# scholatex **Print-ready teaching worksheets, without writing LaTeX.** — A small, consistent tag language for the documents a teacher actually makes. [![CTAN](https://img.shields.io/badge/CTAN-scholatex-d35400?style=flat-square)](https://ctan.org/pkg/scholatex) [![Version](https://img.shields.io/badge/version-2.5-2980b9?style=flat-square)](https://ctan.org/pkg/scholatex) [![Engine](https://img.shields.io/badge/engine-LuaLaTeX-1F3A5F?style=flat-square)](https://www.luatex.org/) [![TeX Live](https://img.shields.io/badge/TeX_Live-included-27ae60?style=flat-square)](https://tug.org/texlive/) [![License](https://img.shields.io/badge/license-GPL_v3+-8e44ad?style=flat-square)](https://www.gnu.org/licenses/gpl-3.0) ## Why scholatex? Write a single `.tex` file with a tiny, readable syntax and get a clean, print-ready worksheet — framed exercises, a results table, simple formulas, an image — without `\begin{tabular}{|c|c|}`, without counting ampersands, without remembering which package draws a coloured box. ```latex % !TeX program = lualatex \documentclass[margins=20, size=12]{scholatex} \begin{document} My first scholatex document This is a normal paragraph. {Bold}, {italic}, {red}. { Boxes, tables, images and maths all use the same tag syntax. } \end{document} ``` Compile with `lualatex myfile.tex` — the `scholatex` class reads the body between `\begin{document}` and `\end{document}`, transpiles it to LaTeX, and typesets it. The output has full LaTeX quality; the syntax is meant to be read and edited in minutes by someone who does not know LaTeX. scholatex is a **closed language**: the backslash is an ordinary character, so raw LaTeX commands in the body are typeset literally rather than executed. Everything a worksheet needs is expressed through tags, which keeps documents consistent and safe to share. ## Quick start ```bash tlmgr install scholatex # add sudo on macOS/Linux; see Installation below ``` ```latex \documentclass[margins=20, size=12, lang=en]{scholatex} \begin{document} First topic A paragraph with {bold} and {colour}. \end{document} ``` ## Key features - **🏷️ One tag syntax** — `{content}` covers text, tables, images, maths, boxes, lists and full-page layouts - **🎨 151 colours** — the full CSS / svgnames palette in CamelCase, 22 of them with a lowercase shortcut - **📐 A maths mini-language** — fractions, roots, sums, products, integrals, derivatives, trigonometry, matrices and systems, all in `$...$` - **📦 Framed boxes & grids** — coloured `` panels and CSS-Grid-style named-area page layouts - **📊 Tables without pain** — two-letter cell placement, spans, headers, borders, no ampersand counting - **♻️ Aliases & macros** — factor a style once, name it everywhere; one edit restyles the whole document - **🔁 Control flow** — loops, conditionals and `#{...}` interpolation in the document body - **🔒 Sandbox option** — `untrusted=true` runs document Lua in a restricted environment --- ## The one rule Everything is a **tag**: `` followed either by `{content}` (inline) or by a line that ends in `{` (a block). Attribute words follow a single case convention: | Form | Meaning | Examples | |------|---------|----------| | `lowercase` | a short keyword (style, alignment, skip) | `b`, `i`, `c`, `2tab` | | `CamelCase` | an extended CSS colour (151 of them) | `SteelBlue`, `Crimson` | | `UPPERCASE` | a font name | `DEJAVU SANS` | The order of words inside a tag never matters — emission is always normalised (page break, then vertical skips, then alignment, then tabs, then styles). --- ## Installation `scholatex` is on CTAN and ships with TeX Live, so on a current, fully updated TeX Live or MacTeX it is already there — compile with `lualatex` and nothing more is needed. If your installation predates the package, install it once with the TeX Live manager; the same two commands work on **macOS, Linux and Windows**: ```bash tlmgr update --self tlmgr install scholatex ``` On macOS (MacTeX) and most Linux setups `tlmgr` needs administrator rights, so prefix both with `sudo`. On Windows, open the *TeX Live Command-Line* (or a terminal as Administrator) and run them without `sudo`. MiKTeX users install through the MiKTeX Console (*Packages* → search `scholatex` → *Install*), or with `mpm --install=scholatex`. `tlmgr update --self` comes first because the manager refuses to install packages when its own version is older than the repository's. After installing, check the class is found: ```bash kpsewhich scholatex.cls ``` It should print a path under your TeX tree. From then on `\documentclass{scholatex}` works from any folder. If `tlmgr install scholatex` reports the package is *not present in the repository*, your mirror has not yet synced a recent release; either wait a day or switch to the main CTAN mirror and retry: ```bash sudo tlmgr option repository https://mirror.ctan.org/systems/texlive/tlnet sudo tlmgr update --self sudo tlmgr install scholatex ``` ### Manual install (any OS, no waiting) To use the package immediately without `tlmgr`, drop the files into your personal TeX tree, mirroring the CTAN layout, then refresh the filename database. The home tree is `~/Library/texmf` on macOS, `~/texmf` on Linux, and `%USERPROFILE%\texmf` on Windows: ```bash mkdir -p ~/texmf/tex/luatex/latex/scholatex cp scholatex.cls scholatex.lua scholatex-*.lua ~/texmf/tex/luatex/latex/scholatex/ mktexlsr ~/texmf ``` A LuaLaTeX engine is required (`lualatex`); the package does **not** compile with `pdflatex` or `xelatex`. --- ## Class options Set in `\documentclass[...]