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MathMLを使用してWebブラウザー上で数式を美麗に表示します。
https://decimalbasic.ninja-web.net/log/article/b/basic/106/jiiymf/jiiymf.html
数値微分公式をWebブラウザー上で表示させます。
OPTION ARITHMETIC RATIONAL
OPTION BASE 0
PUBLIC NUMERIC MAXLEVEL
LET MAXLEVEL=51
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
OPEN #1:NAME "数値"&STR$(NN)&"次微分公式.html"
ERASE #1
PRINT #1:"<!DOCTYPE html>"
PRINT #1:"<html>"
PRINT #1:"<head>"
PRINT #1:" <title>数値"&STR$(NN)&"次微分公式</title>"
PRINT #1:" <script async src=";CHR$(34);"https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.2/MathJax.js?config=TeX-MML-AM_CHTML";CHR$(34);"></script>"
PRINT #1:"</head>"
PRINT #1:"<body>"
PRINT #1:"<h1>数値"&STR$(NN)&"次微分公式</h1>"
FOR N=NN+N1 TO MAXLEVEL STEP 2
LET P=INT(N/2+1) !'中央差分式
!' FOR P=1 TO N
FOR K=1 TO N
MAT Y=ZER
LET Y(0)=1
FOR I=1 TO N
IF K<>I THEN
LET X(0)=-I
LET X(1)=1
CALL MUL(Y,X)
END IF
NEXT I
LET L(K)=HORNER(Y,K)
FOR I=1 TO NN
CALL DERIVATIVE(Y)
NEXT I
LET M(K)=HORNER(Y,P)
NEXT K
PRINT #1:"<math>"
PRINT #1:"<mfrac>"
PRINT #1:" <mrow>"
PRINT #1:" <msup>"
PRINT #1:" <mi>d</mi>"
IF NN>1 THEN PRINT #1:" <mn>";STR$(NN);"</mn>"
PRINT #1:" </msup>"
PRINT #1:" </mrow>"
PRINT #1:" <mrow>"
PRINT #1:" <msup>"
PRINT #1:" <mi>dx</mi>"
IF NN>1 THEN PRINT #1:" <mn>";STR$(NN);"</mn>"
PRINT #1:" </msup>"
PRINT #1:" </mrow>"
PRINT #1:"</mfrac>"
PRINT #1:"<mi>f</mi>"
PRINT #1:"<mfenced>"
PRINT #1:" <mi>x</mi>"
PRINT #1:"</mfenced>"
PRINT #1:"<mo>=</mo>"
FOR I=1 TO N
LET GM=GCD(M(I),L(I))
LET M(I)=M(I)/GM
LET L(I)=L(I)/GM
NEXT I
LET LM=L(1)
FOR I=2 TO N
LET LM=LCM(LM,L(I))
NEXT I
FOR I=1 TO N
LET B=LM/L(I)
LET M(I)=M(I)*B
LET L(I)=L(I)*B
NEXT I
PRINT #1:"<mfrac>"
PRINT #1:"<mrow>"
FOR I=1 TO N
IF ABS(M(I))<>0 THEN
IF M(I)*L(I)<0 THEN
PRINT #1:"<mo>-</mo>"
ELSE
IF I>1 THEN PRINT #1:"<mo>+</mo>"
END IF
IF ABS(M(I))<>1 THEN PRINT #1:"<mn>";STR$(ABS(M(I)));"</mn>"
PRINT #1:"<mi>f</mi>"
PRINT #1:"<mfenced>"
PRINT #1:"<mrow>"
PRINT #1:"<mi>x</mi>"
IF ABS(P-I)>0 THEN
IF P-I<0 THEN PRINT #1:"<mo>+</mo>" ELSE PRINT #1:"<mo>-</mo>"
IF ABS(P-I)>1 THEN PRINT #1:"<mn>";STR$(ABS(P-I));"</mn>"
PRINT #1:"<mi>h</mi>"
END IF
PRINT #1:"</mrow>"
PRINT #1:"</mfenced>"
END IF
NEXT I
PRINT #1:"</mrow>"
PRINT #1:"<mrow>"
PRINT #1:"<mn>";STR$(ABS(L(1)));"</mn>"
PRINT #1:"<msup>"
PRINT #1:"<mi>h</mi>"
IF NN>1 THEN PRINT #1:"<mn>";STR$(NN);"</mn>"
PRINT #1:"</msup>"
PRINT #1:"</mrow>"
PRINT #1:"</mfrac>"
!'NEXT P
PRINT #1:"</math>"
PRINT #1:CHR$(60);CHR$(98);CHR$(114);CHR$(62)
PRINT #1:CHR$(60);CHR$(98);CHR$(114);CHR$(62)
NEXT N
PRINT #1:"</body>"
PRINT #1:"</html>"
CLOSE #1
END
EXTERNAL SUB MUL(A(),B())
OPTION ARITHMETIC RATIONAL
OPTION BASE 0
DIM C(MAXLEVEL)
FOR I=0 TO 1
FOR J=0 TO MAXLEVEL-I
LET C(I+J)=C(I+J)+A(J)*B(I)
NEXT J
NEXT I
MAT A=C
END SUB
EXTERNAL SUB DERIVATIVE(A())
OPTION ARITHMETIC RATIONAL
OPTION BASE 0
DIM B(MAXLEVEL)
FOR I=MAXLEVEL TO 1 STEP-1
LET B(I-1)=I*A(I)
NEXT I
MAT A=B
END SUB
EXTERNAL FUNCTION HORNER(A(),XX)
OPTION ARITHMETIC RATIONAL
LET Y=A(MAXLEVEL)
FOR I=MAXLEVEL-1 TO 0 STEP-1
LET Y=Y*XX+A(I)
NEXT I
LET HORNER=Y
END FUNCTION
EXTERNAL FUNCTION LCM(A,B)
OPTION ARITHMETIC RATIONAL
LET LCM=A*B/GCD(A,B)
END FUNCTION
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