我有一个代码来计算以下插值多项式的除差：
\documentclass[tikz,border=5]{standalone}
\usepackage{tikz}
\usepackage{amsmath}
\usepackage{fp}
\usepackage{xfp}
\usetikzlibrary{math}
\usepackage{etoolbox}
\usepackage{fp}
\usetikzlibrary{fixedpointarithmetic}
\usepackage{booktabs}
\usepackage{siunitx}
\usepackage{expl3}
\usepackage{etoolbox}
\newcommand{\ar}[1]{\fpeval{round(#1,8)}}
\begin{document}
\tikzset{fixed point arithmetic}
\pgfkeys{/pgf/number format/.cd,fixed,precision=6,zerofill}%
\tikzmath{
\n=3;
\xdado=0.9;
\M=1/4;
int \i;
\i=1;
for \v in {0.67284,0.733849,1.3837}{%Insira as coodenadas dos pontos X
\x{\i} = \v;
\a{\i} = 0;
\i=\i+1;
};
int \j;
\j=1;
for \v in {4.12,3.83,3.57}{%Insira as coodenadas dos pontos Y
\y{\j} = \v;
\D{\j} = \v;
\j=\j+1;
};
\a{1} = \y{1};
for \j in {1,...,\n}{
for \i in {1,...,\n}{
\R{\i,\j} = 0.0;
};
};
}
\tikzmath{
int \i;
int \j;
for \i in {1,...,\fpeval{\n-1}}{
for \j in {1,...,\fpeval{\n-\i}}{
\D{\j} = (\D{\fpeval{\j+1}}-\D{\j})/(\x{\fpeval{\j+\i}}-\x{\j});
\R{\j,\i} = \D{\j};
};
\a{\fpeval{\i+1}} = \D{1};
};
}
\def\tmp{$i$ & $x_i$ & $y_i$ & ordem 1 & ordem 2\\ \midrule}%
\edef\k{0}%
\loop
\edef\k{\the\numexpr\k+1}%
\xappto\tmp{$\fpeval{\k-1}$ & $\fpeval{round(\x{\k},4)}$& $\fpeval{round(\y{\k},4)}$ & $\fpeval{round(\R{\k,1},4)}$ & $\fpeval{round(\R{\k,2},4)}$}%
\gappto\tmp{\\}%
\ifnum\k<\n\repeat
\begin{tikzpicture}
%\clip (-9,-3) rectangle (9,3);
\node at (0,0) {\parbox{20cm}{
\underline{Método de Newton} para calcular o polinômio interpolador sobre os pontos: \\
$\foreach \i in {1,...,\n}{(\ar{\x{\i}},\ar{\y{\i}}),}$ \\
e para tanto, usamos a Tabela das \underline{Diferenças Divididas} resumida a seguir:\\
\begin{tabular}{r|r|r|r|r}
\toprule
\tmp
\bottomrule
\end{tabular}\\[0.5cm]
Os cálculos estão detalhados a seguir.
}};
\end{tikzpicture}
\end{document}
我使用以下结构：
\def\tmp{$i$ & $x_i$ & $y_i$ & ordem 1 & ordem 2\\ \midrule}%
\edef\k{0}%
\loop
\edef\k{\the\numexpr\k+1}%
\xappto\tmp{$\fpeval{\k-1}$ & $\fpeval{round(\x{\k},4)}$& $\fpeval{round(\y{\k},4)}$ & $\fpeval{round(\R{\k,1},4)}$ & $\fpeval{round(\R{\k,2},4)}$}%
\gappto\tmp{\\}%
\ifnum\k<\n\repeat
构建表格，其中包含\R上述代码中计算的变量（矩阵）。此矩阵对角线下方有空组件，我不想在此表格中打印这些组件（组件\R{3,1}, \R{2,2}, \R{3,2}）。在这种情况下，我想在迭代表中打印符号 *。我该怎么做？
答案1
\fpeval是完全可扩展的，因此您可以（直接）将其结果与零进行比较：
% using \protected\def will make each \fpeval evaluated only once
\protected\def\zeroToStar[1]{%
\ifdim#1pt=0pt\relax*\else#1\fi
}
% then use
$\zeroToStar{\fpeval{<math expression>}}$
完整示例
\documentclass[tikz,border=5]{standalone}
\usepackage{tikz}
\usepackage{amsmath}
\usepackage{fp}
\usepackage{xfp}
\usetikzlibrary{math}
\usepackage{etoolbox}
\usetikzlibrary{fixedpointarithmetic}
\usepackage{booktabs}
\usepackage{siunitx}
\usepackage{expl3}
\usepackage{etoolbox}
\newcommand{\ar}[1]{\fpeval{round(#1,8)}}
\begin{document}
\tikzset{fixed point arithmetic}
\pgfkeys{/pgf/number format/.cd,fixed,precision=6,zerofill}%
\tikzmath{
\n=3;
\xdado=0.9;
\M=1/4;
int \i;
\i=1;
for \v in {0.67284,0.733849,1.3837}{%Insira as coodenadas dos pontos X
\x{\i} = \v;
\a{\i} = 0;
\i=\i+1;
};
int \j;
\j=1;
for \v in {4.12,3.83,3.57}{%Insira as coodenadas dos pontos Y
\y{\j} = \v;
\D{\j} = \v;
\j=\j+1;
};
\a{1} = \y{1};
for \j in {1,...,\n}{
for \i in {1,...,\n}{
\R{\i,\j} = 0.0;
};
};
}
\tikzmath{
int \i;
int \j;
for \i in {1,...,\fpeval{\n-1}}{
for \j in {1,...,\fpeval{\n-\i}}{
\D{\j} = (\D{\fpeval{\j+1}}-\D{\j})/(\x{\fpeval{\j+\i}}-\x{\j});
\R{\j,\i} = \D{\j};
};
\a{\fpeval{\i+1}} = \D{1};
};
}
\newcommand\zeroToStar[1]{%
\ifdim#1pt=0pt\relax*\else#1\fi
}
\def\tmp{$i$ & $x_i$ & $y_i$ & ordem 1 & ordem 2\\ \midrule}%
\edef\k{0}%
\loop
\edef\k{\the\numexpr\k+1}%
\xappto\tmp{$\fpeval{\k-1}$ & $\fpeval{round(\x{\k},4)}$ & $\fpeval{round(\y{\k},4)}$ & $\zeroToStar{\fpeval{round(\R{\k,1},4)}}$ & $\zeroToStar{\fpeval{round(\R{\k,2},4)}}$}%
\gappto\tmp{\\}%
\ifnum\k<\n\repeat
\begin{tikzpicture}
%\clip (-9,-3) rectangle (9,3);
\node at (0,0) {\parbox{20cm}{
\underline{Método de Newton} para calcular o polinômio interpolador sobre os pontos: \\
$\foreach \i in {1,...,\n}{(\ar{\x{\i}},\ar{\y{\i}}),}$ \\
e para tanto, usamos a Tabela das \underline{Diferenças Divididas} resumida a seguir:\\
\begin{tabular}{r|r|r|r|r}
\toprule
\tmp
\bottomrule
\end{tabular}\\[0.5cm]
Os cálculos estão detalhados a seguir.
}};
\end{tikzpicture}
\end{document}
