多列和多行划分差异

Question

是否有一个包可以自动排版用于计算牛顿除差算法中使用的系数的三角表？但是在像下图这样的表格中

Answer 1

含钛钾Z 很容易创建一些计算条目的东西。这个答案定义了这样的图片。你需要说的是

\begin{tikzpicture}
 \pic{difftable={0,1,3,5}{3,2,4,-1}};
\end{tikzpicture}

其中第一个列表包含，xi第二个列表包含fi。

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{positioning,patterns}
\usepackage{eqparbox}
\newbox\eqnodebox
\tikzset{equal size/.style={execute at begin
    node={\setbox\eqnodebox=\hbox\bgroup},
    execute at end node={\egroup\eqmakebox[#1][c]{\copy\eqnodebox}}},
    equal size/.default=A,}
\newcounter{difftable}  
\makeatletter
\pgfmathdeclarefunction{Dim}{1}{%
\begingroup%
\pgfutil@tempcnta0%
\@for\pgfutil@tempa:=#1\do{\advance\pgfutil@tempcnta1}%
\edef\pgfmathresult{\the\pgfutil@tempcnta}%
\pgfmathsmuggle\pgfmathresult\endgroup%
}
\pgfmathdeclarefunction{diffquots}{2}{%
\begingroup%
\pgfutil@tempcnta1%
\pgfmathtruncatemacro{\pgfutil@tempa}{min(Dim("#1"),Dim("#2"))}%\typeout{dim=\pgfutil@tempa}%
\pgfutil@loop
\pgfmathsetmacro{\pgfutil@tempb}{{#1}[\the\pgfutil@tempcnta]-{#1}[\the\numexpr\pgfutil@tempcnta-1]}%
\pgfmathsetmacro{\pgfutil@tempc}{{#2}[\the\pgfutil@tempcnta]-{#2}[\the\numexpr\pgfutil@tempcnta-1]}%
\ifdim\pgfutil@tempc pt=0pt\relax
\tikzerror{You asked me to divide by zero. Terminating.}%
\fi
\pgfmathsetmacro{\pgfutil@tempd}{\pgfutil@tempb/\pgfutil@tempc}%
\pgfmathsetmacro{\pgfutil@tempe}{{#2}[\the\pgfutil@tempcnta]/2+{#2}[\the\numexpr\pgfutil@tempcnta-1]/2}%
\ifnum\pgfutil@tempcnta=1\relax
\edef\pgfutil@tempf{\pgfutil@tempd}%
\edef\pgfutil@tempg{\pgfutil@tempe}%
\else
\edef\pgfutil@tempf{\pgfutil@tempf,\pgfutil@tempd}%
\edef\pgfutil@tempg{\pgfutil@tempg,\pgfutil@tempe}%
\fi
\advance\pgfutil@tempcnta1%
\ifnum\pgfutil@tempcnta<\the\numexpr\pgfutil@tempa-1%
\pgfutil@repeat
\edef\pgfmathresult{"\pgfutil@tempf","\pgfutil@tempg"}%
\pgfmathsmuggle\pgfmathresult\endgroup%
}%
\makeatother
\tikzset{result/.style={draw,text height=1em,text depth=0.35ex,
 inner xsep=0.5ex,align=center,equal size=\pgfkeysvalueof{/tikz/difftable/id}-#1},
 pics/difftable/.style 2 args={code={\stepcounter{difftable}
   \tikzset{difftable/id=\number\value{difftable}}
   \node[result=1] (xi-1) {$x_i$}; %
   \path foreach \X [count=\Y] in {#1}
    {node[result=1,below={-\pgflinewidth} of xi-\Y,alias=xi-last] 
      (xi-\the\numexpr\Y+1)   {\pgfmathprintnumber{\X}}};
   % 
   \node[result=2,right={-\pgflinewidth} of xi-1] (fi-1) {$f(x_i)$}; 
   \path foreach \X [count=\Y] in {#2}
    {node[result=2,below={-\pgflinewidth} of fi-\Y,alias=fi-last] (fi-\the\numexpr\Y+1) 
    {\pgfmathprintnumber{\X}}};
   % 
   \pgfmathsetmacro{\myresultA}{diffquots("#1","#2")}
   \pgfmathsetmacro{\lstdfi}{{\myresultA}[0]}
   \pgfmathsetmacro{\lstdxi}{{\myresultA}[1]}
   \node[result=3,right={-\pgflinewidth} of fi-1] (dfi-1) {$DD1$};  
   \path foreach \X [count=\Y starting from 2] in \lstdfi
    {node[result=3,alias=dfi-last]  (dfi-\Y) at 
    (dfi-1|-fi-\Y.south east)  {\pgfmathprintnumber{\X}}};
   %
   \pgfmathsetmacro{\myresultB}{diffquots("\lstdfi","\lstdxi")}
   \pgfmathsetmacro{\lstddfi}{{\myresultB}[0]}
   \pgfmathsetmacro{\lstddxi}{{\myresultB}[1]}
   \node[result=4,right={-\pgflinewidth} of dfi-1] (ddfi-1) {$DD2$};  
   \path foreach \X [count=\Y starting from 2] in \lstddfi
    {node[result=4,alias=ddfi-last]  (ddfi-\Y) at 
    (ddfi-1|-dfi-\Y.south east)  {\pgfmathprintnumber{\X}}};
   %
   \pgfmathsetmacro{\myresultC}{diffquots("\lstddfi","\lstddxi")}
   \pgfmathsetmacro{\lstdddfi}{{\myresultC}[0]}
   \pgfmathsetmacro{\lstdddxi}{{\myresultC}[1]}
   \node[result=5,right={-\pgflinewidth} of ddfi-1] (dddfi-1) {$DD3$};  
   \path foreach \X [count=\Y starting from 2] in \lstdddfi
    {node[result=5,alias=dddfi-last]  (dddfi-\Y) at 
    (dddfi-1|-ddfi-\Y.south east)  {\pgfmathprintnumber{\X}}};
   %
   \path[pattern=north east lines] (fi-2.north east) 
    foreach \X in {d,dd,ddd}
    {|- (\X fi-2.north east) }
    |- cycle
    (fi-last.south east) 
    foreach \X in {d,dd,ddd}
    {|- (\X fi-last.south east) }
    |- cycle;
   \draw[thick] (xi-1.north west) rectangle (xi-last.south-|dddfi-1.east);
   }},
   difftable/.cd,id/.initial=0}
\begin{document}
\begin{tikzpicture}
 \pic{difftable={0,1,3,5}{3,2,4,-1}};
\end{tikzpicture}
\bigskip

\begin{tikzpicture}
 \pic{difftable={0,1,3,5}{2,5,-3,1}};
\end{tikzpicture}

\end{document}