BEGINCAD
DIMENSION
3
INPUTVARIABLES
(P,Q,R)
MINPOLYVARIABLE
(U)
FIELDELEMENTVARIABLE
(U)
INPUTPOLYNOMIALS
(
 256 R^3 - 128 P^2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2  $
)
BASIS
(
 256 R^3 - 128 P^2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2  $
)
CONTENTS
(
)
PROJECTION
(
 82944 P Q^2 - 3072 P^4  $ , 
 256  $ , 
 330225942528 Q^8 + 293534171136 P^3 Q^6 + 86973087744 P^6 Q^4 + 8589934592
 P^9 Q^2  $ , 
 56623104 P Q^2 - 2097152 P^4  $
)
 
CELLS
 
BEGINCELL
INDEX
(1,1,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(- 1 )
(- 1 )
( 1 )
)
DEFININGFORMULA
( ( (  P < 0 ) & ( (  Q < 0 ) & (  27 Q^2 + 8 P^3 > 0 ) ) ) & (  256 R^3 - 128 P^2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 < 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(1,1,2)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 256 U^3 - 128 U^2 - 128 U - 23  $ , 
(1 , 3/2)
POINT
(
(- 1 )
(- 1 )
( U )
)
DEFININGFORMULA
( ( (  P < 0 ) & ( (  Q < 0 ) & (  27 Q^2 + 8 P^3 > 0 ) ) ) & (  256 R^3 - 128 P^2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 = 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(1,1,3)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(- 1 )
(- 1 )
( 3 )
)
DEFININGFORMULA
( ( (  P < 0 ) & ( (  Q < 0 ) & (  27 Q^2 + 8 P^3 > 0 ) ) ) & (  256 R^3 - 128 P^2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 > 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(1,2,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 27 U^2 - 8  $ , 
(-3/4 , -1/2)
POINT
(
(- 1 )
( U )
(- 1/2 )
)
DEFININGFORMULA
( ( (  P < 0 ) & ( (  Q < 0 ) & (  27 Q^2 + 8 P^3 = 0 ) ) ) & ( (  6 R - P^2 
< 0 ) & (  48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 > 0 ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(1,2,2)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 27 U^2 - 8  $ , 
(-3/4 , -1/2)
POINT
(
(- 1 )
( U )
(- 1/12 )
)
DEFININGFORMULA
( ( (  P < 0 ) & ( (  Q < 0 ) & (  27 Q^2 + 8 P^3 = 0 ) ) ) & ( (  6 R - P^2 
< 0 ) & (  48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 = 0 ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(1,2,3)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 27 U^2 - 8  $ , 
(-3/4 , -1/2)
POINT
(
(- 1 )
( U )
( 1/2 )
)
DEFININGFORMULA
( ( (  P < 0 ) & ( (  Q < 0 ) & (  27 Q^2 + 8 P^3 = 0 ) ) ) & ( ( ( (  6 R - P
^2 < 0 ) & (  48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 < 0 ) ) | (  6 R - P^2 = 0
 ) | ( (  6 R - P^2 > 0 ) & (  48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 < 0 ) ) ) 
| ( (  6 R - P^2 > 0 ) & (  48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 = 0 ) ) | ( (
 (  6 R - P^2 > 0 ) & (  48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 > 0 ) ) & (  256
 R^3 - 128 P^2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 < 0 ) )
 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(1,2,4)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 27 U^2 - 8  $ , 
(-3/4 , -1/2)
POINT
(
(- 1 )
( U )
( 2/3 )
)
DEFININGFORMULA
( ( (  P < 0 ) & ( (  Q < 0 ) & (  27 Q^2 + 8 P^3 = 0 ) ) ) & ( ( (  6 R - P^
2 > 0 ) & (  48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 > 0 ) ) & (  256 R^3 - 128 P
^2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 = 0 ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(1,2,5)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 27 U^2 - 8  $ , 
(-3/4 , -1/2)
POINT
(
(- 1 )
( U )
( 2 )
)
DEFININGFORMULA
( ( (  P < 0 ) & ( (  Q < 0 ) & (  27 Q^2 + 8 P^3 = 0 ) ) ) & ( ( (  6 R - P^
2 > 0 ) & (  48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 > 0 ) ) & (  256 R^3 - 128 P
^2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 > 0 ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(1,3,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(- 1 )
(- 1/4 )
(- 2 )
)
DEFININGFORMULA
( ( (  P < 0 ) & ( ( ( (  Q < 0 ) & (  27 Q^2 + 8 P^3 < 0 ) ) | (  Q = 0 ) | (
 (  Q > 0 ) & (  27 Q^2 + 8 P^3 < 0 ) ) ) & (  Q < 0 ) ) ) & ( ( (  6 R - P^2
