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DECLARE EXTERNAL FUNCTION COMB
OPTION BASE 0
DIM X(8),T(8)
!'最小多項式
!'(x-(a+b+c))(x-(a+b-c))(x-(a-b+c))(x-(a-b-c))(x-(-a+b+c))(x-(-a+b-c))(x-(-a-b+c))(x-(-a-b-c))
!'(x-a)(x-b)=x^2-(a+b)x+ab
!'(x-a)(x-b)(x-c)=x^3-(a+b+c)x^2+(ab+bc+ca)x-abc
!'(x-a)(x-b)(x-c)(x-d)=x^4-(a+b+c+d)x^3+(ab+ac+ad+bc+bd+cd)x^2-(abc+abd+bcd+acd)x+abcd
LET A=SQR(2)
LET B=SQR(3)
LET C=SQR(5)
FOR I=1 TO -1 STEP -2
FOR J=1 TO -1 STEP -2
FOR K=1 TO -1 STEP -2
LET N=N+1
LET X(N)=I*A+J*B+K*C
PRINT "(X";SIGN$(-X(N));")";
NEXT K
NEXT J
NEXT I
PRINT
FOR I=N TO 0 STEP-1
LET K=(-1)^(N-I)*COMB(X,N,N-I,T,1)
IF ABS(K)<1E-6 THEN LET K=0
IF ABS(FP(K))<1E-6 THEN LET K=SGN(K)*INT(ABS(K))
IF I=1 THEN
PRINT SIGN$(K);"*X";
ELSEIF I=N THEN
PRINT "X^";STR$(I);
ELSEIF I>0 THEN
IF K<>0 THEN PRINT SIGN$(K);"*X^";STR$(I);
ELSE
PRINT SIGN$(K)
END IF
NEXT I
END
EXTERNAL FUNCTION SIGN$(X)
IF ABS(X)=1 THEN
IF X<0 THEN LET SIGN$="-" ELSE LET SIGN$=""
ELSE
IF X<0 THEN LET SIGN$="-"&STR$(ABS(X)) ELSE LET SIGN$="+"&STR$(X)
END IF
END FUNCTION
EXTERNAL FUNCTION COMB(X(),N,R,A(),K)
IF R=0 THEN
LET S=1
FOR I=1 TO N
IF A(I)=1 THEN LET S=S*X(I)
NEXT I
LET COMB=S
ELSE
FOR I=K TO N-R+1
LET A(I)=1
LET SS=SS+COMB(X,N,R-1,A,I+1)
LET A(I)=0
NEXT I
LET COMB=SS
END IF
END FUNCTION
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