3 Equations and tables
This chapter covers mathematical syntax (inline equations, numbered block equations, advanced environments) and two levels of tables: simple Markdown pipe tables and enriched tables via the quartable extension.
3.1 Inline equations
Inline equations are written between dollar signs: $...$. In PDF they use the native LaTeX math mode; in HTML they are rendered by KaTeX.
Output:
The Fourier transform of a function f is defined by \hat{f}(\xi) = \int_{-\infty}^{\infty} f(x)\,e^{-2\pi i x\xi}\,\mathrm{d}x.
Use \, for thin spaces: f(x)\,\mathrm{d}x gives f(x)\,\mathrm{d}x. Use \mathrm{d} (roman) rather than d (italic) for differentials — this is the ISO 80000-2 standard.
3.2 Numbered block equations
Block equations are delimited by $$...$$. To number them and create a cross-reference, add {#eq-label}:
Output:
i\hbar\frac{\partial \Psi}{\partial t} = \hat{H}\Psi \tag{3.1}
The Schrödinger equation (Équation 3.1) describes the time evolution of a quantum system.
@eq-label without brackets
An equation cross-reference is written @eq-label, without brackets. Brackets [@eq-label] are reserved for bibliographic citations and will not work for equations.
3.3 Advanced mathematical environments
LaTeX environments such as aligned, cases, bmatrix work natively in Quarto, both in PDF (pure LaTeX) and in HTML (KaTeX):
Output:
\begin{cases} \dot{x}(t) = Ax(t) + Bu(t) \\ y(t) = Cx(t) + Du(t) \end{cases} \tag{3.2}
The state-space representation (Équation 3.2) is the standard form in control theory.
$$
\begin{aligned}
\nabla \cdot \mathbf{E} &= \frac{\rho}{\varepsilon_0} \\
\nabla \cdot \mathbf{B} &= 0 \\
\nabla \times \mathbf{E} &= -\frac{\partial \mathbf{B}}{\partial t} \\
\nabla \times \mathbf{B} &= \mu_0\mathbf{J} + \mu_0\varepsilon_0\frac{\partial \mathbf{E}}{\partial t}
\end{aligned}
$$ {#eq-maxwell}Output:
\begin{aligned} \nabla \cdot \mathbf{E} &= \frac{\rho}{\varepsilon_0} \\ \nabla \cdot \mathbf{B} &= 0 \\ \nabla \times \mathbf{E} &= -\frac{\partial \mathbf{B}}{\partial t} \\ \nabla \times \mathbf{B} &= \mu_0\mathbf{J} + \mu_0\varepsilon_0\frac{\partial \mathbf{E}}{\partial t} \end{aligned} \tag{3.3}
Maxwell’s equations (Équation 3.3) in vector notation — a single number for the entire block.
To assign one number per line, use align (without the final d) instead of aligned. The align environment is self-contained — it does not nest inside $$…$$. Pandoc wraps every $$…$$ in \[…\] or \begin{equation}, and nesting \begin{align} inside is invalid (amsmath error). A raw {=latex} block is needed for PDF and $$…$$ for HTML:
::: {.content-visible when-format="pdf"}
```{=latex}
\begin{align}
\nabla \cdot \mathbf{E} &= \frac{\rho}{\varepsilon_0} \\
\nabla \cdot \mathbf{B} &= 0 \\
\nabla \times \mathbf{E} &= -\frac{\partial \mathbf{B}}{\partial t} \\
\nabla \times \mathbf{B} &= \mu_0\mathbf{J}
+ \mu_0\varepsilon_0\frac{\partial \mathbf{E}}{\partial t}
\end{align}
```
:::
::: {.content-visible when-format="html"}
$$
\begin{align}
\nabla \cdot \mathbf{E} &= \frac{\rho}{\varepsilon_0} \\
\nabla \cdot \mathbf{B} &= 0 \\
\nabla \times \mathbf{E} &= -\frac{\partial \mathbf{B}}{\partial t} \\
\nabla \times \mathbf{B} &= \mu_0\mathbf{J}
+ \mu_0\varepsilon_0\frac{\partial \mathbf{E}}{\partial t}
\end{align}
$$
:::Output:
\begin{align} \nabla \cdot \mathbf{E} &= \frac{\rho}{\varepsilon_0} \\ \nabla \cdot \mathbf{B} &= 0 \\ \nabla \times \mathbf{E} &= -\frac{\partial \mathbf{B}}{\partial t} \\ \nabla \times \mathbf{B} &= \mu_0\mathbf{J} + \mu_0\varepsilon_0\frac{\partial \mathbf{E}}{\partial t} \end{align}
Each \\ receives its own sequential number. To suppress the number on a line, add \notag before the \\. To reference an individual line, use \label{my-label} inside the {=latex} block and \eqref{my-label} in the text (PDF only — KaTeX does not generate addressable labels).
