ì ï ï í ï ï î |
|
(1) |
t1 | t2 | t3 |
10.85770360 | 0.7795480449 | 0.7795480451 |
- 10.85770360 | - 0.7795480449 | - 0.7795480451 |
0.3320730984 | 4.625181601 | 4.625181601 |
- 0.3320730984 | - 4.625181601 | - 4.625181601 |
0.7795480449 | 0.7795480449 | 0.7795480451 |
0.7795480449 | 10.85770360 | 0.7795480451 |
0.7795480440 | 0.7795480457 | 10.85770360 |
4.625181601 | 4.625181601 | 4.625181601 |
4.625181601 | 0.3320730984 | 4.625181601 |
4.625181600 | 4.625181613 | 0.3320730984 |
- 0.7795480440 | - 0.7795480457 | - 10.85770360 |
- 0.7795480449 | - 0.7795480449 | - 0.7795480451 |
- 0.7795480449 | - 10.85770360 | - 0.7795480451 |
- 4.625181600 | - 4.625181613 | - 0.3320730984 |
- 4.625181601 | - 4.625181601 | - 4.625181601 |
- 4.625181601 | - 0.3320730984 | - 4.625181601 |
[-310+959*x[2]^2+774*x[3]^2+1389*x[2]*x[3]+1313*x[2]^2*x[3]^2, -365+755*x[3]^2+917*x[1]^2+1451*x[1]*x[3]+1269*x[3]^2*x[1]^2, -413+837*x[1]^2+838*x[2]^2+1655*x[1]*x[2]+1352*x[1]^2*x[2]^2];
[.86605*x[2]^2*x[3]^2+.50000*x[2]^2+2.*x[2]*x[3]+.50000*x[3]^2-.86605, .86605*x[3]^2*x[1]^2+.50000*x[1]^2+2.*x[1]*x[3]+.50000*x[3]^2-.86605, .86605*x[1]^2*x[2]^2+.50000*x[1]^2+2.*x[1]*x[2]+.50000*x[2]^2-.86605];
[ 1.334568086*x[2]^2*x[3]^2+.8485720485*x[2]^2+1.302855903*x[2]*x[3]+ .8485720484*x[3]^2-.2888519406, 1.334568086*x[1]^2*x[3]^2+.8485720484*x[1]^2+1.302855903*x[1]*x[3]+ .8485720485*x[3]^2-.2888519406, 1.334568086*x[1]^2*x[2]^2+.8485720485*x[1]^2+1.302855903*x[1]*x[2]+ .8485720484*x[2]^2-.2888519406];
parameter:= a; [a*x[2]^2*x[3]^2+1/2*x[2]^2+2*x[2]*x[3]+1/2*x[3]^2-a, a*x[3]^2*x[1]^2+1/2*x[1]^2+2*x[1]*x[3]+1/2*x[3]^2-a, a*x[1]^2*x[2]^2+1/2*x[1]^2+2*x[1]*x[2]+1/2*x[2]^2-a,4*a^2-3];
S1 | S2 | S3 | ||||||||||
T1 | T2 | T3 | e | T1 | T2 | T3 | e | T1 | T2 | T3 | e | |
BZ | 0.18 | 2.02 | 0.50 | 3.1 10-11 | 0.35 | 0.68 | 1.87 | 3.0 10 -12 | 0.20 | 25.38 | 1.02 | 1.48 10-4 |
RC | 0.60 | 0.10 | 0.30 | 4.8 10-5 | 0.18 | 0.13 | 1.4 | 2.2 10-9 | 0.58 | 0.82 | 0.28 | 1.5 10-4 |
*----* MuPAD 1.3 --- Multi Processing Algebra Data Tool /| /| *----* | Copyright (c) 1992-96 by B. Fuchssteiner, Automath | *--|-* University of Paderborn. All rights reserved. |/ |/ *----* Demo version, please register with MuPAD-distribution@uni-paderborn.de >> sys:={-y^2*z^2-y^2+24*y*z-z^2-13,-x^2*z^2-x^2+24*x*z-z^2-13, &> -x^2*y^2-x^2+24*x*y-y^2-13}: >> time((sol:=solve(sys))); 3 s >> lprint(sol); {[x = z, y = z*43/3 + z^3*(-2/3), z = -(3^(1/2)*(-6) + 11)^(1/2)], [x = z,\ y = z*43/3 + z^3*(-2/3), z = (3^(1/2)*(-6) + 11)^(1/2)], [x = z, y = z*43\ /3 + z^3*(-2/3), z = (3^(1/2)*6 + 11)^(1/2)], [x = z, y = z*43/3 + z^3*(-2\ /3), z = -(3^(1/2)*6 + 11)^(1/2)], [x = z*23/3 + z^3*(-1/3) + (z^2*532 + z\ ^4*(-46) + z^6-78)^(1/2)*(-1/3), y = z, z = -(3^(1/2)*(-6) + 11)^(1/2)], [\ x = z*23/3 + z^3*(-1/3) + (z^2*532 + z^4*(-46) + z^6-78)^(1/2)*(-1/3), y =\ z, z = (3^(1/2)*(-6) + 11)^(1/2)], [x = z*23/3 + z^3*(-1/3) + (z^2*532 + \ z^4*(-46) + z^6-78)^(1/2)*(-1/3), y = z, z = (3^(1/2)*6 + 11)^(1/2)], [x =\ z*23/3 + z^3*(-1/3) + (z^2*532 + z^4*(-46) + z^6-78)^(1/2)*(-1/3), y = z,\ z = -(3^(1/2)*6 + 11)^(1/2)], [x = z*23/3 + z^3*(-1/3) + (z^2*532 + z^4*(\ -46) + z^6-78)^(1/2)*1/3, y = z, z = -(3^(1/2)*(-6) + 11)^(1/2)], [x = z*2\ 3/3 + z^3*(-1/3) + (z^2*532 + z^4*(-46) + z^6-78)^(1/2)*1/3, y = z, z = (3\ ^(1/2)*(-6) + 11)^(1/2)], [x = z*23/3 + z^3*(-1/3) + (z^2*532 + z^4*(-46) \ + z^6-78)^(1/2)*1/3, y = z, z = (3^(1/2)*6 + 11)^(1/2)], [x = z*23/3 + z^3\ *(-1/3) + (z^2*532 + z^4*(-46) + z^6-78)^(1/2)*1/3, y = z, z = -(3^(1/2)*6\ + 11)^(1/2)], [x = z*237/17 + z^3*(-2/17), y = z*237/17 + z^3*(-2/17), z \ = -(3^(1/2)*(-34) + 59)^(1/2)], [x = z*237/17 + z^3*(-2/17), y = z*237/17 \ + z^3*(-2/17), z = (3^(1/2)*(-34) + 59)^(1/2)], [x = z*237/17 + z^3*(-2/17\ ), y = z*237/17 + z^3*(-2/17), z = (3^(1/2)*34 + 59)^(1/2)], [x = z*237/17\ + z^3*(-2/17), y = z*237/17 + z^3*(-2/17), z = -(3^(1/2)*34 + 59)^(1/2)]} >> lprint(allvalues(sol)); {[x = -0.77954804500, y = -0.77954804500, z = -10.857703590], [x = 0.77954\ 804500, y = 0.77954804500, z = 10.857703590], [x = 4.6251816010, y = 4.625\ 1816010, z = 0.33207309830], [x = -4.6251816010, y = -4.6251816010, z = -0\ .33207309830], [x = -0.33207309830, y = -4.6251816010, z = -4.6251816010],\ [x = 4.6251816010, y = 4.6251816010, z = 4.6251816010], [x = 10.857703590\ , y = 0.77954804500, z = 0.77954804500], [x = -0.77954804500, y = -0.77954\ 804500, z = -0.77954804500], [x = -4.6251816010, y = -4.6251816010, z = -4\ .6251816010], [x = 0.33207309830, y = 4.6251816010, z = 4.6251816010], [x \ = 0.77954804500, y = 0.77954804500, z = 0.77954804500], [x = -10.857703590\ , y = -0.77954804500, z = -0.77954804500], [x = -4.6251816010, y = -0.3320\ 7309830, z = -4.6251816010], [x = 4.6251816010, y = 0.33207309830, z = 4.6\ 251816010], [x = 0.77954804500, y = 10.857703590, z = 0.77954804500], [x =\ -0.77954804500, y = -10.857703590, z = -0.77954804500]}
Computation required: Problem User time System Real Memory PageFault Host 0.21 0.01 0.26 134552 0 nello Computed Pairs Summary: Total Useful Useless Discarded 32 19 13 0 @ #0 z8-140z6+2622z4-1820z2+169 #1 17yz4-374yz2+221y+2z7-281z5+5240z3-3081z #2 204y2+136yz3-3128yz+z6-149z4+2739z2+117 #3 17xz4-374xz2+221x+2z7-281z5+5240z3-3081z #4 136xy-136xz-136yz+2z6-281z4+5376z2-3081 #5 204x2+136xz3-3128xz+z6-149z4+2739z2+117Trying to triangularize, one remarks that eq. 1 is
#0 z4-22z2+13 #1 3y2+2yz3-46yz-z2+26 #2 xy-xz-yz+z2 #3 3x2+2xz3-46xz-z2+26eq. 2 is x(y-z)+..., hence we add y-z: (in 0.01")
#0 z4-22z2+13 #1 y-z #2 3x2+2xz3-46xz-z2+26or divide by y-z: (in 0.02")
#0 z4-22z2+13 #1 3y+2z3-43z #2 x-zor divide the original eq. by z4-22z2+13: (in 0.22")
#0 z4-118z2+13 #1 17y+2z3-237z #2 17x+2z3-237zHence reducing to three triangular systems solvable through square roots.