多項式平方根
F(X)=A+B*X+C*X^2+D*X^3+...
G(X)=A'+B'*X+C'*X^2+D'*X^3...
F(X)=G(X)^2 G(X)を求める
恒等式 (A+B*X+C*X^2+D*X^3+E*X^4+...)=(A'+B'*X+C'*X^2+D'*X^3+E'*X^4+...)^2
A=A'^2
B=2A'B'
C=2A'C'+B'^2
D=2A'D'+2B'C'
:
A'=SQR(A)
B'=B/2A'
C'=(C-B'^2)/2A'
D'=(D-2B'C')/2A'
:
OPTION BASE 0
PUBLIC NUMERIC MAXLEVEL
!'1/(1-SIN(X)^2)=1/COS(X)^2=1+SIN(X)^2+SIN(X)^4+SIN(X)^6+...
LET MAXLEVEL=40
DIM C(MAXLEVEL),X(MAXLEVEL)
!'1+X^2+X^4+X^6+X^8+...=1/(1-X^2)
FOR I=0 TO MAXLEVEL/2 STEP 2
LET C(I)=1
NEXT I
CALL SINE(X)
CALL HORNER(C,X)
PRINT "1/(1-SIN(X)^2)"
CALL DISPLAY(C)
CALL SQRT(C)
PRINT "1/COS(X)"
CALL DISPLAY(C)
END
EXTERNAL SUB SQRT(C())
OPTION BASE 0
DIM XX(MAXLEVEL),X(MAXLEVEL),CC(MAXLEVEL)
FOR M=0 TO MAXLEVEL
IF C(M)<>0 THEN EXIT FOR
NEXT M
IF MOD(M,2)=1 OR C(M)<0 THEN
PRINT "計算不可"
EXIT SUB
END IF
FOR MM=MAXLEVEL TO M STEP -1
IF C(MM)<>0 THEN EXIT FOR
NEXT MM
IF MOD(MM,2)=1 THEN
PRINT "計算不可"
EXIT SUB
END IF
FOR I=0 TO MAXLEVEL-M
LET CC(I)=C(I+M)
LET C(I)=0
NEXT I
LET X(0)=SQR(CC(0))
FOR K=1 TO MM/2
CALL CLR(XX)
FOR I=0 TO MAXLEVEL
FOR J=0 TO MAXLEVEL-I
LET XX(I+J)=XX(I+J)+X(I)*X(J)
NEXT J
NEXT I
LET X(K)=(CC(K)-XX(K))/(2*X(0))
NEXT K
FOR I=0 TO MAXLEVEL-M
LET C(I+M/2)=X(I)
NEXT I
END SUB
EXTERNAL SUB COPY(X(),Y())
FOR I=0 TO MAXLEVEL
LET X(I)=Y(I)
NEXT I
END SUB
EXTERNAL SUB CLR(X())
FOR I=0 TO MAXLEVEL
LET X(I)=0
NEXT I
END SUB
EXTERNAL SUB DISPLAY(A())
LET N=DIMCHECK(A)
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$(ABS(A(1)));"*X";
ELSEIF ABS(A(1))=1 THEN
PRINT "X";
END IF
END IF
IF A(0)<>0 THEN
IF A(0)<0 THEN PRINT "-"; ELSE PRINT "+";
PRINT STR$(ABS(A(0)));
END IF
PRINT
END SUB
EXTERNAL FUNCTION DIMCHECK(X())
FOR N=MAXLEVEL TO 0 STEP -1
IF X(N)<>0 THEN EXIT FOR
NEXT N
LET DIMCHECK=N
END FUNCTION
EXTERNAL SUB HORNER(F(),X())
!'F(X(XX))
OPTION BASE 0
DIM Y(MAXLEVEL)
LET N=DIMCHECK(F)
LET Y(0)=F(N)
FOR I=N-1 TO 0 STEP -1
CALL MUL(Y,X)
LET Y(0)=Y(0)+F(I)
NEXT I
CALL COPY(F,Y)
END SUB
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