 < 0 ) & (  48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 > 0 ) ) & (  256 R^3 - 128 P^2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 < 0 ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(1,3,2)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 65536 U^3 - 32768 U^2 + 1792 U + 37  $ , 
(-1 , 0)
POINT
(
(- 1 )
(- 1/4 )
( U )
)
DEFININGFORMULA
( ( (  P < 0 ) & ( ( ( (  Q < 0 ) & (  27 Q^2 + 8 P^3 < 0 ) ) | (  Q = 0 ) | (
 (  Q > 0 ) & (  27 Q^2 + 8 P^3 < 0 ) ) ) & (  Q < 0 ) ) ) & ( ( (  6 R - P^2
 < 0 ) & (  48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 > 0 ) ) & (  256 R^3 - 128 P^2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 = 0 ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(1,3,3)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(- 1 )
(- 1/4 )
( 1/16 )
)
DEFININGFORMULA
( ( (  P < 0 ) & ( ( ( (  Q < 0 ) & (  27 Q^2 + 8 P^3 < 0 ) ) | (  Q = 0 ) | (
 (  Q > 0 ) & (  27 Q^2 + 8 P^3 < 0 ) ) ) & (  Q < 0 ) ) ) & ( ( ( (  6 R - P^2 < 0 ) & (  48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 > 0 ) ) & (  256 R^3 - 128 
P^2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 > 0 ) ) | ( (  6 R 
- P^2 < 0 ) & (  48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 = 0 ) ) | ( ( ( (  6 R -
 P^2 < 0 ) & (  48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 < 0 ) ) | (  6 R - P^2 =
 0 ) | ( (  6 R - P^2 > 0 ) & (  48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 < 0 ) ) 
) & (  256 R^3 - 128 P^2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 > 0 ) ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(1,3,4)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 65536 U^3 - 32768 U^2 + 1792 U + 37  $ , 
(1/16 , 3/32)
POINT
(
(- 1 )
(- 1/4 )
( U )
)
DEFININGFORMULA
( ( (  P < 0 ) & ( ( ( (  Q < 0 ) & (  27 Q^2 + 8 P^3 < 0 ) ) | (  Q = 0 ) | (
 (  Q > 0 ) & (  27 Q^2 + 8 P^3 < 0 ) ) ) & (  Q < 0 ) ) ) & ( ( ( (  6 R - P^2 < 0 ) & (  48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 < 0 ) ) | (  6 R - P^2 = 0 
) | ( (  6 R - P^2 > 0 ) & (  48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 < 0 ) ) ) &
 (  256 R^3 - 128 P^2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 
= 0 ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(1,3,5)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(- 1 )
(- 1/4 )
( 3/8 )
)
DEFININGFORMULA
( ( (  P < 0 ) & ( ( ( (  Q < 0 ) & (  27 Q^2 + 8 P^3 < 0 ) ) | (  Q = 0 ) | (
 (  Q > 0 ) & (  27 Q^2 + 8 P^3 < 0 ) ) ) & (  Q < 0 ) ) ) & ( ( ( ( (  6 R - 
P^2 < 0 ) & (  48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 < 0 ) ) | (  6 R - P^2 = 
0 ) | ( (  6 R - P^2 > 0 ) & (  48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 < 0 ) ) )
 & (  256 R^3 - 128 P^2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^
2 < 0 ) ) | ( (  6 R - P^2 > 0 ) & (  48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 = 0
 ) ) | ( ( (  6 R - P^2 > 0 ) & (  48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 > 0 ) 
) & (  256 R^3 - 128 P^2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 < 0 ) ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(1,3,6)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 65536 U^3 - 32768 U^2 + 1792 U + 37  $ , 
(3/8 , 7/16)
POINT
(
(- 1 )
(- 1/4 )
( U )
)
DEFININGFORMULA
( ( (  P < 0 ) & ( ( ( (  Q < 0 ) & (  27 Q^2 + 8 P^3 < 0 ) ) | (  Q = 0 ) | (
 (  Q > 0 ) & (  27 Q^2 + 8 P^3 < 0 ) ) ) & (  Q < 0 ) ) ) & ( ( (  6 R - P^2
 > 0 ) & (  48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 > 0 ) ) & (  256 R^3 - 128 P^2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 = 0 ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(1,3,7)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(- 1 )
(- 1/4 )
( 3/2 )
)
DEFININGFORMULA
( ( (  P < 0 ) & ( ( ( (  Q < 0 ) & (  27 Q^2 + 8 P^3 < 0 ) ) | (  Q = 0 ) | (
 (  Q > 0 ) & (  27 Q^2 + 8 P^3 < 0 ) ) ) & (  Q < 0 ) ) ) & ( ( (  6 R - P^2
 > 0 ) & (  48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 > 0 ) ) & (  256 R^3 - 128 P^2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 > 0 ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(1,4,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(- 1 )
(0)
(- 1/8 )
)
DEFININGFORMULA
( ( (  P < 0 ) & (  Q = 0 ) ) & ( ( (  6 R - P^2 < 0 ) & (  48 R^2 - 16 P^2 R