{scholatex}`: | Option | Default | Meaning | |--------|---------|---------| | `margins` | `20` | `N` (all sides) or `{top,right,bottom,left}` in mm | | `font` | `Latin Modern Roman` | main text font | | `mathfont` | `Latin Modern Math` | math font | | `size` | `11` | base font size in pt | | `imgdir` | `img` | folder(s) searched for bare image names; comma-separated list, e.g. `{IMG, IMAGES/PNG}` | | `tabwidth` | `8` | width of one tab, in mm (a large Seyès square) | | `lineheight` | `8` | height of one explicit line skip (``, ``), in mm | | `linespread` | `1.0` | overall line spacing (1.5 = one-and-a-half); tall maths never touches even at 1.0 | | `scriptscale` | `100` | scale (%) of `up`/`down` scripts | | `padding` | `2` | inner padding (mm) between a box/grid frame and its content; override locally with `sep:N` | | `lang` | `fr` | decimal separator: `fr` (comma) or `en` (point); affects typed and interpolated decimals alike | | `precision` | `-1` | decimals a computed `#{...}` value is rounded to for display (`-1` = no rounding); `round(x, d)` overrides locally | | `untrusted` | `false` | run document Lua in a restricted sandbox — see [Security](#security) | Headings carry no extra vertical space or built-in colour: to style one, fold a heading keyword into an alias, e.g. `let h = ` then `My title`. --- ## Text attributes **Inline styles** — `b` bold, `i` italic, `u` underline, `emph`, `sf` sans-serif, `sc` small caps. They combine in one tag: `{bold italic red}`. **Colours** — a colour is always one of the 151 CSS colours, written in CamelCase: `Navy`, `Red`, `Tomato`, `SteelBlue`, `ForestGreen`, …. One rule, no lowercase shortcuts — the everyday colours are simply capitalised (`Red`, `Blue`, `Green`, `Gray`). See the [colour reference](#colour-reference). **Fonts and sizes** — a font name in CAPITALS (`{…}`); sizes as `Npt` or `Npx` (`<14pt>{…}`). **Alignment** — `l` left, `c` centre, `r` right, `j` justified. **Tabs and skips** (the number is always a prefix) — `Ntab` indents the first line by N tabs; vertical skips obey singular/plural agreement: `line` or `1line` skips one, `2lines`, `3lines`, … skip several. Bare `tab` = `1tab`. **Scripts** — `upN` raises text by N mm, `downN` lowers it: `x{2}`, `H{2}O`. **Page break** — `nextpage`. **Section headings** — `section`, `subsection`, `subsubsection` give the three levels, numbered automatically: ```
First topic A detail A finer point ``` renders as `1 First topic`, `1.1 A detail`, `1.1.1 A finer point`. A **table of contents** is printed with ``; give it a title in braces: `{Table of contents}`. **Numbering style** — by default the numbers are hierarchical (`1`, then `1.1`, then `1.1.1`). A counter keyword on a heading changes the style of *that* level, on its own — no inherited prefix: `num` (1, 2, 3), `roman` (i, ii, iii), `ROMAN` (I, II, III), `alpha` (a, b, c), `ALPHA` (A, B, C). For example `let study = ` and `let step = ` give sections `I`, `II` and, under each, steps `1`, `2`, `3` (not `I.1`). Each level is independent; without a keyword, the default hierarchical numbering stands. --- ## Aliases and macros — the factoring tool Define a style **once**, at the top of the document, then name it everywhere instead of repeating its attributes. One edit at the definition restyles the whole document. ``` let title = % style alias let h1 = % a heading style, reusable let p = % a standard indented paragraph My heading <h1>First topic <p>{ A paragraph, indented and justified, named not described. } let n = 7 % value, usable in #{...} Seven squared is #{n*n}. let greet{name} = Hello #name! % text macro with parameters ``` Change `let h1 = <Navy b section>` to `<ForestGreen b section>` once and **every** first-level heading follows — the single point of control that keeps a long worksheet consistent. --- ## Tables Columns are declared in brackets, **one two-letter placement code per column**. The first letter is vertical (`t`/`m`/`b`), the second horizontal (`l`/`c`/`r`): `mc` is middle-centre, `br` bottom-right. This is the only placement syntax scholatex uses — in tables as in boxes and grids. ``` <table [mc, ml, mc, mc] borders header fill:AliceBlue line:Navy headerfill:Navy headertext:White>{ <colspan:4 mc>{Term report} Day | Subject | Mark | Coef. <rowspan:2 mc>{Monday} | Maths | 15 | 4 . | French | 12 | 3 } ``` One row per line, `|` between cells. `<colspan:N>` and `<rowspan:N>` span cells; `.