6. Maths

Mathematical equations written using LaTeX syntax can be specified inline or as a block level equation.

For example, the inline equation \(e=mc^2\) is specified in markdown using the {math} role: {math}`e=mc^2`

We can also use a {math} directive to define an equation block:

```{math}
:label: my-equation
w_{t+1} = (1 + r_{t+1})
s(w_t) + y_{t+1}
```

(6.1)\[w_{t+1} = (1 + r_{t+1}) s(w_t) + y_{t+1}\]

These corresponding OU-XML is then a <ProgramListing> to show the script that is used to defined the equation, and an Equation block from which the rendered equation can be generated:

<ProgramListing>
    <Paragraph>```{math}</Paragraph>
    <Paragraph>:label: my-equation</Paragraph>
    <Paragraph>w_{t+1} = (1 + r_{t+1})</Paragraph>
    <Paragraph>s(w_t) + y_{t+1}</Paragraph>
    <Paragraph>```</Paragraph>
</ProgramListing>
        
<Equation id="my-equation">
    <TeX>w_{t+1} = (1 + r_{t+1})
s(w_t) + y_{t+1}</TeX>
</Equation>

Dollar math syntax may also be used to define block equations:

$$
\label{maxwell}
\begin{aligned}
\nabla \times \vec{e}+\frac{\partial \vec{b}}{\partial t}&=0 \\
\nabla \times \vec{h}-\vec{j}&=\vec{s}\_{e}
\end{aligned}
$$

$$ \label{maxwell} \begin{aligned} \nabla \times \vec{e}+\frac{\partial \vec{b}}{\partial t}&=0 \ \nabla \times \vec{h}-\vec{j}&=\vec{s}_{e} \end{aligned} $$

In OU-XML, we again render the two elements above as a listing and an equation type:

<ProgramListing>
    <Paragraph>$$</Paragraph>
    <Paragraph>\label{maxwell}</Paragraph>
    <Paragraph>\begin{aligned}</Paragraph>
    <Paragraph>\nabla \times \vec{e}+\frac{\partial \vec{b}}{\partial t}&amp;amp;=0 \\</Paragraph>
    <Paragraph>\nabla \times \vec{h}-\vec{j}&amp;amp;=\vec{s}\_{e}</Paragraph><Paragraph>\end{aligned}</Paragraph
    ><Paragraph>$$</Paragraph>
</ProgramListing>

<Equation>
    <TeX>
        \label{maxwell}
        \begin{aligned}
        \nabla \times \vec{e}+\frac{\partial \vec{b}}{\partial t}&amp;=0 \
        \nabla \times \vec{h}-\vec{j}&amp;=\vec{s}_{e}
        \end{aligned}
    </TeX>
</Equation>

The $$ syntax also works as a one-liner. For example, the single line:

$$ \label{one-liner} Ax=b $$

will ultimately render as the formatted equation:

$$ \label{one-liner} Ax=b $$