y**2 + X**2 - 1 = 0 
) ) ) & (  Z < 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,4,2)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 4 U**2 - 3  $ , 
(0 , 1)
POINT
(
(- 1/2 )
( U )
(0)
)
DEFININGFORMULA
( ( ( (  X + 1 > 0 ) & (  X - 1 < 0 ) ) & ( (  Y > 0 ) & (  Y**2 + X**2 - 1 = 0 
) ) ) & (  Z = 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,4,3)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 4 U**2 - 3  $ , 
(0 , 1)
POINT
(
(- 1/2 )
( U )
( 2 )
)
DEFININGFORMULA
( ( ( (  X + 1 > 0 ) & (  X - 1 < 0 ) ) & ( (  Y > 0 ) & (  Y**2 + X**2 - 1 = 0 
) ) ) & (  Z > 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,5,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(- 1/2 )
( 3 )
(0)
)
DEFININGFORMULA
( ( ( (  X + 1 > 0 ) & (  X - 1 < 0 ) ) & ( (  Y > 0 ) & (  Y**2 + X**2 - 1 > 0 
) ) ) & ( 0= 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(4,1,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U - 1  $ , 
(0 , 2)
POINT
(
( 1 )
(- 1 )
(0)
)
DEFININGFORMULA
( ( (  X - 1 = 0 ) & (  Y < 0 ) ) & ( 0= 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(4,2,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U - 1  $ , 
(0 , 2)
POINT
(
( 1 )
(0)
(- 1 )
)
DEFININGFORMULA
( ( (  X - 1 = 0 ) & (  Y = 0 ) ) & (  Z < 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(4,2,2)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U - 1  $ , 
(0 , 2)
POINT
(
( 1 )
(0)
(0)
)
DEFININGFORMULA
( ( (  X - 1 = 0 ) & (  Y = 0 ) ) & (  Z = 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(4,2,3)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U - 1  $ , 
(0 , 2)
POINT
(
( 1 )
(0)
( 2 )
)
DEFININGFORMULA
( ( (  X - 1 = 0 ) & (  Y = 0 ) ) & (  Z > 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(4,3,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U - 1  $ , 
(0 , 2)
POINT
(
( 1 )
( 2 )
(0)
)
DEFININGFORMULA
( ( (  X - 1 = 0 ) & (  Y > 0 ) ) & ( 0= 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(5,1,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
( 3 )
(0)
(0)
)
DEFININGFORMULA
( ( (  X - 1 > 0 ) & ( 0= 0 ) ) & ( 0= 0 ) ) $
ENDCELL
 
 
INDUCEDCAD
BEGINCAD
DIMENSION
2
INPUTVARIABLES
(X,Y)
MINPOLYVARIABLE
(U)
FIELDELEMENTVARIABLE
(U)
INPUTPOLYNOMIALS
(
 1  $ , 
 4 Y**2 + 4 X**2 - 4  $
)
BASIS
(
 Y**2 + X**2 - 1  $
)
CONTENTS
(
)
PROJECTION
(
 1  $ , 
- 4 X**2 + 4  $
)
 
CELLS
 
BEGINCELL
INDEX
(1,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(- 3 )
(0)
)
DEFININGFORMULA
( (  X + 1 < 0 ) & ( 0= 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(2,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U + 1  $ , 
(-2 , -1)
POINT
(
(- 1 )
(- 1 )
)
DEFININGFORMULA
( (  X + 1 = 0 ) & (  Y < 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(2,2)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U + 1  $ , 
(-2 , -1)
POINT
(
(- 1 )
(0)
)
DEFININGFORMULA
( (  X + 1 = 0 ) & (  Y = 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(2,3)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U + 1  $ , 
(-2 , -1)
POINT
(
(- 1 )
( 2 )
)
DEFININGFORMULA
( (  X + 1 = 0 ) & (  Y > 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(- 1/2 )
(- 1 )
)
DEFININGFORMULA
( ( (  X + 1 > 0 ) & (  X - 1 < 0 ) ) & ( (  Y < 0 ) & (  Y**2 + X**2 - 1 > 0 ) 
) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,2)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 4 U**2 - 3  $ , 
(-1 , -3/4)
POINT
(
(- 1/2 )
( U )
)
DEFININGFORMULA
( ( (  X + 1 > 0 ) & (  X - 1 < 0 ) ) & ( (  Y < 0 ) & (  Y**2 + X**2 - 1 = 0 ) 
) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,3)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(- 1/2 )
(0)
)
DEFININGFORMULA
( ( (  X + 1 > 0 ) & (  X - 1 < 0 ) ) & ( ( (  Y < 0 ) & (  Y**2 + X**2 - 1 < 0 
) ) | (  Y = 0 ) | ( (  Y > 0 ) & (  Y**2 + X**2 - 1 < 0 ) ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,4)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 4 U**2 - 3  $ , 
(0 , 1)
POINT
(
(- 1/2 )
( U )
)
DEFININGFORMULA
( ( (  X + 1 > 0 ) & (  X - 1 < 0 ) ) & ( (  Y > 0 ) & (  Y**2 + X**2 - 1 = 0 ) 
) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,5)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(- 1/2 )
( 3 )
)
DEFININGFORMULA
( ( (  X + 1 > 0 ) & (  X - 1 < 0 ) ) & ( (  Y > 0 ) & (  Y**2 + X**2 - 1 > 0 ) 
) ) $
ENDCELL
 
BEGINCELL
INDEX
(4,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U - 1  $ , 
(0 , 2)
POINT
(
( 1 )
(- 1 )
)
DEFININGFORMULA
( (  X - 1 = 0 ) & (  Y < 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(4,2)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U - 1  $ , 
(0 , 2)
POINT
(
( 1 )
(0)
)
DEFININGFORMULA
( (  X - 1 = 0 ) & (  Y = 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(4,3)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U - 1  $ , 
(0 , 2)
POINT
(
( 1 )
( 2 )
)
DEFININGFORMULA
( (  X - 1 = 0 ) & (  Y > 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(5,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
( 3 )
(0)
)
DEFININGFORMULA
( (  X - 1 > 0 ) & ( 0= 0 ) ) $
ENDCELL
 
 
INDUCEDCAD
BEGINCAD
DIMENSION
1
INPUTVARIABLES
(X)
MINPOLYVARIABLE
(U)
FIELDELEMENTVARIABLE
(U)
INPUTPOLYNOMIALS
(
 1  $ , 
- 4 X**2 + 4  $
)
BASIS
(
 X + 1  $ , 
 X - 1  $
)
CONTENTS
(
)
PROJECTION
(
)
 
CELLS
 
BEGINCELL
INDEX
(1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(- 3 )
)
DEFININGFORMULA
(  X + 1 < 0 ) $
ENDCELL
 
BEGINCELL
INDEX
(2)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U + 1  $ , 
(-2 , -1)
POINT
(
(- 1 )
)
DEFININGFORMULA
(  X + 1 = 0 ) $
ENDCELL
 
BEGINCELL
INDEX
(3)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(- 1/2 )
)
DEFININGFORMULA
( (  X + 1 > 0 ) & (  X - 1 < 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(4)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U - 1  $ , 
(0 , 2)
POINT
(
( 1 )
)
DEFININGFORMULA
(  X - 1 = 0 ) $
ENDCELL
 
BEGINCELL
INDEX
(5)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
( 3 )
)
DEFININGFORMULA
(  X - 1 > 0 ) $
ENDCELL
 
 
ENDCAD
ENDCAD
ENDCAD