` marks a cell covered by a span above. `N:` before a placement code fixes a column width in mm. --- ## Images ``` <img 30>{photo.png} % 30 mm wide <img 40x25>{photo.png} % 40 mm × 25 mm <img>{photo.png} % full available width, never enlarged ``` A bare name is searched in each folder of `imgdir` in turn, then at the project root. An explicit path always works (`<img 20>{IMG/PNG/chat.png}`). --- ## Maths Wrap maths in `$…$`. A small mini-language keeps it light: | You write | You get | |-----------|---------| | `*` | × | | `+-` | ± | | `<=` `>=` `!=` | ≤ ≥ ≠ | | `a/b` | fraction (chained `a/b/c` reads as `(a/b)/c`) | | `x^2` `x_i` | power / index (bind tighter than `/`, so `x^2/y` is `\frac{x^2}{y}`) | | `sqrt(2)` | √2 | | `sum(i=1, n) i` | ∑ with bounds, display style | | `prod(k=1, n) k` | ∏ with bounds, display style | | `int(x) f(x)` | ∫ f(x) dx (primitive; the differential is added) | | `int(x=a, b) f(x)` | ∫ from a to b, f(x) dx | | `contourint(C) f(z)` | ∮ contour integral | | `pvint(x=a, b) f(x)` | p.v. ∫ Cauchy principal value | | `meanint(x=a, b) f(x)` | ⨍ average (normalised) integral | | `dy/dx`, `df/dx` | derivative, upright differential d (ISO) | | `sin(x)` `cos(x)` `ln(x)` … | upright function names | | `abs(x)` | \|x\| | | `norm(v)` | ‖v‖ | | `vec(AB)` | →AB (over-arrow vector) | | `floor(x)` `ceil(x)` | ⌊x⌋ ⌈x⌉ (integer part) | | `bar(z)`, `conj(z)` | z̄ (conjugate, mean, closure) | | `not(A cup B)` | (A∪B)‾ (logical negation, same overline) | | `lim(x->0) f(x)` | limit, `->` becomes the arrow, target under the word | | `partial`, `nabla` | ∂, ∇ (use `(partial f)/(partial x)` for ∂f/∂x) | | `pi`, `alpha`, … | Greek letters | | `inf` | ∞ | The helpers nest, so the secondary-school staples come for free: `norm(vec(AB))` is the norm of a vector, `vec(AB) + vec(BC) = vec(AC)` is Chasles' relation. ### Sets, logic and relations From collège to the upper years a worksheet needs the standard notation. It is carried as plain words and ASCII shortcuts, so a statement reads as one types it. **Number sets** — a doubled capital gives the blackboard-bold set (the ASCIIMath convention). Doubling avoids any clash with a one-letter variable: | You write | You get | |---|---| | `NN` `ZZ` `DD` `QQ` `RR` `CC` | ℕ ℤ 𝔻 ℚ ℝ ℂ | | `PP` `KK` `HH` `FF` `EE` `UU` | ℙ 𝕂 ℍ 𝔽 𝔼 𝕌 (advanced) | **Quantifiers and logic** — `forall` ∀, `exists` ∃; connectives `and` ∧, `or` ∨, `lnot` ¬, `neg` ¬. Implication and equivalence come both as words and as arrows: `=>` or `implies` ⇒, `<=>` or `iff` ⇔ (inside a formula; in running prose double the chevrons as `<<=>>`). The longer arrow forms win over the comparison they contain, so `abs(x) <= 1 <=> -1 <= x <= 1` parses correctly. **Negation** — one rule: `!` before a relation or quantifier negates it, picking the proper struck-through glyph. So `!in` is ∉, `!exists` is ∄, `!subset` is ⊄, `!subseteq` is ⊈, `!equiv` is ≢. (`!=` stays "not equal", ≠.) **Set relations** — `in` ∈, `subset` ⊂, `supset` ⊃, `subseteq` ⊆, `supseteq` ⊇, `cup` ∪, `cap` ∩, `setminus` ∖, `emptyset` ∅ (negate any with `!`). **Arrows** — `->` or `to` →, `mapsto` ↦. ``` $forall epsilon > 0, exists eta > 0$ $x in RR setminus QQ$ $x !in QQ$ $(P and Q) => P$ ``` ### Brackets and accents The integer part and a few one-argument wrappers follow the same `name(...)` shape as `abs` and `vec`: `floor(x)` ⌊x⌋, `ceil(x)` ⌈x⌉, `set(x : x > 0)` a brace set, `abr(u, v)` ⟨u, v⟩ an inner product. An overline is named by intent — the same rule under two words: `bar(...)` for the generic bar (complex conjugate, mean, closure of a set) and `not(...)` for logical negation, so `bar(z)` is z̄ and `not(A cup B)` is (A∪B)‾. The usual accents complete the set: `hat(f)`, `tilde(x)`. ### Limits with an arrow `lim(x->0) f(x)` already sets a limit with its target under the word. For the running phrase "uₙ tends to ℓ" written over an arrow, use `arrow(...)`: `u_n arrow(n to +inf) l` sets a long right arrow with the condition underneath. `to` and `->` are interchangeable inside it. ``` $lim(n -> +inf) u_n = l$ $u_n arrow(n to +inf) l$ ``` ### Operators with an index: sum, prod, lim `sum`, `prod` and `lim` carry their index in `(...)` and set their whole expression in display style, so a fraction in the body keeps full size and a limit's target sits **under** the word, as on a blackboard. The body runs to the end of the formula or to the first `=`: ``` $sum(i=1, n) i = n(n+1)/2$ $prod(k=1, n) k$ $lim(x->0) sin(x)/x = 1$ $lim(x->+inf) 1/x$ ``` ### Functions and trigonometry Function names are set upright automatically — no backslashes. The set covers `sin cos tan cot sec csc`, the inverses `arcsin arccos arctan`, the hyperbolics `sinh cosh tanh coth`, and `ln log exp det dim gcd deg ker arg max min sup`. A name glued to `(...)` takes its argument as one atom, so fractions and powers behave: ``` $sin(x)^2 + cos(x)^2 = 1$ $cos(a+b) = cos(a)cos(b) - sin(a)sin(b)$ $tan(x) = sin(x)/cos(x)$ ``` ### Integrals The integral family writes its variable and bounds in the head `(...)