10 REM **********************
11 REM * PROGRAM GAUSS, VERSION I, BY SHLOMO GINSBURG, MAY 1984
12 REM * THIS SOLVES A SYSTEM OF N LINEAR EQUATIONS WITH N UNKNOWNS
13 REM * IT NOTIFIES THE USER WHEN THERE IS NO SOLUTION
14 REM * VARIABLES:
15 REM * N      = NUMBER OF EQUATIONS
16 REM * A(I,J) = ELEMENTS OF THE COEFFICIENT MATRIX  I,J=1,2,...,N
17 REM * B(I)   = ELEMENTS OF THE RIGHT HAND SIDE (CONSTANTS)
18 REM * K      = STEP INDICATOR (A TOTAL OF N-1 STEPS IS RTREQUIRED)
19 REM * R      = DIAGONAL ELEMENT BY WHICH EQUATIONS ARE DIVIDED
20 REM * T      = TEMPORARY STORAGE FOR ROW INTERCHANGE
21 REM **********************
22 REM *
23 REM *
24 POKE 53280,11:POKE 53281,0
25 PRINT"[147]     A SYSTEM OF N LINEAR EQUATIONS     ";
26 PRINT"            GAUSS ELIMINATION           [146]"
30 REM * BEGINNING OF PROGRAM - INPUT
40 INPUT " [158]NUMBER OF EQUATIONS (N[158])";N
45 IFN<1ORN>80THENPRINT"TRY A BETTER NUMBER!":FORDL=1TO500:NEXT:GOTO40
46 PRINT"                          "
50 DIM A(N,N),B(N)
60 PRINT" INPUT THE COEFFICIENTS OF A[158]"
70 FOR I=1 TO N
80 FOR J=1 TO N
90 PRINT "  A("I","J")";
100 INPUT "";A(I,J)
110 NEXT J:NEXT I
120 PRINT" INPUT THE COEFFICIENTS OF [150]B[158]"
130 FOR I=1 TO N
140 PRINT "  B("I")";
150 INPUT B(I)
160 NEXT I
170 IF N=1 THEN 540: REM SINGLE EQUATION
180 FOR K=1 TO N-1: REM STEP COUNTER
190 R=A(K,K)
200 REM * CHECK FOR ZERO DIAGONAL. INSTEAD OF ZERO WE USE 1/1000000
210 IF ABS(R)>.000001 THEN 390: REM NO NEED FOR INTERCHANGE
220 REM * INTERCHANGE ROWS
230 FOR J=(K+1) TO N
240 IF ABS(A(J,K))>.000001 THEN 260: REM FOUND THE ROW FOR INTERCHANGE
250 GOTO 350: REM KEEP LOOKING FOR ROW
260 FOR L=K TO N: REM INTERCHANGE ROW J WITH ROW K - A'S
270 T=A(K,L)
280 A(K,L)=A(J,L)
290 A(J,L)=T
300 NEXT L
310 T=B(K): REM INTERCHANGE B'S
320 B(K)=B(J)
330 B(J)=T
340 GOTO 390
350 NEXT J
360 PRINT "               NO SOLUTION !            "
370 GOTO 700
380 REM * DIVIDING ROW BY DIAGONAL ELEMENT A(K,K)
390 R=A(K,K)
400 FOR J=(K+1) TO N
410 A(K,J)=A(K,J)/R
420 NEXT J
430 B(K)=B(K)/R
440 REM * ELIMINATION OF X(K) FROM ROWS K+1, K+2, ... , N
450 FOR I=(K+1) TO N
460 R=A(I,K)
470 FOR J=(K+1) TO N
480 A(I,J)=A(I,J)-R*A(K,J)
490 NEXT J
500 B(I)=B(I)-R*B(K)
510 NEXT I
520 NEXT K: REM END OF STEPS
530 REM * LAST EQUATION FOR A(N,N)
540 IF ABS(A(N,N))>.000001 THEN 570
550 PRINT "              NO  SOLUTION !            "
560 GOTO 700
570 B(N)=B(N)/A(N,N)
580 REM * BACKSUBSTITUTION
590 FOR I=1 TO (N-1)
600 K=N-I
610 FOR J=(K+1) TO N
620 B(K)=B(K)-A(K,J)*B(J)
630 NEXT J:NEXT I
640 PRINT"[147]                 RESULTS                "
650 FOR I=1 TO N
660 PRINT"  TOUCH ANY KEY TO CONTINUE"
670 PRINT"   X("I") =";B(I)
680 GET A$:IF A$="" THEN 680
690 NEXT I
700 GOTO60000
800 :
60000 FORDL=1TO500:NEXTDL
60001 PRINT"[147]WOULD YOU LIKE TO TRY ANOTHER?";
60002 POKE198,0:WAIT198,1:GETA$:IFA$<>"Y"ANDA$<>"N"THENPOKE53280,RND(1)*15:GOTO60002
60004 IFA$="Y"THENCLR:RESTORE:GOTO21
60006 GOTO63000
60010 :
63000 REM    CONNECT BACK TO L.S.
63002 PRINT"[147]LOAD"CHR$(34)"PAYLOAD"CHR$(34)",8":PRINT"RUN"
63004 POKE198,0:POKE631,13:POKE632,13:POKE198,2:END