和の公式

ΣX^Nを求める

PUBLIC NUMERIC MAXLEVEL
LET MAXLEVEL=20
DIM Y(MAXLEVEL+1),X(MAXLEVEL+1)
FOR I=1 TO MAXLEVEL
PRINT "ΣX^";STR$(I);"=";
CALL SUM(X,I)
CALL DISPLAY(X,I+1)
NEXT I
END

EXTERNAL SUB SUM(X(),N)
!'Σ(X^M)=A*N+B*N^2+C*N^3+...+D*N^(M+1)
!' 1
!'1^1*A+1^2*B+1^3*C=Σ(N^2)=1^2
!' N=1
!' 2
!'2^1*A+2^2*B+2^3*C=Σ(N^2)=1^2+2^2
!' N=1
!' 3
!'3^1*A+3^2*B+3^3*C=Σ(N^2)=1^2+2^2+3^2
!' N=1
DIM A(N+1,N+1),B(N+1)
FOR I=1 TO N+1
FOR J=1 TO N+1
LET A(I,J)=I^J
NEXT J
LET B(I)=SUMN(N,I)
NEXT I
MAT A=INV(A)
MAT X=A*B
END SUB

EXTERNAL FUNCTION SUMN(M,X)
FOR I=1 TO X
LET S=S+I^M
NEXT I
LET SUMN=S
END FUNCTION

EXTERNAL SUB DISPLAY(A(),N)
IF N>1 THEN
IF A(N)<0 THEN PRINT "-";
IF ABS(A(N))<>1 THEN
PRINT STR$(ABS(A(N)));"*X^";STR$(N);
ELSE
PRINT "X^";STR$(N);
END IF
END IF
FOR I=N-1 TO 2 STEP -1
IF A(I)<>0 THEN
IF A(I)<0 THEN PRINT "-"; ELSE PRINT "+";
IF ABS(A(I))<>1 THEN
PRINT STR$(ABS(A(I)));"*X^";STR$(I);
ELSEIF ABS(A(I))=1 THEN
PRINT "X^";STR$(I);
END IF
END IF
NEXT I
IF A(1)<>0 THEN
IF N>1 THEN
IF A(1)<0 THEN PRINT "-"; ELSE PRINT "+";
END IF
IF ABS(A(1))<>1 THEN
PRINT STR$(ABS(A(1)));"*X";
ELSEIF ABS(A(1))=1 THEN
PRINT "X";
END IF
END IF
PRINT
END SUB

和の公式	返事を書くノートメニュー
しばっち <dihjvcfsyu> 2008/02/10 17:36:38
ΣX^Nを求める PUBLIC NUMERIC MAXLEVEL LET MAXLEVEL=20 DIM Y(MAXLEVEL+1),X(MAXLEVEL+1) FOR I=1 TO MAXLEVEL PRINT "ΣX^";STR$(I);"="; CALL SUM(X,I) CALL DISPLAY(X,I+1) NEXT I END EXTERNAL SUB SUM(X(),N) !'Σ(X^M)=AN+BN^2+CN^3+...+DN^(M+1) !' 1 !'1^1A+1^2B+1^3C=Σ(N^2)=1^2 !' N=1 !' 2 !'2^1A+2^2B+2^3C=Σ(N^2)=1^2+2^2 !' N=1 !' 3 !'3^1A+3^2B+3^3C=Σ(N^2)=1^2+2^2+3^2 !' N=1 DIM A(N+1,N+1),B(N+1) FOR I=1 TO N+1 FOR J=1 TO N+1 LET A(I,J)=I^J NEXT J LET B(I)=SUMN(N,I) NEXT I MAT A=INV(A) MAT X=AB END SUB EXTERNAL FUNCTION SUMN(M,X) FOR I=1 TO X LET S=S+I^M NEXT I LET SUMN=S END FUNCTION EXTERNAL SUB DISPLAY(A(),N) IF N>1 THEN IF A(N)<0 THEN PRINT "-"; IF ABS(A(N))<>1 THEN PRINT STR$(ABS(A(N)));"X^";STR$(N); ELSE PRINT "X^";STR$(N); END IF END IF FOR I=N-1 TO 2 STEP -1 IF A(I)<>0 THEN IF A(I)<0 THEN PRINT "-"; ELSE PRINT "+"; IF ABS(A(I))<>1 THEN PRINT STR$(ABS(A(I)));"X^";STR$(I); ELSEIF ABS(A(I))=1 THEN PRINT "X^";STR$(I); END IF END IF NEXT I IF A(1)<>0 THEN IF N>1 THEN IF A(1)<0 THEN PRINT "-"; ELSE PRINT "+"; END IF IF ABS(A(1))<>1 THEN PRINT STR$(ABS(A(1)));"*X"; ELSEIF ABS(A(1))=1 THEN PRINT "X"; END IF END IF PRINT END SUB