` and captures the integrand as its body; the differential `\,dx` is appended automatically. No bounds gives a primitive, a comma-separated pair a definite integral: ``` $int(x) f(x)$ ∫ f(x) dx $int(x=a, b) f(x)$ ∫ from a to b of f(x) dx ``` **Multiple integrals** — separate several domains with `;`. The count of domains chooses ∫, ∬ or ∭; the differentials come out in reverse order (Fubini): ``` $int(x=a, b ; y=c, d) f(x,y)$ ∬ … dy dx $int(x=a, b ; y=c, d ; z=e, g) f$ ∭ … dz dy dx ``` A single named domain is a region integral: `int(D) f` gives ∬_D f dω. **Named integrals**: `contourint(C) f(z)` is a contour integral ∮, `pvint(x=a, b) f(x)` a Cauchy principal value, `meanint(x=a, b) f(x)` the average integral ⨍. ### Derivatives A Leibniz derivative is written as the fraction it is, and the differential `d` is set upright (ISO 80000-2), matching the `d` of the integrals — **only** when both sides of the fraction carry it, so a variable named `d` is never disturbed (`d/2` stays the fraction d over 2): ``` $dy/dx$ dy/dx, upright d $(d^2 y)/(dx^2)$ second derivative $dy/dx + y = 0$ a differential equation ``` Partial derivatives use `partial` (∂); parenthesise each side so the fraction groups correctly: ``` $(partial f)/(partial x)$ $(partial u)/(partial t) = (partial^2 u)/(partial x^2)$ ``` `nabla` (∇) is available for gradients and divergences. ### Maths blocks Matrices and systems are blocks: **one line is one row**, and inside a matrix `;` separates the entries. Every cell still goes through the mini-language. ``` <matrix>{ 1 ; 2 ; 3 4 ; 5 ; 6 } ``` `<matrix>` draws parentheses, `<det>` the bars of a determinant, `<bmatrix>` square brackets. A single `|` inside a row draws the bar of an **augmented matrix** (allowed on `matrix` and `bmatrix`, never on `det`). A `<system>` stacks equations under a brace, aligned on the first relational operator: ``` <system>{ 2x + 3y = 7 x - y = 1 } ``` Inject a computed value with `#{expr}` (or `#name`), including inside maths: `$#k^2$`. Decimal numbers follow the `lang` option. **The expression computes with a full function library.** Inside `#{...}` you have the transcendental functions, in radians by default: - circular `sin cos tan cot sec csc` and their inverses `arcsin arccos arctan`; the degree variants `sind cosd tand` and `arcsind arccosd arctand` take or return degrees, so `#{sind(30)}` is `0.5` and `#{arcsind(0.5)}` is `30`; - hyperbolic `sinh cosh tanh coth sech csch` and inverses `arcsinh arccosh arctanh`; - exponential and logarithms `exp`, `ln` (natural), `log` (base 10), `log2`, `logb(v, b)` (base *b*); - algebraic and rounding `sqrt cbrt abs sign min max floor ceil` and `round(x, d)` (to *d* decimals, ties away from zero), with the constants `pi` and `e`. So `#{sin(pi/6)}`, `#{exp(1)}`, `#{logb(81, 3)}` all evaluate. The same library backs `<plot>`, so a curve of `cosh(x)` or `arctan(x)` draws from the identical definition. **Rounding for display: `precision`.** The class option `precision:N` rounds every computed `#{...}` value to *N* decimals, dropping trailing zeros (`3.50` prints `3.5`, `4.0` prints `4`). The default `-1` prints the number as computed. `precision` sets the document-wide default; `round(x, d)` overrides it locally in any single expression. So `precision:2` turns `#{1/3}` into `0.33` while `#{round(1/3, 5)}` still gives `0.33333`. ### Advanced vocabulary For the upper years, the mini-language carries the named notation of probability, linear algebra and vector analysis. Each entry keeps the `name(...)` shape, and the rendering is the canonical LaTeX a textbook uses. **Counting and probability** — the binomial coefficient and arrangement are recognised by their **two** arguments, so a one-argument `C(t)` stays an ordinary function. Probability and expectation are the doubled blackboard letters, with the conditional bar written `mid`: | You write | You get | |---|---| | `C(n, k)` | binomial coefficient ⁽ⁿₖ⁾ | | `A(n, k)` | arrangement Aₙᵏ | | `factorial(n)` or `n!` | n! | | `PP(A)`, `PP(A mid B)` | ℙ(A), ℙ(A ∣ B) | | `EE(X)` | 𝔼(X) | | `var(X)` `std(X)` `cov(X, Y)` | Var(X), σ(X), Cov(X, Y) | | `normal(mu, sigma)` | 𝒩(μ, σ²) | | `poisson(lambda)` | 𝒫(λ) | | `binomial(n, p)` | ℬ(n, p) | | `repart(X, x)` `densite(X, x)` | F\_X(x), f\_X(x) | **Linear algebra** — named operators on top of the matrix blocks: | You write | You get | |---|---| | `ker(f)` `im(f)` `rank(A)` | Ker(f), Im(f), rg(A) | | `span(u, v)` `tr(A)` `com(A)` | Span(u, v), tr(A), com(A) | | `transpose(A)` `inv(A)` | Aᵀ, A⁻¹ | | `eigen(A)` `adj(A)` | Sp(A) (spectrum), adj(A) | **Vector analysis and transforms** — the differential operators, the Landau notations (spelt out so the letters `o`/`O` stay free), and the integral transforms: | You write | You get | |---|---| | `grad(f)` `div(F)` `curl(F)` | grad f, div F, rot F | | `lap(f)` | Δf (prefixes its operand, no parentheses) | | `dirderiv(f, u)` | ∇\_u f | | `bigO(...)` `litO(...)