AXIOM SESSIONscale=2.5]
N := NonNegativeInteger
(3) NonNegativeInteger
Type: Domain
Time: 0 sec
P := Polynomial Integer
(4) Polynomial Integer
Type: Domain
Time: 0 sec
epsilon := 1/10^21 :: Float
(5) 0.1 E -20
Type: Float
Time: 0 sec
syst(n:N): List P == [x^n+y+z-1, x+y^n+z-1, x+y+z^n-1]
Type: Void
Time: 0 sec
completeExactSolve(syst(1))
(7) [[z= - %D - %C + 1,y= %C,x= %D]]
Type: List List Equation Fraction Polynomial Integer
Time: 0.03 (IN) = 0.03 sec
completeExactSolve(syst(2))
(8)
[[z= 0,y= 0,x= 1], [z= 0,y= 1,x= 0], [z= 1,y= 0,x= 0],
2
[z= x,y= x,x + 2x - 1= 0]]
Type: List List Equation Fraction Polynomial Integer
Time: 0.09 (EV) = 0.09 sec
realApproximateSolve(syst(2),[x,y,z],epsilon)
(9)
[[- 2.4142135623 730950488,- 2.4142135623 730950488,- 2.4142135623 730950488]
,
[0.4142135623 730950488,0.4142135623 730950488,0.4142135623 730950488],
[1.0,0.0,0.0], [0.0,1.0,0.0], [0.0,0.0,1.0]]
Type: List List Float
Time: 0.10 (EV) + 0.02 (OT) = 0.12 sec
completeExactSolve(syst(3))
(10)
[[z= - 1,y= 1,x= 1], [z= 0,y= 0,x= 1], [z= 1,y= - 1,x= 1], [z= 0,y= 1,x= 0],
[z= 1,y= 0,x= 0], [z= 1,y= 1,x= - 1],
2 2 3
[z= - y - x,y + x y + x - 1= 0,x - x - 1= 0],
3 3
3 - x + 1 - x + 1 4 2
[z= x,y= x,x + 2x - 1= 0], [z= --------,y= --------,x - x - 2x + 3= 0],
2 2
3 4 3 2
[z= x,y= - x - x + 1,x + x + 2x + 1= 0],
3 4 3 2
[z= - x - x + 1,y= x,x + x + 2x + 1= 0]]
Type: List List Equation Fraction Polynomial Integer
Time: 0.01 (IN) + 1.58 (EV) + 0.01 (OT) + 0.13 (GC) = 1.73 sec
realApproximateSolve(syst(3),[x,y,z],epsilon)
(11)
[[0.4533976515 1640376765,0.4533976515 1640376765,0.4533976515 1640376765],
[1.0,1.0,- 1.0], [1.0,0.0,0.0], [0.0,1.0,0.0], [1.0,- 1.0,1.0],
[0.0,0.0,1.0], [- 1.0,1.0,1.0]]
Type: List List Float
Time: 1.56 (EV) + 0.01 (OT) + 0.12 (GC) = 1.69 sec
completeExactSolve(syst(4))
(12)
[[z= 0,y= 0,x= 1], [z= 0,y= 1,x= 0], [z= 1,y= 0,x= 0],
4
[z= x,y= x,x + 2x - 1= 0],
4 11 8 7 5 4 3
[z= - x - x + 1,y= x,x + 2x - 3x + 2x - 4x + 3x - 2x + 2= 0],
4 11 8 7 5 4 3
[z= x,y= - x - x + 1,x + 2x - 3x + 2x - 4x + 3x - 2x + 2= 0],
4 4
- x + 1 - x + 1
[z= --------, y= --------,
2 2
11 10 9 8 7 6 4 3 2
x + x + x - x - 4x - 4x + 4x + 7x - x - 5x - 7= 0]
,
4 2 4 8 5 4 2
[z= - y - x + 1, y + (x - 1)y + x - x - 2x + x + x + 1= 0,
12 9 8 6 5 4 2
x - 2x - 3x + 2x + 4x + 3x - 2x - 2x - 2= 0]
]
Type: List List Equation Fraction Polynomial Integer
Time: 0.01 (IN) + 9.63 (EV) + 0.03 (OT) + 0.96 (GC) = 10.63 sec
realApproximateSolve(syst(4),[x,y,z],epsilon)
(13)
[[- 0.8755550011 8456161483,- 0.8755550011 8456161483,1.2878847152 284854786]
,
[- 0.8755550011 8456161482,1.2878847152 284854786,- 0.8755550011 8456161482]
,
[1.2878847152 284854786,- 0.8755550011 8456161482,- 0.8755550011 8456161482]
,
[- 1.3953369944 670730188,- 1.3953369944 670730188,- 1.3953369944 670730188]
,
[0.4746266175 6260555033,0.4746266175 6260555033,0.4746266175 6260555033],
[1.0,0.0,0.0], [0.0,1.0,0.0], [0.0,0.0,1.0]]
Type: List List Float
Time: 9.63 (EV) + 0.01 (OT) + 0.83 (GC) = 10.47 sec
-- completeExactSolve(syst(5)) MORE THAN FIVE MUNITES !!!!