Multicols inside algorithm environment

Question

I'm trying to write an algorithm, but since it doesn't fit in one page, I'm trying to put it in two columns.

The code I'm trying to write it this

\makebox[\linewidth]{
    \begin{minipage}[H]{.85\textwidth}
        \begin{algorithm}[H]
            \caption{Point addition in projective coordinates}
            \label{alg:projective_add}
            \begin{algorithmic}[1]
                \Require $P = (X_1 \colon Y_1 \colon Z_1), Q = (X_2 \colon Y_2 \colon Z_2), E\colon Y^2Z = X^3 -3XZ^2 + bZ^3$
                \Ensure $P + Q = (X_3 \colon Y_3 \colon Z_3)$

                \begin{multicols}{2}
                    \State $t_0 \gets X_1 \cdot X_2$
                    \State $t_1 \gets Y_1 \cdot Y_2$
                    \State $t_2 \gets Z_1 \cdot Z_2$
                    
                    \State $t_3 \gets X_1 + Y_1$
                    \State $t_4 \gets X_2 + Y_2$
                    \State $t_3 \gets t_3 \cdot t_4$
                    
                    \State $t_4 \gets t_0 + t_1$
                    \State $t_3 \gets t_3 - t_4$
                    \State $t_4 \gets Y_1 + Z_1$
                    
                    \State $X3 \gets Y_2 + Z_2$
                    \State $t4 \gets t_4 \cdot X_3$
                    \State $X3 \gets t_1 + t_2$
                    
                    \State $t4 \gets t_4 - X_3$
                    \State $X3 \gets X_1 + Z_1$
                    \State $Y3 \gets X_2 + Z_2$
                    
                    \State $X_3 \gets X_3 \cdot Y_3$
                    \State $Y_3 \gets t_0 + t_2$
                    \State $Y_3 \gets X_3 - Y_3$
                    
                    \State $Z_3 \gets b \cdot t_2$
                    \State $X_3 \gets Y_3 - Z_3$
                    \State $Z_3 \gets X_3 + X_3$
                    
                    \State $X_3 \gets X_3 + Z_3$
                    \State $Z_3 \gets t_1 - X_3$
                    \State $X_3 \gets t_1 + X_3$
                    
                    \State $Y_3 \gets b \cdot Y_3$
                    \State $t_1 \gets t_2 + t_2$
                    \State $t_2 \gets t_1 + t_2$
                    
                    \State $Y_3 \gets Y_3 - t_2$
                    \State $Y_3 \gets Y_3 - t_0$
                    \State $t_1 \gets Y_3 + Y_3$
                    
                    \State $Y_3 \gets t_1 + Y_3$
                    \State $t_1 \gets t_0 + t_0$
                    \State $t_0 \gets t_1 + t_0$
                    
                    \State $t_0 \gets t_0 - t_2$
                    \State $t_1 \gets t_4 \cdot Y_3$
                    \State $t_2 \gets t_0 \cdot Y_3$
                    
                    \State $Y_3 \gets X_3 \cdot Z_3$
                    \State $Y_3 \gets Y_3 + t_2$
                    \State $X_3 \gets t_3 \cdot X_3$
                    
                    \State $X_3 \gets X_3 - t_1$
                    \State $Z_3 \gets t_4 \cdot Z_3$
                    \State $t_1 \gets t_3 \cdot t_0$
                    
                    \State $Z_3 \gets Z_3 + t_1$    
                \end{multicols}
                
            \end{algorithmic}
        \end{algorithm}
    \end{minipage}
}

But I get an error when I try this. If i start the multicols before the \Require, it works but I dont want to do that. I have already imported algpseudocode and algorithm. Does anyone know how I can get this to work?

Answer 1

Split your \Require and \Ensure components from the rest of your statements using two separate algorithmic environments. Then wrap the second one inside a multicols with some vertical adjustment.

\documentclass{article}

\usepackage{algorithm,algpseudocode}
\usepackage{multicol}

\begin{document}

\noindent
\begin{minipage}{.85\textwidth}
  \begin{algorithm}[H]
    \caption{Point addition in projective coordinates}
    \begin{algorithmic}
      \Require $P = (X_1 \colon Y_1 \colon Z_1), Q = (X_2 \colon Y_2 \colon Z_2), E\colon Y^2Z = X^3 -3XZ^2 + bZ^3$
      \Ensure $P + Q = (X_3 \colon Y_3 \colon Z_3)$
    \end{algorithmic}
    \vspace{-.5\baselineskip}% Adjust to suit your needs
    \begin{multicols}{2}
      \begin{algorithmic}[1]
        \State $t_0 \gets X_1 \cdot X_2$
        \State $t_1 \gets Y_1 \cdot Y_2$
        \State $t_2 \gets Z_1 \cdot Z_2$

        \State $t_3 \gets X_1 + Y_1$
        \State $t_4 \gets X_2 + Y_2$
        \State $t_3 \gets t_3 \cdot t_4$

        \State $t_4 \gets t_0 + t_1$
        \State $t_3 \gets t_3 - t_4$
        \State $t_4 \gets Y_1 + Z_1$

        \State $X3 \gets Y_2 + Z_2$
        \State $t4 \gets t_4 \cdot X_3$
        \State $X3 \gets t_1 + t_2$

        \State $t4 \gets t_4 - X_3$
        \State $X3 \gets X_1 + Z_1$
        \State $Y3 \gets X_2 + Z_2$

        \State $X_3 \gets X_3 \cdot Y_3$
        \State $Y_3 \gets t_0 + t_2$
        \State $Y_3 \gets X_3 - Y_3$

        \State $Z_3 \gets b \cdot t_2$
        \State $X_3 \gets Y_3 - Z_3$
        \State $Z_3 \gets X_3 + X_3$

        \State $X_3 \gets X_3 + Z_3$
        \State $Z_3 \gets t_1 - X_3$
        \State $X_3 \gets t_1 + X_3$

        \State $Y_3 \gets b \cdot Y_3$
        \State $t_1 \gets t_2 + t_2$
        \State $t_2 \gets t_1 + t_2$

        \State $Y_3 \gets Y_3 - t_2$
        \State $Y_3 \gets Y_3 - t_0$
        \State $t_1 \gets Y_3 + Y_3$

        \State $Y_3 \gets t_1 + Y_3$
        \State $t_1 \gets t_0 + t_0$
        \State $t_0 \gets t_1 + t_0$

        \State $t_0 \gets t_0 - t_2$
        \State $t_1 \gets t_4 \cdot Y_3$
        \State $t_2 \gets t_0 \cdot Y_3$

        \State $Y_3 \gets X_3 \cdot Z_3$
        \State $Y_3 \gets Y_3 + t_2$
        \State $X_3 \gets t_3 \cdot X_3$

        \State $X_3 \gets X_3 - t_1$
        \State $Z_3 \gets t_4 \cdot Z_3$
        \State $t_1 \gets t_3 \cdot t_0$

        \State $Z_3 \gets Z_3 + t_1$    
      \end{algorithmic}
    \end{multicols}
    \vspace{-.5\baselineskip}% Adjust to suit your needs
  \end{algorithm}
\end{minipage}

\end{document}