` | O(·), o(·) | | `laplace(f)` `fourier(f)` | ℒ{f}, ℱ{f} | | `ilaplace(f)` `ifourier(f)` | ℒ⁻¹{f}, ℱ⁻¹{f} | | `surfint(S)` `volint(V)` `flux(F, S)` | ∯\_S, ∭\_V, a flux | **Arithmetic, number theory and sets** — and a few calculation templates: | You write | You get | |---|---| | `lcm(a, b)` `gcd(a, b)` `sign(x)` | lcm, gcd, sgn | | `card(A)` `powerset(A)` | card(A), 𝒫(A) | | `range(1, n)` | ⟦1, n⟧ (integer interval) | | `set(x mid x > 0)` | {x ∣ x > 0} (the keyword `mid` spaces the bar) | | `euler(n)` `mobius(n)` | φ(n), μ(n) | | `a equiv b mod n` | a ≡ b (mod n) | | `taylor(f, x, a, n)` | the Taylor form (template) | | `jacobian(f, n)` `hessian(f, n)` | the generic partial-derivative matrices | ``` $EE(X) = sum(k=1, n) k PP(X = k)$ $var(X) = EE(X^2) - EE(X)^2$ $dim(ker(f)) + rank(f) = dim(E)$ $lap(f) = div(grad(f))$ $flux(F, S) = volint(V) div(F)$ ``` --- ## Function studies Three tags turn a function into a variation table and a curve. They share one source of truth: a **function object** built once with `<fn>`, then read by `<vartab>` (the table) and `<plot>` (the graph). ### The function object: `<fn>` The equation form reads as the board does and registers itself under its left-hand name — the variable is declared in situ, and a study is then three lines that read like the exercise: ``` <fn f(x) = (x+2)(x-3)> <signtab f> <plot f x:{-4, 5}> ``` Table attributes stay attributes after the expression: ``` <fn g(t) = t^2 - 2t x:{-inf | 1 | +inf} deriv:{- | +} var:{+inf \ -1 / +inf}> ``` A tabular-only object (a table without a formula) takes the head without `=` — `<fn v(x) x:{...} deriv:{...} var:{...}>`. Objects rebind **sequentially**: a later `<fn f(x) = ...>` shadows the name for what follows, never for what precedes — each `<signtab f>` or `<plot f>` sees the definition above it. The 2.4 `name:`/`expr:` attributes still parse but are deprecated; the equation form is the canonical one: ``` let k = <fn name:{k(x)} expr:{(x^2+1)/(x-1)} x:{-inf | 1-sqrt(2) | 1 | 1+sqrt(2) | +inf} second:{- | - || + | +} deriv:{+ | - || - | +} var:{-inf / 2-2sqrt(2) \ -inf || +inf \ 2+2sqrt(2) / +inf}> ``` `let NAME = <fn …>` stores the object under `NAME` (the assignment may span several lines, up to the closing `>`). Fields: - `name:{k(x)}` — the function and its variable; sets the row labels `x`, `k'(x)`, `k(x)` (and `k''(x)` when a second-derivative line shows). `name:{k}` alone uses `x`; omit `name:` for `f(x)`. - `expr:{…}` — the formula, in the maths mini-language. **Read only by `<plot>`**; `<vartab>` ignores it. - `x:{… | … | …}` — the remarkable abscissas, separated by `|`. - `deriv:{…}` — the sign of the first derivative, one sign per interval. - `second:{…}` — the sign of the second derivative (convexity), one per interval. Optional. - `var:{…}` — the variation line (see below). ### The table: `<vartab>` `<vartab k>` reads the object `k`. Or write the data inline: `<vartab x:{…} deriv:{…} var:{…}>`. **Four shapes** are allowed, depending on which sign lines you give. Only `x:` and `var:` are required; `deriv:` and `second:` are each optional: | shape | fields | rows | |-------|--------|------| | full study | `second:` + `deriv:` | x, f″(x), f′(x), f(x) | | classic variation | `deriv:` | x, f′(x), f(x) | | convexity only | `second:` | x, f″(x), f(x) | | value table | neither | x, f(x) | `f″` always sits above `f′`. The value table (no sign line) just joins the listed values by arrows. **Sign lines** (`deriv:`, `second:`) take one sign per interval: `+`, `-`, or empty. `||` (a double bar) marks a forbidden value (a pole): the bar crosses every row. Zeros at sign changes are placed automatically — you don't write them. **The variation line** (`var:`) alternates value and connector. A connector is `/` (rising) or `\` (falling), **surrounded by spaces** — glued, as in `2/3`, it is a fraction, not an arrow. `||` carries the two limits around a pole. Values may be numbers, `+inf`/`-inf`, or any maths expression (`2-2sqrt(2)`, `27/4`). Rules the table enforces: a value between two arrows of the **same** direction is rejected — a variation table lists only bounds and extrema, never a point on a monotone branch (that point belongs on the plot). When `f″` and `f′` show together, `x:` must list the **union** of their zeros, since all rows share the same columns. ### The sign table: `<signtab>` The companion of `<vartab>` for factored expressions. **Automatic**: the rows are computed from a product/quotient of affine factors — exact rational zeros, a forbidden value at each denominator zero, even multiplicities known not to change sign: ``` <fn f(x) = (x+2)(x-3)> <signtab f> <fn g(x) = (x+1)/(x-2)> <signtab g> <fn h(x) = -2(x+1)^2 (x - 1/2)> <signtab h> ``` **Manual** (the general form, for rows the affine engine cannot derive) — one row per factor, usually a conclusion row last: ``` <signtab x:{-inf | -2 | 3 | +inf}>{ x+2 : - | 0 | + | + x-3 : - | - | 0 | + f(x) : + | 0 | - | 0 | + } ``` A cell is a sign per interval; a `0` marks a zero **at the boundary it follows**, `||` a forbidden value. The invariant is checked at compile time: a row that changes sign without a `0` or a `||` at the boundary is an error, not a wrong table in print — an expression cannot change sign without vanishing or ceasing to exist there. ### The graph: `<plot>` ``` <plot k samples:200 x:{-4, 6} y:{-10, 12}> ``` `<plot k>` reads `expr:` and `name:` from the object. Options: - `x:{a, b}` — horizontal display window (comma between