tikz-horner.sty

\ProvidesPackage{tikz-horner}[2020/11/03 v1.0 Horner schema]

\RequirePackage{tikz,xstring}
\usetikzlibrary{arrows.meta}

% Just to avoid duplication in multiple
\newcounter{hornerLast}
% [#1] animation offset
% #2 list
% #3 multiplier
\newcommand*\tikzHorner[3][5]{
% bincode w/ shift of 3:
\setcounter{hornerLast}{-1}
\foreach[count=\i, evaluate=\i as \ci using {int(\i+#1)},
    evaluate=\i as \xi using {1.55*\i}, remember=\i as \li (initially 0)] \b in {#2} {
        % double last
        \ifnum\i>1
            \setcounter{hornerLast}{#3*\value{hornerLast}}
        \fi
        \onslide<\ci->{%
            \node at (\xi,0) {\b};
            \node at (\xi,-0.5) {+};
            \ifnum\value{hornerLast}<0%
            \node (p\i) at (\xi, -1) {};
            \else
            \node (p\i) at (\xi, -1) {\arabic{hornerLast}};
            \fi
            \node at (\xi,-1.5) {=};
            % decode if hexadecimal?
            \IfInteger{\b}{}{
                \pgfmathsetmacro\db{int(0x\b)}
                \xdef\b{\db}
            }
            \ifnum\i=1%
                \setcounter{hornerLast}{\b}
            \else
                \addtocounter{hornerLast}{\b}
            \fi
            \node (\i) at (\xi,  -2) {\arabic{hornerLast}};
            \ifnum\i>1% arrow *2
                \draw[-Kite] (\li) to[edge node={node[above,sloped,scale=0.75] {\({}\cdot{}\,\)#3}}] (p\i);
            \fi
        }
    }
}
% [#1] animation offset
% #2 list
% #3 multiplier
\newcommand*\tikzHornerReverse[3][5]{
% bincode w/ shift of 3:
\setcounter{hornerLast}{0}
% First: get length
\foreach[count=\i] \ignored in {#2} {\setcounter{hornerLast}{\i}}
\xdef\TotalCount{\thehornerLast}% store value
\setcounter{hornerLast}{-1}% reset
\foreach[count=\i, evaluate=\i as \ci using {int(\TotalCount-\i+#1)},
    evaluate=\i as \xi using {1.55*\i}, remember=\i as \li (initially 0)] \b in {#2} {
        % double last
        \ifnum\i>1
            \setcounter{hornerLast}{#3*\value{hornerLast}}
        \fi
        \onslide<\ci->{%
            \node at (\xi,0) {\b};
            \node at (\xi,-0.5) {+};
            \ifnum\value{hornerLast}<0%
            \node (p\i) at (\xi, -1) {};
            \else
            \node (p\i) at (\xi, -1) {\arabic{hornerLast}};
            \fi
            \node at (\xi,-1.5) {=};
            % decode if hexadecimal?
            \IfInteger{\b}{}{
                \pgfmathsetmacro\db{int(0x\b)}
                \xdef\b{\db}
            }
            \ifnum\i=1%
                \setcounter{hornerLast}{\b}
            \else
                \addtocounter{hornerLast}{\b}
            \fi
            \node (\i) at (\xi,  -2) {\arabic{hornerLast}};
        }
    }
\foreach[count=\i, evaluate=\i as \ci using {int(\TotalCount-\i+#1+1)},
    evaluate=\i as \xi using {1.55*\i}, remember=\i as \li (initially 0)] \b in {#2} {
        \ifnum\i>1% arrow *2
            \onslide<\ci->{%
                \draw[Kite-] (\li) to[edge node={node[above,sloped,scale=0.75] {\({}\div{}\,\)#3}}] (p\i);
            }
        \fi

    }
}
\newcommand*\TikzHorner[3][5]{%
    \vfill\begin{center}
        \begin{tikzpicture}
            \tikzHorner[#1]{#2}{#3}
        \end{tikzpicture}
    \end{center}\vfill\null
}
\newcommand*\TikzHornerReverse[3][5]{%
    \vfill\begin{center}
        \begin{tikzpicture}
            \tikzHornerReverse[#1]{#2}{#3}
        \end{tikzpicture}
    \end{center}\vfill\null
}
\endinput