テイラー展開

PUBLIC NUMERIC H
LET H=1/128
LET X=0
LET N=5
PRINT DIFF(X,A)
FOR A=1 TO N
PRINT DIFF(X,A)/FAC(A);"* (X";SIGN$(X);") ^";A
NEXT A
END

EXTERNAL FUNCTION F(X)
LET F=1/(1+X)
!'LET F=COS(X)^SIN(X)
!'LET F=1/COS(X)
!'LET F=TAN(X)
!'LET F=EXP(SIN(X))
END FUNCTION

EXTERNAL FUNCTION DIFF(X,M)
IF M>0 THEN
LET DIFF=(DIFF(X+H,M-1)-DIFF(X-H,M-1))/(2*H)
EXIT FUNCTION
END IF
IF M=0 THEN LET DIFF=F(X)
END FUNCTION

EXTERNAL FUNCTION FAC(X)
LET S=1
FOR I=2 TO X
LET S=S*I
NEXT I
LET FAC=S
END FUNCTION

EXTERNAL FUNCTION SIGN$(X)
IF X<0 THEN LET SIGN$=" + "& STR$(ABS(X)) ELSE LET SIGN$=" - "& STR$(ABS(X))
END FUNCTION

2変数版

PUBLIC NUMERIC H
LET H=1/128
LET X=0
LET Y=0
LET M=5
PRINT F(X,Y)
FOR N=1 TO M
FOR B=0 TO N
LET A=N-B
PRINT DIFF(X,A,Y,B)/FAC(A)/FAC(B);"* (X";SIGN$(X);") ^";A;"* (Y";SIGN$(Y);") ^";B
NEXT B
NEXT N
END

EXTERNAL FUNCTION F(X,Y)
LET F=EXP(X)*SIN(Y)
END FUNCTION

EXTERNAL FUNCTION DIFF(X,M,Y,N)
IF M>0 THEN
LET DIFF=(DIFF(X+H,M-1,Y,N)-DIFF(X-H,M-1,Y,N))/(2*H)
EXIT FUNCTION
END IF
IF N>0 THEN
LET DIFF=(DIFF(X,M,Y+H,N-1)-DIFF(X,M,Y-H,N-1))/(2*H)
EXIT FUNCTION
END IF
IF M=0 OR N=0 THEN LET DIFF=F(X,Y)
END FUNCTION

EXTERNAL FUNCTION FAC(X)
LET S=1
FOR I=2 TO X
LET S=S*I
NEXT I
LET FAC=S
END FUNCTION

EXTERNAL FUNCTION SIGN$(X)
IF X<0 THEN LET SIGN$=" + "& STR$(ABS(X)) ELSE LET SIGN$=" - "& STR$(ABS(X))
END FUNCTION

テイラー展開	返事を書くノートメニュー
しばっち <dihjvcfsyu> 2008/02/05 23:17:12 ** この記事は1回修正されてます
PUBLIC NUMERIC H LET H=1/128 LET X=0 LET N=5 PRINT DIFF(X,A) FOR A=1 TO N PRINT DIFF(X,A)/FAC(A);"* (X";SIGN$(X);") ^";A NEXT A END EXTERNAL FUNCTION F(X) LET F=1/(1+X) !'LET F=COS(X)^SIN(X) !'LET F=1/COS(X) !'LET F=TAN(X) !'LET F=EXP(SIN(X)) END FUNCTION EXTERNAL FUNCTION DIFF(X,M) IF M>0 THEN LET DIFF=(DIFF(X+H,M-1)-DIFF(X-H,M-1))/(2H) EXIT FUNCTION END IF IF M=0 THEN LET DIFF=F(X) END FUNCTION EXTERNAL FUNCTION FAC(X) LET S=1 FOR I=2 TO X LET S=SI NEXT I LET FAC=S END FUNCTION EXTERNAL FUNCTION SIGN$(X) IF X<0 THEN LET SIGN$=" + "& STR$(ABS(X)) ELSE LET SIGN$=" - "& STR$(ABS(X)) END FUNCTION 2変数版 PUBLIC NUMERIC H LET H=1/128 LET X=0 LET Y=0 LET M=5 PRINT F(X,Y) FOR N=1 TO M FOR B=0 TO N LET A=N-B PRINT DIFF(X,A,Y,B)/FAC(A)/FAC(B);"* (X";SIGN$(X);") ^";A;"* (Y";SIGN$(Y);") ^";B NEXT B NEXT N END EXTERNAL FUNCTION F(X,Y) LET F=EXP(X)SIN(Y) END FUNCTION EXTERNAL FUNCTION DIFF(X,M,Y,N) IF M>0 THEN LET DIFF=(DIFF(X+H,M-1,Y,N)-DIFF(X-H,M-1,Y,N))/(2H) EXIT FUNCTION END IF IF N>0 THEN LET DIFF=(DIFF(X,M,Y+H,N-1)-DIFF(X,M,Y-H,N-1))/(2H) EXIT FUNCTION END IF IF M=0 OR N=0 THEN LET DIFF=F(X,Y) END FUNCTION EXTERNAL FUNCTION FAC(X) LET S=1 FOR I=2 TO X LET S=SI NEXT I LET FAC=S END FUNCTION EXTERNAL FUNCTION SIGN$(X) IF X<0 THEN LET SIGN$=" + "& STR$(ABS(X)) ELSE LET SIGN$=" - "& STR$(ABS(X)) END FUNCTION