Theorems, proofs and algorithms

Theorem-like environments

\begin{theorem}[Cauchy--Schwarz]\label{thm:cs}
For all $u, v$: $|\langle u, v\rangle| \le \|u\|\,\|v\|$.
\end{theorem}

\begin{proof}
Expand $\|u - tv\|^2 \ge 0$ and take the discriminant.
\end{proof}

This renders as Theorem 1 (Cauchy–Schwarz). For all …, followed by Proof. … ∎

Built-in environments

Environment	Head	Head in Chinese documents	Numbered
`theorem`	Theorem	定理	Yes
`lemma`	Lemma	引理	Yes
`corollary`	Corollary	推论	Yes
`proposition`	Proposition	命题	Yes
`definition`	Definition	定义	Yes
`remark`	Remark	注	Yes
`example`	Example	例	Yes
`proof`	Proof	证明	No; ends with ∎

Each environment has its own counter: Theorem 1, Lemma 1, Theorem 2, Lemma 2. Numbers count through the whole document, not per section.
The starred forms (theorem*, lemma*, …) are not numbered.
The optional argument is a note shown in parentheses after the number: \begin{theorem}[Name] gives "Theorem 1 (Name)." On proof it is added the same way: \begin{proof}[of Theorem 1] gives "Proof (of Theorem 1)." It does not replace the word "Proof" as amsthm does.
A \label anywhere inside the environment makes it the target of \ref (the number) and \autoref/\cref ("Theorem 1").
The head is set in bold, and the body continues on the same line. The body may contain several paragraphs, lists, maths and other blocks.
The ∎ goes at the end of the proof's last paragraph. \qedhere is dropped, since the ∎ is placed automatically.

Your own environments

\newtheorem works in the preamble or the body:

You write	Result
`\newtheorem{hyp}{Hypothesis}`	`hyp` environments numbered Hypothesis 1, 2, …
`\newtheorem{conj}[theorem]{Conjecture}`	Shares `theorem`'s counter: Theorem 1, Conjecture 2, Theorem 3
`\newtheorem*{claim}{Claim}`	Unnumbered
`\newtheorem{lem}{Lemma}[section]`	The `[section]` is accepted and ignored; numbering stays global
`\newtheorem{theorem}{Satz}`	Renames a built-in environment

\theoremstyle{…} degrades to nothing visible (its argument text is kept, so write it in the preamble), and every theorem-like environment looks the same. amsthm's \newtheoremstyle is not supported.

Algorithms

HaTeX implements the algorithmicx / algpseudocode commands:

\begin{algorithm}
  \caption{Gradient descent}\label{alg:gd}
  \begin{algorithmic}[1]
    \Require step size $\eta$, iterations $T$
    \Ensure parameters $\theta$
    \State $\theta \gets \theta_0$
    \For{$t = 1, \dots, T$}
      \State $g \gets \nabla L(\theta)$ \Comment{gradient}
      \If{$\|g\| < \epsilon$}
        \State \textbf{break}
      \EndIf
      \State $\theta \gets \theta - \eta g$
    \EndFor
    \State \Return $\theta$
  \end{algorithmic}
\end{algorithm}

The float

algorithm is a float like figure: with a \caption it is numbered "Algorithm 1:" (算法 1), with its own counter, and \label makes it a target. The caption is left-aligned above the lines. algorithmic also works without the float.

Line numbers

\begin{algorithmic}[1] numbers every line. Any optional argument turns numbering on, since LaTeX's "number every n-th line" isn't supported. Lines from \Statex, \Require, \Ensure, \Input, \Output and \Initialize are not numbered.

Commands

Command	Line
`\State text`	text. An empty `\State` adds no line, so `\State \Return x` is one line.
`\Statex text`	text, unnumbered
`\If{c}` … `\ElsIf{c}` … `\Else` … `\EndIf`	if c then … else if c then … else … end if
`\For{c}` … `\EndFor`	for c do … end for
`\ForAll{c}` … `\EndFor`	for all c do … end for
`\While{c}` … `\EndWhile`	while c do … end while
`\Repeat` … `\Until{c}`	repeat … until c
`\Loop` … `\EndLoop`	loop … end loop
`\Function{name}{args}` … `\EndFunction`	function name(args) … end function
`\Procedure{name}{args}` … `\EndProcedure`	procedure name(args) … end procedure
`\Require`, `\Ensure`, `\Input`, `\Output`, `\Initialize`	Require: …, Ensure: …, and so on
`\Return x`	return x
`\Call{name}{args}`	name(args), in the current line
`\Comment{text}`	▷ text, at the end of the current line
`\algstore`, `\algrestore`, `\algsetup`	Ignored

The body of each block is indented by one level (1.4em). The text of a line runs up to the next algorithmic command, so it can contain maths, formatting and \textbf.

Not supported

algorithm2e (\KwIn, \eIf, \SetKwFunction, …) and the older algorithmic package (\STATE, \IF): their commands degrade to text. Rewrite them with algpseudocode commands.
\algnewcommand, \algrenewcommand and custom block definitions.

Previous: TikZ · Contents · Next: Code

#Theorems, proofs and algorithms

#Theorem-like environments

#Built-in environments

#Your own environments

#Algorithms

#The float

#Line numbers

#Commands

#Not supported