 + 9 P Q^2 + P^4 > 0 ) ) & (  256 R^3 - 128 P^2 R^2 + 144 P Q^2 R + 16 P^
4 R - 27 Q^4 - 4 P^3 Q^2 < 0 ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(1,4,2)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(- 1 )
(0)
(0)
)
DEFININGFORMULA
( ( (  P < 0 ) & (  Q = 0 ) ) & ( ( (  6 R - P^2 < 0 ) & (  48 R^2 - 16 P^2 R
 + 9 P Q^2 + P^4 > 0 ) ) & (  256 R^3 - 128 P^2 R^2 + 144 P Q^2 R + 16 P^
4 R - 27 Q^4 - 4 P^3 Q^2 = 0 ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(1,4,3)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(- 1 )
(0)
( 1/8 )
)
DEFININGFORMULA
( ( (  P < 0 ) & (  Q = 0 ) ) & ( ( ( (  6 R - P^2 < 0 ) & (  48 R^2 - 16 P^2
 R + 9 P Q^2 + P^4 > 0 ) ) & (  256 R^3 - 128 P^2 R^2 + 144 P Q^2 R + 16 P
^4 R - 27 Q^4 - 4 P^3 Q^2 > 0 ) ) | ( (  6 R - P^2 < 0 ) & (  48 R^2 - 16 
P^2 R + 9 P Q^2 + P^4 = 0 ) ) | ( ( (  6 R - P^2 < 0 ) & (  48 R^2 - 16 P^
2 R + 9 P Q^2 + P^4 < 0 ) ) | (  6 R - P^2 = 0 ) | ( (  6 R - P^2 > 0 ) & ( 
 48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 < 0 ) ) ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(1,4,4)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(- 1 )
(0)
( 1/4 )
)
DEFININGFORMULA
( ( (  P < 0 ) & (  Q = 0 ) ) & ( (  6 R - P^2 > 0 ) & (  48 R^2 - 16 P^2 R +
 9 P Q^2 + P^4 = 0 ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(1,4,5)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(- 1 )
(0)
( 5/4 )
)
DEFININGFORMULA
( ( (  P < 0 ) & (  Q = 0 ) ) & ( (  6 R - P^2 > 0 ) & (  48 R^2 - 16 P^2 R +
 9 P Q^2 + P^4 > 0 ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(1,5,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(- 1 )
( 1/2 )
(- 9/128 )
)
DEFININGFORMULA
( ( (  P < 0 ) & ( (  Q > 0 ) & ( ( (  Q < 0 ) & (  27 Q^2 + 8 P^3 < 0 ) ) | (
  Q = 0 ) | ( (  Q > 0 ) & (  27 Q^2 + 8 P^3 < 0 ) ) ) ) ) & ( ( (  6 R - P^2
 < 0 ) & (  48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 > 0 ) ) & (  256 R^3 - 128 P^2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 < 0 ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(1,5,2)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 256 U^2 - 144 U - 11  $ , 
(-35/512 , -17/256)
POINT
(
(- 1 )
( 1/2 )
( U )
)
DEFININGFORMULA
( ( (  P < 0 ) & ( (  Q > 0 ) & ( ( (  Q < 0 ) & (  27 Q^2 + 8 P^3 < 0 ) ) | (
  Q = 0 ) | ( (  Q > 0 ) & (  27 Q^2 + 8 P^3 < 0 ) ) ) ) ) & ( ( (  6 R - P^2
 < 0 ) & (  48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 > 0 ) ) & (  256 R^3 - 128 P^2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 = 0 ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(1,5,3)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(- 1 )
( 1/2 )
(- 33/512 )
)
DEFININGFORMULA
( ( (  P < 0 ) & ( (  Q > 0 ) & ( ( (  Q < 0 ) & (  27 Q^2 + 8 P^3 < 0 ) ) | (
  Q = 0 ) | ( (  Q > 0 ) & (  27 Q^2 + 8 P^3 < 0 ) ) ) ) ) & ( ( ( (  6 R - P^2 < 0 ) & (  48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 > 0 ) ) & (  256 R^3 - 128 
P^2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 > 0 ) ) | ( (  6 R 
- P^2 < 0 ) & (  48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 = 0 ) ) | ( ( ( (  6 R -
 P^2 < 0 ) & (  48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 < 0 ) ) | (  6 R - P^2 =
 0 ) | ( (  6 R - P^2 > 0 ) & (  48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 < 0 ) ) 
) & (  256 R^3 - 128 P^2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 > 0 ) ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(1,5,4)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(- 1 )
( 1/2 )
(- 1/16 )
)
DEFININGFORMULA
( ( (  P < 0 ) & ( (  Q > 0 ) & ( ( (  Q < 0 ) & (  27 Q^2 + 8 P^3 < 0 ) ) | (
  Q = 0 ) | ( (  Q > 0 ) & (  27 Q^2 + 8 P^3 < 0 ) ) ) ) ) & ( ( ( (  6 R - P^2 < 0 ) & (  48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 < 0 ) ) | (  6 R - P^2 = 0 
) | ( (  6 R - P^2 > 0 ) & (  48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 < 0 ) ) ) &
 (  256 R^3 - 128 P^2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 
= 0 ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(1,5,5)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(- 1 )