\begin{align} is incompatible with $$…$$ in Quarto
Quarto (Pandoc) wraps every $$…$$ in \[…\] (without label) or \begin{equation}…\end{equation} (with {#eq-}). Both forms create invalid nesting with \begin{align}, which amsmath rejects:
Package amsmath Error: Erroneous nesting of equation structuresThe systematic solution is the dual {.content-visible} pattern: raw {=latex} block for PDF, $$\begin{align}…\end{align}$$ for HTML (KaTeX supports align natively).
aligned vs align — what is the difference?
| Environment | Quarto syntax | Numbering | @eq- |
|---|---|---|---|
aligned |
$$\begin{aligned} … \end{aligned}$$ |
one number for the block | \checkmark |
align |
{=latex} + $$…$$ (dual) |
one number per line | \times |
align* |
{=latex} + $$…$$ (dual) |
none | — |
Practical rule: calculation development → aligned (one number, @eq- possible). Independent equations → align with the dual pattern.
subequations
For (3.1a), (3.1b)… numbering, combine subequations and align in a {=latex} block (KaTeX does not support subequations):
::: {.content-visible when-format="pdf"}
```{=latex}
\begin{subequations}\label{eq-navier}
\begin{align}
\rho\,\frac{D\mathbf{u}}{Dt}
&= -\nabla p + \mu\,\nabla^2\mathbf{u} + \mathbf{f}
\label{eq-navier-momentum} \\
\nabla \cdot \mathbf{u} &= 0
\label{eq-navier-incomp}
\end{align}
\end{subequations}
```
:::\label{eq-navier} references the group; \label{eq-navier-momentum} and \label{eq-navier-incomp} reference the lines — accessible with \eqref{}. Add a sibling {.content-visible when-format="html"} block with $$\begin{align}…\end{align}$$ for HTML rendering.
3.4 Simple Markdown tables
Pandoc/Quarto’s pipe table syntax creates tables with per-column alignment. The caption, preceded by :, must be placed immediately after the table:
| Command | PDF format | HTML format |
|:------------------|:-------------:|:-------------:|
| `@fig-label` | figure number | hyperlink |
| `@tbl-label` | table number | hyperlink |
| `@eq-label` | eq. number | hyperlink |
| `@sec-label` | section num. | hyperlink |
: Quarto cross-reference prefixes. {#tbl-crossref}Output:
| Command | PDF format | HTML format |
|---|---|---|
@fig-label |
figure number | hyperlink |
@tbl-label |
table number | hyperlink |
@eq-label |
eq. number | hyperlink |
@sec-label |
section num. | hyperlink |
Table 3.1 summarises the four prefixes to know.
:---— left-aligned:---:— centred---:— right-aligned
The line |:---|:---:|---:| defines the alignment of each column.
The : Caption. {#tbl-label} line must be placed immediately after the table, with no blank line in between. A blank line breaks the table-caption association and produces an orphan caption with no numbering.
3.5 Advanced tables with quartable
The quartable extension (listed in the filters: key of _quarto.yml) adds three capabilities to Markdown tables:
- Rowspan:
[text]{rs=N}merges N rows;^continues the merged cell - Colspan:
[text]{cs=N}merges N columns - Midrules:
===inserts a horizontal separator;===2-4a partial rule spanning columns 2 to 4.
quartable extension
To see all the features of this extension (inspired by the LaTeX booktabs package), see https://github.com/zinc75/quarto-quartable/ and https://zinc75.github.io/quarto-quartable/test_quartable.pdf/.
| Family | Feature | Chapter |
|:--------------------|:---------------------|:-------:|
| === | | |
| [Structure]{rs=3} | Headings and levels | 1 |
| ^ | Cross-references | 1 |
| ^ | Inline formatting | 1 |
| === | | |
| [Visuals]{rs=3} | Static figures | 2 |
| ^ | Python figures | 2 |
| ^ | Multi-column | 2 |
| === | | |
| [Math & data]{rs=3} | Equations | 3 |
| ^ | Simple tables | 3 |
| ^ | `quartable` | 3 |
: Summary of features by family. {#tbl-recap}Output:
| Family | Feature | Chapter |
|---|---|---|
| Structure | Headings and levels | 1 |
| Cross-references | 1 | |
| Inline formatting | 1 | |
| Visuals | Static figures | 2 |
| Python figures | 2 | |
| Multi-column | 2 | |
| Math & data | Equations | 3 |
| Advanced equations | 3 | |
| Simple tables | 3 |
quartable must be in filters:
The [text]{rs=N} syntax is only recognised if quartable is listed in the filters: key of _quarto.yml. Without this, the curly braces remain displayed as-is in the output.
===N-M
===2-4 inserts a rule that spans only columns 2 to 4 (inclusive). Useful for underlining a sub-group of columns without separating the entire row.