| name | qmd-math |
| description | Math notation conventions for Quarto/EPQ documents rendered via lualatex. Use when: writing or adding a formula, equation, or mathematical expression to a .qmd file; asked about display math, inline math, or LaTeX notation in a QMD/Quarto context; defining a where-clause or variable definitions for an equation; converting prose variable descriptions into structured math notation; fixing math that renders badly in a PDF; using \lvert, \begin{aligned}, \tfrac, \text{where}, or any LaTeX math command in a Quarto document. Triggers on: "write a formula", "add an equation", "math notation", "where clause", "display math", "LaTeX equation", "define variables", "simplify the formula", "typeset this". |
qmd-math — Math Notation in Quarto/lualatex
Core Rule: Display Math for Non-Trivial Equations
Use $$...$$ display blocks for any equation with more than one operation. Inline $...$ is for single-symbol references in prose only.
<!-- WRONG — hard to scan, subscript stacking mangles copy-paste from PDF -->
The formula is $\text{NRE}_f = \frac{r_i}{8} \cdot \frac{5}{7} \sum_{\text{seg}} \frac{\Delta t_{\text{seg}}}{\lvert\mathcal{F}_{\text{seg},i}\rvert}$ where ...
<!-- CORRECT — opening and closing $$ each on their own line -->
$$
\text{NRE}_f = \frac{r_i}{8} \cdot \frac{5}{7} \sum_{\text{seg}} \frac{\Delta t_{\text{seg}}}{\lvert\mathcal{F}_{\text{seg},i}\rvert}
$$
Where-Clause Pattern
Preferred: inline \text{where} with \begin{aligned} — keeps definitions inside the math block, aligned at =, no list markup needed. Use when definitions are short phrases.
$$
\text{NRE}_f = \frac{r_i}{8} \cdot \frac{5}{7} \sum_{\text{seg}} \frac{\Delta t_{\text{seg}}}{\lvert\mathcal{F}_{\text{seg},i}\rvert}
\quad \text{where} \quad
\begin{aligned}
r_i/8 &= \text{assignee hourly rate (daily rate} \div 8\text{)} \\
\Delta t_{\text{seg}} &= \text{wall-clock hours in segment} \\
\lvert\mathcal{F}_{\text{seg},i}\rvert &= \text{distinct carrier families active in that segment} \\
5/7 &= \text{wall-clock to business-day conversion}
\end{aligned}
$$
This renders as: equation left · "where" center · aligned definitions right. No overflow on a 6.5in text block if definitions stay under ~40 chars. Verified in lualatex/scrartcl letter.
Fallback: bulleted list — use when definitions are long phrases that would overflow inline.
$$
\text{NRE}_f = \frac{r_i}{8} \cdot \frac{5}{7} \sum_{\text{seg}} \frac{\Delta t_{\text{seg}}}{\lvert\mathcal{F}_{\text{seg},i}\rvert}
$$
where:
- $r_i / 8$ — assignee hourly rate (daily rate ÷ 8 hours)
- $\Delta t_{\text{seg}}$ — wall-clock hours in sweep segment
- $\lvert\mathcal{F}_{\text{seg},i}\rvert$ — distinct carrier families with open pre-first-label tickets in that segment
- $5/7$ — wall-clock to business-day conversion
Each bullet: symbol (inline math) — plain-English definition. One line per term. No nesting.
Never: run-on prose embedding symbols — where $\Delta t$ is the wall-clock hours... $\lvert\mathcal{F}\rvert$ is the count...
Repeated Formulas
When a second formula shares terms with a previous one, use a two-row \begin{aligned} where-block: one row for the new term, one back-reference row for the shared terms.
$$
C_{\text{maint},f} = \frac{r_i}{8} \cdot \frac{5}{7} \sum_{\text{seg} \geq t_{0,f}} \frac{\Delta t_{\text{seg}}}{\lvert\mathcal{F}_{\text{seg},i}\rvert}
\quad \text{where} \quad
\begin{aligned}
t_{0,f} &= \text{first label date for carrier family } f \\
r_i/8,\, \Delta t_{\text{seg}},\, \lvert\mathcal{F}_{\text{seg},i}\rvert &= \text{as defined above}
\end{aligned}
$$
Sub-Formulas in the Where-Block
When a where-term is itself derived from other quantities, define it with a formula row — don't flatten it to prose. Use \tfrac (text-fraction) instead of \frac for compact inline fractions within an aligned block, and add the secondary definition on the same row after a \quad:
$$
\text{NRE}_f = w_i \sum_{\text{seg}} \frac{\Delta t_{\text{seg}}}{\lvert\mathcal{F}_{\text{seg},i}\rvert}
\quad \text{where} \quad
\begin{aligned}
w_i &= \tfrac{5 r_i}{56}, \quad r_i = \text{assignee daily rate} \\
\Delta t_{\text{seg}} &= \text{wall-clock hours in segment} \\
\lvert\mathcal{F}_{\text{seg},i}\rvert &= \text{distinct carrier families active in that segment}
\end{aligned}
$$
When a second formula reuses a named term (w_i), the where-block only needs to define what's new — everything else is already established:
$$
C_{\text{maint},f} = w_i \sum_{\text{seg} \geq t_{0,f}} \frac{\Delta t_{\text{seg}}}{\lvert\mathcal{F}_{\text{seg},i}\rvert}
\quad \text{where} \quad
t_{0,f} = \text{first label date for carrier family } f
$$
Single-term where-clauses don't need \begin{aligned} — inline \quad \text{where} \quad term = definition is sufficient.
epq Audit Gotcha: \texttt Inside Math Blocks
The epq audit flags \texttt{...} anywhere in QMD source, including inside $$ blocks. Use \mathtt{...} for monospace in math mode, or just \text{...} (non-monospace). Better: avoid font commands in math entirely and reference the variable symbol instead.
Delimiters: \lvert\rvert Over |...|
For absolute value and set cardinality, always use \lvert...\rvert. The bare | is a fixed-height fence — it mismatches tall fractions.
<!-- WRONG — bars don't scale with the fraction -->
|\mathcal{F}_{\text{seg},i}|
<!-- CORRECT — scales to match the numerator/denominator height -->
\lvert\mathcal{F}_{\text{seg},i}\rvert
Subscript Formatting
- Label subscripts (words, abbreviations): wrap in
\text{} — _{\text{seg}}, _{\text{maint}}. Unwrapped subscripts render as italicized variable sequences (seg → s·e·g).
- Index subscripts (single-letter variables): no wrapping —
_i, _f.
- Set names: use
\mathcal{} — \mathcal{F} for a set of families.
Inline Math in lualatex Prose — What Works and What Breaks
Safe in prose (renders correctly):
- Variable references:
$\Delta t_{\text{seg}}$, $r_i$, $5/7$
- Inline fractions:
$r_i / 8$
$\div$, $\times$ operators- Comparison:
$4\times$ (e.g., "capped at $4\times$")
Breaks in lualatex prose (renders as literal dollar signs or garbles):
$\geq$, $\leq$ — use Unicode ≥, ≤ or plain English ("at least", "no more than")$\to$, $\rightarrow$ — use → (Unicode) or plain arrow prose
Safe Unicode in lualatex prose (Latin Modern font supports these):
≥ ≤ ≠ ≈ → ÷
Unsafe Unicode (not in Latin Modern, will fail):
× (multiplication sign U+00D7) — write "times" or use $\times$ in math mode only.
Checklist Before Committing Math
