Proofs, Theorems, and Algorithms¶

Infrastructure to support items such as proof and algorithm style formatting is provided by the sphinx-proof extension.

This extension supports the html and pdflatex builders.

sphinx-proof includes support for the following directives:

Installation¶

警告

This is not currently a default package in jupyter-book as is a relatively new package.

It needs to be enabled through the _config.yml after installation.

To install you can use pip:

pip install sphinx-proof

Adding extension through `_config.yml`¶

Open _config.yml and add sphinx_proof to:

sphinx:
  extra_extensions:
    - sphinx_proof

Using sphinx-proof ¶

This package uses a prf sphinx domain.

All markup objects follow the {prf:<typeset>} (such as {prf:proof}) pattern and allows the directives to be referenced using the inline role {prf:ref}.

警告

When referencing directives in sphinx-proof you need to use the {prf:ref}`<label>` inline role. Using other cross-referencing facilities will not work such as [](<label>)

Below we show an example using the {prf:algorithm} directive.

A similar pattern can be followed for the other syntax supported by sphinx-proof.

In MyST Markdown, you can add an algorithm to your document using the algorithm directive:

```{prf:algorithm} Ford–Fulkerson
:label: my-algorithm

**Inputs** Given a Network $G=(V,E)$ with flow capacity $c$, a source node $s$, and a sink node $t$

**Output** Compute a flow $f$ from $s$ to $t$ of maximum value

1. $f(u, v) \leftarrow 0$ for all edges $(u,v)$
2. While there is a path $p$ from $s$ to $t$ in $G_{f}$ such that $c_{f}(u,v)>0$
	for all edges $(u,v) \in p$:

	1. Find $c_{f}(p)= \min \{c_{f}(u,v):(u,v)\in p\}$
	2. For each edge $(u,v) \in p$

		1. $f(u,v) \leftarrow f(u,v) + c_{f}(p)$ *(Send flow along the path)*
		2. $f(u,v) \leftarrow f(u,v) - c_{f}(p)$ *(The flow might be "returned" later)*
```

will be rendered as

Algorithm 1 (Ford–Fulkerson)

Inputs Given a Network \(G=(V,E)\) with flow capacity \(c\), a source node \(s\), and a sink node \(t\)

Output Compute a flow \(f\) from \(s\) to \(t\) of maximum value

\(f(u, v) \leftarrow 0\) for all edges \((u,v)\)
While there is a path \(p\) from \(s\) to \(t\) in \(G_{f}\) such that \(c_{f}(u,v)>0\) for all edges \((u,v) \in p\):
1. Find \(c_{f}(p)= \min \{c_{f}(u,v):(u,v)\in p\}\)
2. For each edge \((u,v) \in p\)
  1. \(f(u,v) \leftarrow f(u,v) + c_{f}(p)\) (Send flow along the path)
  2. \(f(u,v) \leftarrow f(u,v) - c_{f}(p)\) (The flow might be “returned” later)

and can be referenced using the label assigned to the algorithm such as {prf:ref}`ford-fulkerson` which will provide a link such as Algorithm 1.

Proofs, Theorems, and Algorithms¶

Installation¶

Adding extension through _config.yml¶

Using sphinx-proof¶

Additional Documentation¶

Adding extension through `_config.yml`¶

Using sphinx-proof ¶