the two bounds). Defaults to the finite abscissas of the table. - `y:{c, d}` — vertical window. Required when the function runs to infinity (a pole), so the view is framed. - `samples:N` — number of points computed (default 100). `expr:` is translated to the plotter's syntax: the variable becomes the plotting variable, trigonometric calls get the degree conversion, and implicit products (`2x`, `2(x-1)`) become explicit. Poles are handled so no spurious vertical line joins the branches. Supported in `expr:`: `+ - * / ^`, parentheses, `sin cos tan exp ln log sqrt abs`, and `pi`. `<vartab>` is declarative, `<plot>` is computed. If `var:` does not match `expr:`, the table and the curve contradict each other silently — keeping them consistent is yours to ensure. **Areas.** `area:{a,b}` shades the region between the curve and the x-axis on [a, b], with dashed verticals at the bounds; `between:g` shades between two curves instead (clipped to `area:` when given): ``` <plot f x:{-1, 4} area:{1, 3}> <plot f x:{-1, 4} between:g area:{0, 3}> ``` **Sequences: the cobweb.** `cobweb:{u0}` (or `cobweb:{u0, n}`, default n = 8) draws the bisector y = x and the staircase of u(n+1) = f(u(n)); the iterates are computed at compile time and the first three labelled on the axis: ``` let h = <fn name:{h(x)} expr:{sqrt(2x+3)}> <plot h x:{0, 4} y:{0, 4} cobweb:{0.2, 10}> ``` **Probability laws.** The two laws of the lycée need no `<fn>` object; `area:` highlights P(a ≤ X ≤ b) on both — shaded under the Gaussian, stronger bars on the binomial. The normal window defaults to μ ± 4σ; the binomial masses are computed exactly: ``` <plot normal:{0, 1} area:{-1, 1.5}> <plot binomial:{12, 0.4} area:{3, 6}> ``` > Maths note: in prose use the mini-language spellings `!=`, `+-`, `>=`, `<=` (not `\neq`, `\pm`, …). Write `$f(x)$` to typeset a formula; an unbracketed `f(x)/x` parses as `f` times `(x)/x`, so phrase it as "the ratio of `$f(x)$` to `$x$`". --- ## The lycée toolbox Five more figures complete the secondary curriculum (2.5). **The weighted probability tree** — `<tree>`, the most-drawn object of première and terminale. Each line reads `LABEL PROBABILITY`, an optional brace opening the children; a leading `!` is the complementary event (overline). Probabilities may be numbers or symbols (`p`, `1-p`). A node with exactly one branch receives its complement automatically — the only case that is mathematically determined; siblings that sum to something other than 1 are a compile error. `products:on` writes P(A ∩ B) = 0.18 at each leaf — the exact product when numeric, the symbolic chain otherwise. The layout is computed: leaves evenly spaced, nodes at the mean height of their children. ``` <tree products:on>{ A 0.3 { B 0.6 } !A 0.7 { B 0.1 } } ``` **Descriptive statistics** — one tag, `<stats>`, five `kind:`s, every number computed at compile time: ``` <stats kind:bars data:{1: 4 | 2: 7 | 3: 2}> <stats kind:bars data:{Walk: 5 | Bus: 3 | Bike: 2}> <stats kind:histogram bounds:{0, 5, 10, 20} counts:{3, 7, 2}> <stats kind:pie data:{Walk: 5 | Bus: 3 | Bike: 2}> <stats kind:boxplot data:{12, 15, 9, 21, 14, 15, 18}> <stats kind:scatter data:{(1, 2.1) (2, 2.6) (3, 3.4)} fit:on> ``` The dictionary `key: value | …` is the form of the *mappings* — bars (numeric keys give a numeric axis, words give categories) and pie; pairs `(x, y)` remain the form of the *clouds*, where an abscissa may repeat. **Data variables.** A Lua table declared with `let` is passed by name — the natural home of data reused across figures: ``` let notes = { Mathematiques = 15.5, Francais = 12.0, Anglais = 18.0 } <stats kind:bars data:notes> <stats kind:pie data:notes> ``` A Lua table has no writing order, so map keys come out **sorted** (numbers numerically, words alphabetically); when the order matters, write a list of pairs, which keeps it: `let trimestres = {{"T1", 11.5}, {"T2", 13.0}}`. Lists of numbers feed `boxplot`, lists of `{x, y}` pairs feed `scatter`, and two list variables feed `histogram` through `bounds:` and `counts:`. Three honesty guarantees, because a statistics figure teaches by its construction: the histogram draws **density** (count over class width), so unequal classes stay truthful; the boxplot uses the French secondary-school quartiles (Q1 the smallest value with at least a quarter of the data at or below it, Q3 likewise at three quarters); `fit:on` draws the least-squares line — computed, not eyeballed. **The number line** — `<numberline>`, the figure of inequalities and absolute values. **Solved**: the block form takes one inequality (the tag's braces cannot carry `<` and `>`) and computes the set exactly — an affine expression against a constant, a product/quotient of affine factors against 0, or `abs(affine)` against a constant. Strictness decides open/closed; a denominator zero is always excluded; an isolated solution is a point: ``` <numberline x:{-5, 5}>{ abs(x - 1/2) >= 5/2 } ``` **Declared**, when the set is given rather than solved — brackets follow the international convention (`[ ]` included, `( )` excluded); a bound may be `inf`, the segment then runs to the arrow; `points:` pins isolated values: ``` <numberline x:{-5, 5} set:{[-2, 3) union (4, inf)} points:{-4}> ``` **The trigonometric circle** — one `<draw>` line: the circle, its axes, and the sixteen remarkable angles labelled by their principal measure in (−π, π]. `values:on` adds the dashed cos/sin projections (exact values at the remarkable angles, two decimals elsewhere). Dynamic: `step:{pi/12}` draws the multiples of the step, `range:{0, pi/2}` restricts to an arc — the first-quadrant close-up. Labels too crowded to read are a compile error suggesting a larger step: ``` <draw>trigcircle radius:4 values:on <draw>trigcircle radius:4 step:{pi/6} <draw>trigcircle radius:4 range:{0, pi/2} step:{pi/12} values:on ``` **Space geometry** — `solid` lines inside `<draw>` render the full repertoire in the French *perspective cavalière* (receding axis at 45°, ratio 0.5; override with `angle:`/`ratio:`). Hidden edges are **computed, not declared**: a face of a convex solid is visible exactly when the projection preserves its outward orientation, and an edge is dashed exactly when both of its faces are hidden. Several solids in one block sit side by side. Vertex names are optional on `cube`, `cuboid` (eight letters, base then top) and `pyramid` (apex first). Plane sections are deferred to a later release. ``` <draw>{ solid cube ABCDEFGH edge:4 solid pyramid SABCD base:4 height:5 } <draw>{ solid cuboid sides:{5, 3, 2} solid cylinder radius:1.5 height:4 solid cone radius:2 height:4.5 solid sphere radius:2.5 } ``` --- ## Boxes ``` <box line:Crimson fill:MistyRose radius:4 title:{A note}>{ Content here. } ``` Options: `line:` frame colour, `fill:` background, `text:` text colour, `radius:N` rounded corners (mm), `width:N` or `width:N%`, `boxrule:N`, `sep:N` (inner padding, mm; `boxsep:N` is a synonym), `break:yes`, `title:{…}`, `titlefill:`, `titletext:`. A line containing only `---` splits a box into two regions. `<row gap:N>{ … }` lays its child boxes side by side, equal widths and equalised heights. A box also takes a two-letter placement code (`tl`…`br`, default `tl`); the vertical part needs a `height:` to act. --- ## Grid (named-area layout) For full-page layouts — a worksheet header with a logo, a title bar, info fields, and a body — `<grid>` borrows CSS Grid's named-area idea. A `template:[ … ]` of quoted rows draws the layout; each word names a cell. A name repeated horizontally spans columns, vertically spans rows; a dot `.` is empty. ``` <grid template:[ "title title logo" "intro info logo" "body body body" ] gap:4>{ <area title>{ <Red b 16pt>Maths assessment } <area logo >{ <img>{blason.png} } <area intro>{ Instructions: no calculator. } <area info >{ Name: \\ First name: } <area body >{ <s1>Exercise 1 Solve the equation... } } ``` An area can be framed like a box (`line:`, `fill:`, `radius:`, `title:`). The grid takes `width:` and `height:`; an area or the grid takes a two-letter placement code for content position within cells. --- ## Lists A list is `<list:STYLE>` — the style follows the name, one item per line, no item tag: ``` <list:decimal>{ Read the instructions Underline the key words Write your answer } ``` Styles — bullets: `none` `disc` `circle` `square`; numbered: `decimal` `alpha` `ALPHA` `roman` `ROMAN` (the case of the keyword sets the case of the letters); checkboxes: `check`. A list written under an item becomes its sub-list, nested as deep as you like. Text attributes on the tag wrap the whole list: `<list:ROMAN TIMES NEW ROMAN 12pt i>{ … }`. --- ## Block aliases Define a reusable component once; `#param` placeholders are filled at the call site, and the call-site body becomes the block content — so it may contain sub-blocks of its own. ``` let card{title, frame} = <box title:{#title} line:#frame radius:2> <card First, Crimson>{ Called with two arguments. } <card Second, Navy>{ Same component, different look. } ``` --- ## Control flow ``` for n in 1..3 { <c Navy b>Sheet #n } for f in [chat.png, chien.png] { <img 16>{#f} } if score >= 10 { <Green>Passed. } else { <Red>Try again. } ``` Loops and conditions work in the document body, inside boxes, and inside table bodies. The loop variable interpolates everywhere via `#`. --- ## Escapes To print a character that scholatex treats specially, **double it**: `<<` `>>` `{{` `}}` `##` give a literal `<` `>` `{` `}` `#`. The backslash is an ordinary character — a path like `C:\Users\Leo` or a regex `\d+\s*\w` prints verbatim, nothing to escape. The characters `_ & % ~` are escaped automatically. A line break inside a paragraph is the tag `<nextline>`. A line whose first non-space character is `%` is a comment. A bare `#` not followed by a name or `{…}` is a literal `#`. Braces carry structure, so a **literal brace must be balanced**: write the pair `{{…}}` to print `{…}`. A lone, unmatched `{{` or `}}` is reported as an unbalanced brace naming its line, rather than silently corrupting the surrounding block — so set-builder notation like `{{ x : x > 0 }}` is written as a pair. Angle brackets and hashes need