高階数値微分式
OPTION BASE 0
PUBLIC NUMERIC N
LET MAXLEVEL=15
DIM X(1),Y(MAXLEVEL),L(MAXLEVEL),M(MAXLEVEL)
INPUT PROMPT "微分階数=":NN
IF MOD(NN,2)=0 THEN LET N1=1 ELSE LET N1=2
FOR N=NN+N1 TO MAXLEVEL STEP 2
LET P=INT(N/2+1) !'中央差分式
!' FOR P=1 TO N
FOR K=1 TO N
FOR I=1 TO N
LET Y(I)=0
NEXT I
LET Y(0)=1
FOR I=1 TO N
IF K<>I THEN
LET X(0)=-I
LET X(1)=1
CALL MUL(Y,X)
END IF
NEXT I
LET L(K)=HORNER(Y,K)
FOR I=1 TO NN
CALL DERIVATIVE(Y)
NEXT I
LET M(K)=HORNER(Y,P)
NEXT K
PRINT "d^";STR$(NN);"/dx^";STR$(NN);"F(X)=";
FOR I=1 TO N
LET GM=GCD(M(I),L(I))
LET M(I)=M(I)/GM
LET L(I)=L(I)/GM
NEXT I
LET LM=L(1)
FOR I=2 TO N
LET LM=LCM(LM,L(I))
NEXT I
FOR I=1 TO N
LET B=LM/L(I)
LET M(I)=M(I)*B
LET L(I)=L(I)*B
NEXT I
PRINT "(";
FOR I=1 TO N
IF M(I)*L(I)<0 THEN PRINT "-"; ELSE PRINT "+";
PRINT STR$(ABS(M(I)));"*F(X";
IF (P-I)<0 THEN PRINT "+"; ELSE PRINT "-";
PRINT STR$(ABS(P-I));"*H)";
NEXT I
PRINT ")/(";STR$(ABS(L(1)));"*H^";STR$(NN);")"
!'NEXT P
!'PRINT
NEXT N
END
EXTERNAL SUB MUL(A(),B())
OPTION BASE 0
DIM C(N)
FOR I=0 TO 1
FOR J=0 TO N-I
LET C(I+J)=C(I+J)+A(J)*B(I)
NEXT J
NEXT I
FOR I=0 TO N
LET A(I)=C(I)
NEXT I
END SUB
EXTERNAL SUB DERIVATIVE(A())
OPTION BASE 0
DIM B(N)
FOR I=N TO 1 STEP -1
LET B(I-1)=I*A(I)
NEXT I
FOR I=0 TO N
LET A(I)=B(I)
NEXT I
END SUB
EXTERNAL FUNCTION HORNER(A(),XX)
LET Y=A(N)
FOR I=N-1 TO 0 STEP -1
LET Y=Y*XX+A(I)
NEXT I
LET HORNER=Y
END FUNCTION
EXTERNAL FUNCTION GCD(M,N)
DO WHILE N<>0
LET T=MOD(M,N)
LET M=N
LET N=T
LOOP
LET GCD=M
END FUNCTION
EXTERNAL FUNCTION LCM (A, B)
LET LCM=A*B/GCD(A,B)
END FUNCTION
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