( 1/2 )
( 1/2 )
)
DEFININGFORMULA
( ( (  P < 0 ) & ( (  Q > 0 ) & ( ( (  Q < 0 ) & (  27 Q^2 + 8 P^3 < 0 ) ) | (
  Q = 0 ) | ( (  Q > 0 ) & (  27 Q^2 + 8 P^3 < 0 ) ) ) ) ) & ( ( ( ( (  6 R - 
P^2 < 0 ) & (  48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 < 0 ) ) | (  6 R - P^2 = 
0 ) | ( (  6 R - P^2 > 0 ) & (  48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 < 0 ) ) )
 & (  256 R^3 - 128 P^2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^
2 < 0 ) ) | ( (  6 R - P^2 > 0 ) & (  48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 = 0
 ) ) | ( ( (  6 R - P^2 > 0 ) & (  48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 > 0 ) 
) & (  256 R^3 - 128 P^2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 < 0 ) ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(1,5,6)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 256 U^2 - 144 U - 11  $ , 
(1/2 , 1)
POINT
(
(- 1 )
( 1/2 )
( U )
)
DEFININGFORMULA
( ( (  P < 0 ) & ( (  Q > 0 ) & ( ( (  Q < 0 ) & (  27 Q^2 + 8 P^3 < 0 ) ) | (
  Q = 0 ) | ( (  Q > 0 ) & (  27 Q^2 + 8 P^3 < 0 ) ) ) ) ) & ( ( (  6 R - P^2
 > 0 ) & (  48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 > 0 ) ) & (  256 R^3 - 128 P^2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 = 0 ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(1,5,7)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(- 1 )
( 1/2 )
( 3 )
)
DEFININGFORMULA
( ( (  P < 0 ) & ( (  Q > 0 ) & ( ( (  Q < 0 ) & (  27 Q^2 + 8 P^3 < 0 ) ) | (
  Q = 0 ) | ( (  Q > 0 ) & (  27 Q^2 + 8 P^3 < 0 ) ) ) ) ) & ( ( (  6 R - P^2
 > 0 ) & (  48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 > 0 ) ) & (  256 R^3 - 128 P^2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 > 0 ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(1,6,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 27 U^2 - 8  $ , 
(1/2 , 3/4)
POINT
(
(- 1 )
( U )
(- 1/2 )
)
DEFININGFORMULA
( ( (  P < 0 ) & ( (  Q > 0 ) & (  27 Q^2 + 8 P^3 = 0 ) ) ) & ( (  6 R - P^2 
< 0 ) & (  48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 > 0 ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(1,6,2)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 27 U^2 - 8  $ , 
(1/2 , 3/4)
POINT
(
(- 1 )
( U )
(- 1/12 )
)
DEFININGFORMULA
( ( (  P < 0 ) & ( (  Q > 0 ) & (  27 Q^2 + 8 P^3 = 0 ) ) ) & ( (  6 R - P^2 
< 0 ) & (  48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 = 0 ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(1,6,3)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 27 U^2 - 8  $ , 
(1/2 , 3/4)
POINT
(
(- 1 )
( U )
( 1/2 )
)
DEFININGFORMULA
( ( (  P < 0 ) & ( (  Q > 0 ) & (  27 Q^2 + 8 P^3 = 0 ) ) ) & ( ( ( (  6 R - P
^2 < 0 ) & (  48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 < 0 ) ) | (  6 R - P^2 = 0
 ) | ( (  6 R - P^2 > 0 ) & (  48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 < 0 ) ) ) 
| ( (  6 R - P^2 > 0 ) & (  48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 = 0 ) ) | ( (
 (  6 R - P^2 > 0 ) & (  48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 > 0 ) ) & (  256
 R^3 - 128 P^2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 < 0 ) )
 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(1,6,4)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 27 U^2 - 8  $ , 
(1/2 , 3/4)
POINT
(
(- 1 )
( U )
( 2/3 )
)
DEFININGFORMULA
( ( (  P < 0 ) & ( (  Q > 0 ) & (  27 Q^2 + 8 P^3 = 0 ) ) ) & ( ( (  6 R - P^
2 > 0 ) & (  48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 > 0 ) ) & (  256 R^3 - 128 P
^2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 = 0 ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(1,6,5)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 27 U^2 - 8  $ , 
(1/2 , 3/4)
POINT
(
(- 1 )
( U )
( 2 )
)
DEFININGFORMULA
( ( (  P < 0 ) & ( (  Q > 0 ) & (  27 Q^2 + 8 P^3 = 0 ) ) ) & ( ( (  6 R - P^
2 > 0 ) & (  48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 > 0 ) ) & (  256 R^3 - 128 P
^2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 > 0 ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(1,7,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(- 1 )
