Jsun Yui Wong
The computer program listed below seeks to solve the following nonlinear system of simultaneous equations from Faires and Burden [3, p. 357]; this system can also be found in Burden and Faires [5, p. 653].
4*X(1)-X(2)+X(3) = X(1)*X(4)
-X(1)+3*X(2)-2*X(3) = X(2)*X(4)
X(1)-2*X(2)+3*X(3) = X(3)*X(4)
X(1)^2 + X(2)^2 +X(3)^2 = 1
While line 160 of the preceding paper is 160 X(B)=(A(B) +RND^3*R), line 160 here is
160 X(B)=(A(B) +RND^6*R).
0 DEFDBL A-Z
1 DEFINT I,J,K
2 DIM B(99),N(99),A(2002),H(99),L(99),U(99),X(2002),D(111),P(111),PS(33),J(99),AA(99),HR(32),HHR(32),PLHS(44),LB(22),UB(22),PX(44),J44(44),PN(22),NN(22)
88 FOR JJJJ=-32000 TO 32000
89 RANDOMIZE JJJJ
90 M=-3D+30
110 FOR J44=1 TO 4
112 A(J44)=-5+(RND*10)
113 NEXT J44
128 FOR I=1 TO 10000
129 FOR KKQQ=1 TO 4
130 X(KKQQ)=A(KKQQ)
131 NEXT KKQQ
139 FOR IPP=1 TO FIX(1+RND*3)
140 B=1+FIX(RND*4)
150 R=(1-RND*2)*A(B)
155 REM IF RND<.5 THEN 160 ELSE 167
160 X(B)=(A(B) +RND^6*R)
165 GOTO 168
167 IF RND<.5 THEN X(B)=CINT(A(B)-1) ELSE X(B)=CINT(A(B) +1)
168 NEXT IPP
253 IF (-X(2)^2#-X(3)^2#+1# )<0# THEN 1670
255 X(1)= (-X(2)^2#-X(3)^2#+1# )^.5#
266 N(1)=4#*X(1)-X(2)+X(3)-X(1)*X(4)
301 N(2)=-X(1)+3#*X(2)-2#*X(3)-X(2)*X(4)
303 N(3)=X(1)-2#*X(2)+3#*X(3)-X(3)*X(4)
322 PD1=-ABS(N(1)) -ABS(N(2)) -ABS(N(3))
1111 IF PD1<=M THEN 1670
1452 M=PD1
1454 FOR KLX=1 TO 4
1455 A(KLX)=X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889 IF M<-.000001 THEN 1999
1904 PRINT A(1),A(2),A(3)
1917 PRINT A(4),M,JJJJ
1999 NEXT JJJJ
This BASIC computer program was run via basica/D of Microsoft's GW-BASIC 3.11 interpreter for DOS. The complete output through JJJJ=-31976 is shown below. What follows is a hand copy from the computer-monitor screen; immediately below there is no rounding by hand.
.8164965809277261 .408248290463863 -.408248290463863
3 -2.220446049250313D-16 -31985
.5773502672333886 -.5773502701677443 .5773502701677444
5.999999994917547 -8.803067830243094-09 -31983
.8164965809277262 .4082482904638624 -.4082482904638632
3.000000000000001 -1.637578961322106D-15 -31976
Two distinct solutions are shown above.
On a personal computer with a Pentium Dual-Core CPU E5200 @2.50GHz, 2.50 GHz, 960 MB of RAM, and the IBM basica/D interpreter, version GW BASIC 3.11, the wall-clock time for obtaining the output through JJJJ=-31976 was 100 seconds.
Acknowledgement
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
References
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[22] Wikipedia, Euler Brick. en.wikipedia.org/wiki/Euler_brick.
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