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REM If N-3<0 THEN AG = 1 ELSE if N=3=0 THEN AG = 2 ELSE AG = 3
"REM" means "remark", so the rest of the line is totally ignored.
ON (2+SGN(N)*1) GOTO 690, 690, 640
The SGN() signum function returns -1, 0 or +1 if the argument is negative, zero, or positive.
The ON () GOTO is a multi-way jump, so if N is negative, zero, or positive, the calculation gives 1, 2, or 3, and then the program jumps to line 690, 690, or 640.
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