( 2 )
( 3/2 )
)
DEFININGFORMULA
( ( (  P < 0 ) & ( (  Q > 0 ) & (  27 Q^2 + 8 P^3 > 0 ) ) ) & (  256 R^3 - 128 P^2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 < 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(1,7,2)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(- 1 )
( 2 )
( 2 )
)
DEFININGFORMULA
( ( (  P < 0 ) & ( (  Q > 0 ) & (  27 Q^2 + 8 P^3 > 0 ) ) ) & (  256 R^3 - 128 P^2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 = 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(1,7,3)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(- 1 )
( 2 )
( 3 )
)
DEFININGFORMULA
( ( (  P < 0 ) & ( (  Q > 0 ) & (  27 Q^2 + 8 P^3 > 0 ) ) ) & (  256 R^3 - 128 P^2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 > 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(2,1,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(0)
(- 1 )
(0)
)
DEFININGFORMULA
( ( (  P = 0 ) & (  Q < 0 ) ) & (  256 R^3 - 128 P^2 R^2 + 144 P Q^2 R + 16 
P^4 R - 27 Q^4 - 4 P^3 Q^2 < 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(2,1,2)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 256 U^3 - 27  $ , 
(0 , 1)
POINT
(
(0)
(- 1 )
( U )
)
DEFININGFORMULA
( ( (  P = 0 ) & (  Q < 0 ) ) & (  256 R^3 - 128 P^2 R^2 + 144 P Q^2 R + 16 
P^4 R - 27 Q^4 - 4 P^3 Q^2 = 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(2,1,3)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(0)
(- 1 )
( 3 )
)
DEFININGFORMULA
( ( (  P = 0 ) & (  Q < 0 ) ) & (  256 R^3 - 128 P^2 R^2 + 144 P Q^2 R + 16 
P^4 R - 27 Q^4 - 4 P^3 Q^2 > 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(2,2,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(0)
(0)
(- 1 )
)
DEFININGFORMULA
( ( (  P = 0 ) & (  Q = 0 ) ) & (  256 R^3 - 128 P^2 R^2 + 144 P Q^2 R + 16 
P^4 R - 27 Q^4 - 4 P^3 Q^2 < 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(2,2,2)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(0)
(0)
(0)
)
DEFININGFORMULA
( ( (  P = 0 ) & (  Q = 0 ) ) & (  256 R^3 - 128 P^2 R^2 + 144 P Q^2 R + 16 
P^4 R - 27 Q^4 - 4 P^3 Q^2 = 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(2,2,3)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(0)
(0)
( 2 )
)
DEFININGFORMULA
( ( (  P = 0 ) & (  Q = 0 ) ) & (  256 R^3 - 128 P^2 R^2 + 144 P Q^2 R + 16 
P^4 R - 27 Q^4 - 4 P^3 Q^2 > 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(2,3,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(0)
( 2 )
(0)
)
DEFININGFORMULA
( ( (  P = 0 ) & (  Q > 0 ) ) & (  256 R^3 - 128 P^2 R^2 + 144 P Q^2 R + 16 
P^4 R - 27 Q^4 - 4 P^3 Q^2 < 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(2,3,2)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 16 U^3 - 27  $ , 
(0 , 2)
POINT
(
(0)
( 2 )
( U )
)
DEFININGFORMULA
( ( (  P = 0 ) & (  Q > 0 ) ) & (  256 R^3 - 128 P^2 R^2 + 144 P Q^2 R + 16 
P^4 R - 27 Q^4 - 4 P^3 Q^2 = 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(2,3,3)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(0)
( 2 )
( 5 )
)
DEFININGFORMULA
( ( (  P = 0 ) & (  Q > 0 ) ) & (  256 R^3 - 128 P^2 R^2 + 144 P Q^2 R + 16 
P^4 R - 27 Q^4 - 4 P^3 Q^2 > 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,1,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
( 1 )
(- 1/4 )
(- 2 )
)
DEFININGFORMULA
( ( (  P > 0 ) & ( (  Q < 0 ) & (  27 Q^2 - P^3 > 0 ) ) ) & (  256 R^3 - 128 
P^2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 < 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,1,2)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 65536 U^3 - 32768 U^2 + 6400 U - 91  $ , 
(0 , 1/8)
POINT
(
( 1 )
(- 1/4 )
( U )
)
DEFININGFORMULA
( ( (  P > 0 ) & ( (  Q < 0 ) & (  27 Q^2 - P^3 > 0 ) ) ) & (  256 R^3 - 128 
P^2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 = 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,1,3)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
( 1 )
(- 1/4 )
( 3 )
)
DEFININGFORMULA
( ( (  P > 0 ) & ( (  Q < 0 ) & (  27 Q^2 - P^3 > 0 ) ) ) & (  256 R^3 - 128 
P^2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 > 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,2,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 27 U^2 - 1  $ , 
