How to start a new line in an equation using $$

Question

So I have got a pretty complex equation (with different types of brackets) and it's too long, so I want to break the equation up to start a new line. The equation is:

\begin{document}
$$
Cl_f(\vec x):=\min\left\lbrace a\in\{1,\cdots,m\} : p_a Tr(F^{(n)}_a\rho^{(n)}_{\vec{x}})=\max_j\left\lbrace p_j Tr ( F^{(n)}_j\rho^{(n)}_{\vec{x}}), 1\le j\le m \right\rbrace\right\rbrace. \notag
$$
\end{document}

How do I start a new line in the equation when using $$? Say for eg., I want to break the equation up to start a new line after the colon sign (:), just before p_a. I would like the output to look something like:

Cl_f(\vec x):=\min\left\lbrace a\in\{1,\cdots,m\} :
              p_a Tr(F^{(n)}_a\rho^{(n)}_{\vec{x}})=\max_j\left\lbrace p_j Tr ( F^{(n)}_j\rho^{(n)}_{\vec{x}}), 1\le j\le m \right\rbrace\right\rbrace. \notag

I have tried using \begin{align*} but it's giving me funny error messages in the log (which I think it's to do with the bracket calls). I am good to use $$, \begin{align*} or any other method as long as I can get the output that I am after, with minimal packages that I need to load if possible.

Answer 1

• $$ syntax for math environment is used in plain TeX, not in LaTeX, where is used \[ and \] instead.
• For multiline math expression you need to use some of the amsmath packages environments: align, gather, etc.
• Your equations contain errors (unpaired braces)

An working example with your equations can be:

\documentclass{article}
\usepackage{amsmath}

\begin{document}
    \begin{align*}
Cl_f(\vec x)
    & := \min\Bigl(a\in\{1,\cdots,m\} : p_a Tr\Bigl(F^{(n)}_a\rho^{(n)}_{\vec{x}}\Bigr) \Bigr)  \\
    &  = \max_j\Bigl(p_j Tr \Bigl( F^{(n)}_j\rho^{(n)}_{\vec{x}}\Bigr)\Bigr),
        \quad 1\le j\le m.
    \end{align*}
\end{document}

which gives:

Addendum: According to your comments below, I guess that you looking for the following:

\documentclass{article}
\usepackage{amsmath}

\begin{document}
    \begin{align*}
Cl_f(\vec x) := {}
    & \min\Bigl(a\in\{1,\cdots,m\} : \\
    & \,p_a Tr\Bigl(F^{(n)}_a\rho^{(n)}_{\vec{x}}\Bigr) \Bigr) 
      = \max_j\Bigl(p_j Tr \Bigl( F^{(n)}_j\rho^{(n)}_{\vec{x}}\Bigr)\Bigr),
        \quad 1\le j\le m.
    \end{align*}
\end{document}

Answer 2

You could use the multline* environment, as in:

\begin{document}
\begin{multline*}
Cl_f(\vec x):=\min\left\lbrace a\in\{1,\cdots,m\} : p_a Tr(F^{(n)}_a\rho^{(n)}_{\vec{x}})=\\=\max_j\left\lbrace p_j Tr ( F^{(n)}_j\rho^{(n)}_{\vec{x}}), 1\le j\le m \right\rbrace\right\rbrace. \notag
\end{multline*}
\end{document}