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 !!!!
Marc Moreno Maza