(-1/4 , -3/16)
POINT
(
( 1 )
( U )
(0)
)
DEFININGFORMULA
( ( (  P > 0 ) & ( (  Q < 0 ) & (  27 Q^2 - P^3 = 0 ) ) ) & (  256 R^3 - 128 
P^2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 < 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,2,2)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 1289945088 U^6 - 1289945088 U^5 + 394149888 U^4 - 13810176 U^3 - 8688384 U^2 + 1848960 U - 214621  $ , 
(-1/4 , -1/8)
POINT
(
( 1 )
( 1146617856/4725745 U^5 - 1000864512/4725745 U^4 + 207180288/4725745 U^3 + 4938624/945149 U^2 - 3698043/4725745 U + 450121/9451490 )
(- 1146617856/4725745 U^5 + 1000864512/4725745 U^4 - 207180288/4725745 U^3 - 
4938624/945149 U^2 + 8423788/4725745 U - 450121/9451490 )
)
DEFININGFORMULA
( ( (  P > 0 ) & ( (  Q < 0 ) & (  27 Q^2 - P^3 = 0 ) ) ) & (  256 R^3 - 128 
P^2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 = 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,2,3)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 27 U^2 - 1  $ , 
(-1/4 , -3/16)
POINT
(
( 1 )
( U )
( 9/8 )
)
DEFININGFORMULA
( ( (  P > 0 ) & ( (  Q < 0 ) & (  27 Q^2 - P^3 = 0 ) ) ) & (  256 R^3 - 128 
P^2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 > 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,3,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
( 1 )
(- 1/16 )
(0)
)
DEFININGFORMULA
( ( (  P > 0 ) & ( ( ( (  Q < 0 ) & (  27 Q^2 - P^3 < 0 ) ) | (  Q = 0 ) | ( (
  Q > 0 ) & (  27 Q^2 - P^3 < 0 ) ) ) & (  Q < 0 ) ) ) & (  256 R^3 - 128 P^
2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 < 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,3,2)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 16777216 U^3 - 8388608 U^2 + 1085440 U - 1051  $ , 
(0 , 1/32)
POINT
(
( 1 )
(- 1/16 )
( U )
)
DEFININGFORMULA
( ( (  P > 0 ) & ( ( ( (  Q < 0 ) & (  27 Q^2 - P^3 < 0 ) ) | (  Q = 0 ) | ( (
  Q > 0 ) & (  27 Q^2 - P^3 < 0 ) ) ) & (  Q < 0 ) ) ) & (  256 R^3 - 128 P^
2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 = 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,3,3)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
( 1 )
(- 1/16 )
( 17/16 )
)
DEFININGFORMULA
( ( (  P > 0 ) & ( ( ( (  Q < 0 ) & (  27 Q^2 - P^3 < 0 ) ) | (  Q = 0 ) | ( (
  Q > 0 ) & (  27 Q^2 - P^3 < 0 ) ) ) & (  Q < 0 ) ) ) & (  256 R^3 - 128 P^
2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 > 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,4,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
( 1 )
(0)
(- 1/8 )
)
DEFININGFORMULA
( ( (  P > 0 ) & (  Q = 0 ) ) & ( ( (  6 R - P^2 < 0 ) & (  48 R^2 - 16 P^2 R
 + 9 P Q^2 + P^4 > 0 ) ) & (  256 R^3 - 128 P^2 R^2 + 144 P Q^2 R + 16 P^
4 R - 27 Q^4 - 4 P^3 Q^2 < 0 ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,4,2)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
( 1 )
(0)
(0)
)
DEFININGFORMULA
( ( (  P > 0 ) & (  Q = 0 ) ) & ( ( (  6 R - P^2 < 0 ) & (  48 R^2 - 16 P^2 R
 + 9 P Q^2 + P^4 > 0 ) ) & (  256 R^3 - 128 P^2 R^2 + 144 P Q^2 R + 16 P^
4 R - 27 Q^4 - 4 P^3 Q^2 = 0 ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,4,3)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
( 1 )
(0)
( 1/8 )
)
DEFININGFORMULA
( ( (  P > 0 ) & (  Q = 0 ) ) & ( ( ( (  6 R - P^2 < 0 ) & (  48 R^2 - 16 P^2
 R + 9 P Q^2 + P^4 > 0 ) ) & (  256 R^3 - 128 P^2 R^2 + 144 P Q^2 R + 16 P
^4 R - 27 Q^4 - 4 P^3 Q^2 > 0 ) ) | ( (  6 R - P^2 < 0 ) & (  48 R^2 - 16 
P^2 R + 9 P Q^2 + P^4 = 0 ) ) | ( ( (  6 R - P^2 < 0 ) & (  48 R^2 - 16 P^
2 R + 9 P Q^2 + P^4 < 0 ) ) | (  6 R - P^2 = 0 ) | ( (  6 R - P^2 > 0 ) & ( 
 48 R^2 - 16 P^2 R + 9 P Q^2 + P^4 < 0 ) ) ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,4,4)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
( 1 )
(0)
( 1/4 )
)
DEFININGFORMULA
( ( (  P > 0 ) & (  Q = 0 ) ) & ( (  6 R - P^2 > 0 ) & (  48 R^2 - 16 P^2 R +
 9 P Q^2 + P^4 = 0 ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,4,5)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
( 1 )
(0)
( 5/4 )
)
DEFININGFORMULA
( ( (  P > 0 ) & (  Q = 0 ) ) & ( (  6 R - P^2 > 0 ) & (  48 R^2 - 16 P^2 R +
