Jsun Yui Wong
The computer program listed below seeks to solve the following system of seven equations, which is based on the system of equations on page 65 of Shacham and Mah [87; one can read this via Google]:
X(1) +X(2) - 1386.3=0
X(2) - X(3) - 415.9=0
X(1) - X(4) - X(5)=0
X(3) + X(4) - X(7) - 415.9=0
X(5) - X(6) - 138.6=0
2.179 * X(2) ^ 2 + 9.075 * X(3) ^ 2 - 18.96 * X(4) ^ 2 - 9.001 * X(1) ^ 2=0
18.96 * X(4) ^ 2 + 40.95 * X(7) ^ 2 - 86.39 * X(6) ^ 2 - 41.07 * X(5) ^ 2=0.
One notes line 162, which is 162 IF RND < .16666 THEN X(j) = A(j) - FIX(1 + RND * 2.3) ELSE IF RND < .33333 THEN X(j) = A(j) + FIX(1 + RND * 2.3) ELSE IF RND < .5 THEN X(j) = A(j) - FIX(1 + RND * 20.3) ELSE IF RND < .66666 THEN X(j) = A(j) + FIX(1 + RND * 20.3) ELSE IF RND < .83333 THEN X(j) = A(j) - FIX(1 + RND * 200.3) ELSE X(j) = A(j) + FIX(1 + RND * 200.3).
0 DEFDBL A-Z
1 DEFINT K
2 DIM B(99), N(99), A(2002), H(99), L(99), U(99), X(2002), D(111), P(111), PS(33), J44(2002), J(99), AA(99), HR(32), HHR(32), LHS(44), PLHS(44), LB(22), UB(22), PX(22), CC(20), RR(20), WW(20), AL(50), SW(50), SV(50), C2(22), C3(22), C4(22), C5(22)
81 FOR JJJJ = -32000 TO 32000
83 RANDOMIZE JJJJ
87 M = -4E+299
120 FOR J44 = 1 TO 7
121 A(J44) = FIX(RND * 6)
122 REM A(J44) = (RND * 2)
123 NEXT J44
128 FOR I = 0 TO FIX(RND * 15000)
129 FOR KKQQ = 1 TO 7
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
135 FOR IPP = 1 TO FIX(1 + RND * 3.3)
143 j = 1 + FIX(RND * 6.5)
154 IF RND < .5 THEN GOTO 156 ELSE GOTO 162
156 REM
157 R = (1 - RND * 2) * (A(j))
160 X(j) = A(j) + (RND ^ (RND * 30)) * R
161 GOTO 169
162 IF RND < .16666 THEN X(j) = A(j) - FIX(1 + RND * 2.3) ELSE IF RND < .33333 THEN X(j) = A(j) + FIX(1 + RND * 2.3) ELSE IF RND < .5 THEN X(j) = A(j) - FIX(1 + RND * 20.3) ELSE IF RND < .66666 THEN X(j) = A(j) + FIX(1 + RND * 20.3) ELSE IF RND < .83333 THEN X(j) = A(j) - FIX(1 + RND * 200.3) ELSE X(j) = A(j) + FIX(1 + RND * 200.3)
169 NEXT IPP
1021 X(2) = -X(1) + 1386.3
1024 X(3) = X(2) - 415.9
1027 X(6) = X(5) - 138.6
1029 X(4) = X(1) - X(5)
1033 X(7) = X(3) + X(4) - 415.9
1234 y1 = 2.179 * X(2) ^ 2 + 9.075 * X(3) ^ 2 - 18.96 * X(4) ^ 2 - 9.001 * X(1) ^ 2
1236 y2 = 18.96 * X(5) ^ 2 + 40.95 * X(7) ^ 2 - 86.39 * X(6) ^ 2 - 41.07 * X(5) ^ 2
1245 P = -ABS(y1) - ABS(y2)
1251 IF P <= M THEN 1670
1420 M = P
1444 FOR KLX = 1 TO 7
1455 A(KLX) = X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1894 IF M < -.0000003 THEN 1999
1924 PRINT A(1), A(2), A(3), A(4), A(5), A(6), A(7), M, JJJJ
1999 NEXT JJJJ
This BASIC computer program was run with QB64v1000-win [111]. The complete output of a single run through JJJJ= -31991 is shown below:
516.4539609177657 869.8460390822343 453.9460390822343
242.826461452387 273.6274994653788 135.0274994653788
280.8725005346211 -1.984290065593086D-09 -32000
516.4539609177657 869.8460390822343 453.9460390822343
242.826461452387 273.6274994653788 135.0274994653788
280.8725005346211 -1.984290065593086D-09 -31997
516.4539609177657 869.8460390822343 453.9460390822343
242.826461452387 273.6274994653788 135.0274994653788
280.8725005346211 -1.984290065593086D-09 -31994
516.4539609177657 869.8460390822343 453.9460390822343
242.826461452387 273.6274994653788 135.0274994653788
280.8725005346211 -1.984290065593086D-09 -31992
516.453960917765 869.846039082235 453.946039082235
242.8264614523862 273.6274994653788 135.0274994653788
280.8725005346211 -2.281285560457036D-08 -31991
.
.
.
Above there is no rounding by hand; it is just straight copying by hand from the monitor screen. On a personal computer with a Processor Intel (R) Core (TM) 2 Duo CPU E8400 @ 3.0 GHz 3.0 GHz, 4.00 GB of RAM (3.9 GB usable), 64-bit Operating System, and QB64v1000-win [111], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -31991 was 1 second, counting from "Starting program...". One can compare the computational results above with those on page 65 of Shacham and Mah [87].
Acknowledgement
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
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