 9 P Q^2 + P^4 > 0 ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,5,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
( 1 )
( 1/8 )
(0)
)
DEFININGFORMULA
( ( (  P > 0 ) & ( (  Q > 0 ) & ( ( (  Q < 0 ) & (  27 Q^2 - P^3 < 0 ) ) | (  
Q = 0 ) | ( (  Q > 0 ) & (  27 Q^2 - P^3 < 0 ) ) ) ) ) & (  256 R^3 - 128 P^
2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 < 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,5,2)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 1048576 U^3 - 524288 U^2 + 74752 U - 283  $ , 
(0 , 1/32)
POINT
(
( 1 )
( 1/8 )
( U )
)
DEFININGFORMULA
( ( (  P > 0 ) & ( (  Q > 0 ) & ( ( (  Q < 0 ) & (  27 Q^2 - P^3 < 0 ) ) | (  
Q = 0 ) | ( (  Q > 0 ) & (  27 Q^2 - P^3 < 0 ) ) ) ) ) & (  256 R^3 - 128 P^
2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 = 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,5,3)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
( 1 )
( 1/8 )
( 17/16 )
)
DEFININGFORMULA
( ( (  P > 0 ) & ( (  Q > 0 ) & ( ( (  Q < 0 ) & (  27 Q^2 - P^3 < 0 ) ) | (  
Q = 0 ) | ( (  Q > 0 ) & (  27 Q^2 - P^3 < 0 ) ) ) ) ) & (  256 R^3 - 128 P^
2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 > 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,6,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 27 U^2 - 1  $ , 
(3/16 , 1/4)
POINT
(
( 1 )
( U )
(0)
)
DEFININGFORMULA
( ( (  P > 0 ) & ( (  Q > 0 ) & (  27 Q^2 - P^3 = 0 ) ) ) & (  256 R^3 - 128 
P^2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 < 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,6,2)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 1289945088 U^6 - 1289945088 U^5 + 394149888 U^4 - 13810176 U^3 - 8688384 U^2 + 1848960 U - 214621  $ , 
(3/16 , 1/4)
POINT
(
( 1 )
( 1146617856/4725745 U^5 - 1000864512/4725745 U^4 + 207180288/4725745 U^3 + 4938624/945149 U^2 - 3698043/4725745 U + 450121/9451490 )
(- 1146617856/4725745 U^5 + 1000864512/4725745 U^4 - 207180288/4725745 U^3 - 
4938624/945149 U^2 + 8423788/4725745 U - 450121/9451490 )
)
DEFININGFORMULA
( ( (  P > 0 ) & ( (  Q > 0 ) & (  27 Q^2 - P^3 = 0 ) ) ) & (  256 R^3 - 128 
P^2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 = 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,6,3)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 27 U^2 - 1  $ , 
(3/16 , 1/4)
POINT
(
( 1 )
( U )
( 9/8 )
)
DEFININGFORMULA
( ( (  P > 0 ) & ( (  Q > 0 ) & (  27 Q^2 - P^3 = 0 ) ) ) & (  256 R^3 - 128 
P^2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 > 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,7,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
( 1 )
( 5/4 )
(- 2 )
)
DEFININGFORMULA
( ( (  P > 0 ) & ( (  Q > 0 ) & (  27 Q^2 - P^3 > 0 ) ) ) & (  256 R^3 - 128 
P^2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 < 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,7,2)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 65536 U^3 - 32768 U^2 + 61696 U - 18475  $ , 
(0 , 1)
POINT
(
( 1 )
( 5/4 )
( U )
)
DEFININGFORMULA
( ( (  P > 0 ) & ( (  Q > 0 ) & (  27 Q^2 - P^3 > 0 ) ) ) & (  256 R^3 - 128 
P^2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 = 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,7,3)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
( 1 )
( 5/4 )
( 3 )
)
DEFININGFORMULA
( ( (  P > 0 ) & ( (  Q > 0 ) & (  27 Q^2 - P^3 > 0 ) ) ) & (  256 R^3 - 128 
P^2 R^2 + 144 P Q^2 R + 16 P^4 R - 27 Q^4 - 4 P^3 Q^2 > 0 ) ) $
ENDCELL
 
 
INDUCEDCAD
BEGINCAD
DIMENSION
2
INPUTVARIABLES
(P,Q)
MINPOLYVARIABLE
(U)
FIELDELEMENTVARIABLE
(U)
INPUTPOLYNOMIALS
(
 82944 P Q^2 - 3072 P^4  $ , 
 256  $ , 
 330225942528 Q^8 + 293534171136 P^3 Q^6 + 86973087744 P^6 Q^4 + 8589934592
 P^9 Q^2  $ , 
 56623104 P Q^2 - 2097152 P^4  $
)
BASIS
(
 Q  $ , 
 27 Q^2 - P^3  $ , 
 27 Q^2 + 8 P^3  $
)
CONTENTS
(
 3072 P  $ , 
 2097152 P  $
)
PROJECTION
(
 1  $ , 
- P^3  $ , 
 8 P^3  $ , 
 27  $ , 
 108 P^3  $ , 
 59049 P^6  $ , 
 27  $ , 
- 864 P^3  $
)
 
CELLS
 
BEGINCELL
INDEX
(1,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(- 1 )
(- 1 )
)
DEFININGFORMULA
( (  P < 0 ) & ( (  Q < 0 ) & (  27 Q^2 + 8 P^3 > 0 ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(1,2)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 27 U^2 - 8  $ , 
(-3/4 , -1/2)
POINT
(
(- 1 )
( U )
)
DEFININGFORMULA
( (  P < 0 ) & ( (  Q < 0 ) & (  27 Q^2 + 8 P^3 = 0 ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(1,3)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(- 1 )
(- 1/4 )
)
DEFININGFORMULA
( (  P < 0 ) & ( ( ( (  Q < 0 ) & (  27 Q^2 + 8 P^3 < 0 ) ) | (  Q = 0 ) | ( (
  Q > 0 ) & (  27 Q^2 + 8 P^3 < 0 ) ) ) & (  Q < 0 ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(1,4)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(- 1 )
(0)
)
DEFININGFORMULA
( (  P < 0 ) & (  Q = 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(1,5)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(- 1 )
( 1/2 )
)
DEFININGFORMULA
( (  P < 0 ) & ( (  Q > 0 ) & ( ( (  Q < 0 ) & (  27 Q^2 + 8 P^3 < 0 ) ) | (  
Q = 0 ) | ( (  Q > 0 ) & (  27 Q^2 + 8 P^3 < 0 ) ) ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(1,6)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 27 U^2 - 8  $ , 
(1/2 , 3/4)
POINT
(
(- 1 )
( U )
)
DEFININGFORMULA
( (  P < 0 ) & ( (  Q > 0 ) & (  27 Q^2 + 8 P^3 = 0 ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(1,7)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(- 1 )
( 2 )
)
DEFININGFORMULA
( (  P < 0 ) & ( (  Q > 0 ) & (  27 Q^2 + 8 P^3 > 0 ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(2,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(0)
(- 1 )
)
DEFININGFORMULA
( (  P = 0 ) & (  Q < 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(2,2)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(0)
(0)
)
DEFININGFORMULA
( (  P = 0 ) & (  Q = 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(2,3)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(0)
( 2 )
)
DEFININGFORMULA
( (  P = 0 ) & (  Q > 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
( 1 )
(- 1/4 )
)
DEFININGFORMULA
( (  P > 0 ) & ( (  Q < 0 ) & (  27 Q^2 - P^3 > 0 ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,2)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 27 U^2 - 1  $ , 
(-1/4 , -3/16)
POINT
(
( 1 )
( U )
)
DEFININGFORMULA
( (  P > 0 ) & ( (  Q < 0 ) & (  27 Q^2 - P^3 = 0 ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,3)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
( 1 )
(- 1/16 )
)
DEFININGFORMULA
( (  P > 0 ) & ( ( ( (  Q < 0 ) & (  27 Q^2 - P^3 < 0 ) ) | (  Q = 0 ) | ( (  
Q > 0 ) & (  27 Q^2 - P^3 < 0 ) ) ) & (  Q < 0 ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,4)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
( 1 )
(0)
)
DEFININGFORMULA
( (  P > 0 ) & (  Q = 0 ) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,5)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
( 1 )
( 1/8 )
)
DEFININGFORMULA
( (  P > 0 ) & ( (  Q > 0 ) & ( ( (  Q < 0 ) & (  27 Q^2 - P^3 < 0 ) ) | (  Q 
= 0 ) | ( (  Q > 0 ) & (  27 Q^2 - P^3 < 0 ) ) ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,6)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 27 U^2 - 1  $ , 
(3/16 , 1/4)
POINT
(
( 1 )
( U )
)
DEFININGFORMULA
( (  P > 0 ) & ( (  Q > 0 ) & (  27 Q^2 - P^3 = 0 ) ) ) $
ENDCELL
 
BEGINCELL
INDEX
(3,7)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
( 1 )
( 5/4 )
)
DEFININGFORMULA
( (  P > 0 ) & ( (  Q > 0 ) & (  27 Q^2 - P^3 > 0 ) ) ) $
ENDCELL
 
 
INDUCEDCAD
BEGINCAD
DIMENSION
1
INPUTVARIABLES
(P)
MINPOLYVARIABLE
(U)
FIELDELEMENTVARIABLE
(U)
INPUTPOLYNOMIALS
(
 3072 P  $ , 
 2097152 P  $ , 
 1  $ , 
- P^3  $ , 
 8 P^3  $ , 
 27  $ , 
 108 P^3  $ , 
 59049 P^6  $ , 
 27  $ , 
- 864 P^3  $
)
BASIS
(
 P  $
)
CONTENTS
(
)
PROJECTION
(
)
 
CELLS
 
BEGINCELL
INDEX
(1)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(- 1 )
)
DEFININGFORMULA
(  P < 0 ) $
ENDCELL
 
BEGINCELL
INDEX
(2)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
(0)
)
DEFININGFORMULA
(  P = 0 ) $
ENDCELL
 
BEGINCELL
INDEX
(3)
SAMPLEPOINT
PRIMITIVESAMPLEPOINT
PRIMITIVEELEMENT
 U  $ , 
(0 , 0)
POINT
(
( 1 )
)
DEFININGFORMULA
(  P > 0 ) $
ENDCELL
 
 
ENDCAD
ENDCAD
ENDCAD
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