no such balancing; only braces do. --- ## Colour reference Every colour is written in **CamelCase** — there is one rule and no lowercase shortcuts. The everyday colours are simply capitalised: `Red` `Blue` `Green` `Navy` `Orange` `Purple` `Teal` `Brown` `Gray`/`Grey` `Pink` `Yellow` `Black` `White` `Violet` `Cyan` `Magenta` `Lime` `Olive` `Aqua` `Silver` `Maroon`. For the full palette, write any of the **151 CSS / svgnames colours in CamelCase** (`<SteelBlue>{…}`, `fill:MistyRose`, `line:DarkOrange`). They are grouped below by family for browsing; all are valid anywhere a colour is expected (`line:` `fill:` `text:` and inline tags). **Reds & pinks** (14) — `Brown`, `Crimson`, `DarkRed`, `FireBrick`, `IndianRed`, `LightCoral`, `LightPink`, `Maroon`, `MistyRose`, `Pink`, `Red`, `RosyBrown`, `Salmon`, `Tomato` **Oranges & browns** (23) — `AntiqueWhite`, `Bisque`, `BlanchedAlmond`, `BurlyWood`, `Chocolate`, `Coral`, `DarkGoldenrod`, `DarkOrange`, `DarkSalmon`, `Goldenrod`, `LightSalmon`, `Moccasin`, `NavajoWhite`, `Orange`, `OrangeRed`, `PapayaWhip`, `PeachPuff`, `Peru`, `SaddleBrown`, `SandyBrown`, `Sienna`, `Tan`, `Wheat` **Yellows & golds** (11) — `Cornsilk`, `DarkKhaki`, `Gold`, `Khaki`, `LemonChiffon`, `LightGoldenrod`, `LightGoldenrodYellow`, `LightYellow`, `Olive`, `PaleGoldenrod`, `Yellow` **Greens** (20) — `Aquamarine`, `Chartreuse`, `DarkGreen`, `DarkOliveGreen`, `DarkSeaGreen`, `ForestGreen`, `Green`, `GreenYellow`, `LawnGreen`, `LightGreen`, `Lime`, `LimeGreen`, `MediumAquamarine`, `MediumSeaGreen`, `MediumSpringGreen`, `OliveDrab`, `PaleGreen`, `SeaGreen`, `SpringGreen`, `YellowGreen` **Cyans & teals** (17) — `Aqua`, `CadetBlue`, `Cyan`, `DarkCyan`, `DarkSlateGray`, `DarkSlateGrey`, `DarkTurquoise`, `DeepSkyBlue`, `LightBlue`, `LightCyan`, `LightSeaGreen`, `MediumTurquoise`, `PaleTurquoise`, `PowderBlue`, `SkyBlue`, `Teal`, `Turquoise` **Blues** (21) — `Blue`, `CornflowerBlue`, `DarkBlue`, `DarkSlateBlue`, `DodgerBlue`, `LightSkyBlue`, `LightSlateBlue`, `LightSlateGray`, `LightSlateGrey`, `LightSteelBlue`, `MediumBlue`, `MediumPurple`, `MediumSlateBlue`, `MidnightBlue`, `Navy`, `NavyBlue`, `RoyalBlue`, `SlateBlue`, `SlateGray`, `SlateGrey`, `SteelBlue` **Purples & violets** (17) — `BlueViolet`, `DarkMagenta`, `DarkOrchid`, `DarkViolet`, `DeepPink`, `Fuchsia`, `HotPink`, `Indigo`, `Magenta`, `MediumOrchid`, `MediumVioletRed`, `Orchid`, `PaleVioletRed`, `Plum`, `Purple`, `Violet`, `VioletRed` **Grays** (10) — `DarkGray`, `DarkGrey`, `DimGray`, `DimGrey`, `Gray`, `Grey`, `LightGray`, `LightGrey`, `Silver`, `Thistle` **Whites & off-whites** (17) — `AliceBlue`, `Azure`, `Beige`, `FloralWhite`, `Gainsboro`, `GhostWhite`, `Honeydew`, `Ivory`, `Lavender`, `LavenderBlush`, `Linen`, `MintCream`, `OldLace`, `Seashell`, `Snow`, `White`, `WhiteSmoke` **Black** (1) — `Black` These are exactly the colours xcolor provides under its `svgnames` option (the 147 CSS Color Module names plus the four X11 extras `LightGoldenrod`, `LightSlateBlue`, `NavyBlue` and `VioletRed`). Names are case-sensitive: write `Seashell`, not `SeaShell`. --- ## Security `scholatex` evaluates `let name = expr`, `#{expr}` and the conditions of `for`/`if`/`while` as Lua at compile time, so by default a document can run arbitrary code — exactly like `\directlua`. Setting `untrusted=true` in `\documentclass[...]{scholatex}` runs that Lua in a restricted environment: only pure, side-effect-free names are visible; `os`, `io`, `package`, `require`, `load`, `debug` and other escape vectors are absent. A blocked access stops the compile with a clear message; a runaway loop is aborted by an instruction-count ceiling; `string.rep`/`string.format` are capped. ```latex \documentclass[untrusted=true]{scholatex} ``` `untrusted` hardens **the scholatex expression layer only**. It does not sandbox LuaLaTeX as a whole — a hostile `.tex` can still call `\directlua`, `\write18`, `\input`. Use it when the scholatex **body** comes from a semi-trusted source while the surrounding `.tex` is your own; for a whole untrusted `.tex`, run `lualatex` without `--shell-escape`, ideally in a container. --- ## Examples The `examples/` folder contains eight self-contained, fully commented documents that together exercise every feature: | File | Covers | |------|--------| | `text-style.tex` | the case rule, styles, colours, fonts, sizes, alignment, tabs, skips, scripts; **factoring styles into aliases**; a table of contents from the heading keywords | | `containers.tex` | tables, boxes and the named-area grid, each built up from its simplest form to a full worksheet header | | `basics.tex` | the inline mini-language, number sets, quantifiers and connectives, negation with `!`, set relations, the integer part, the overline, and arithmetic helpers | | `analysis.tex` | operators with an index, limits, trigonometry, derivatives, the vector operators, the integral family, transforms — then sign tables, the number line, areas and cobwebs, and four full function studies (`<fn>`, `<vartab>`, `<plot>`), from polynomial to hyperbolic | | `algebra.tex` | the matrix / determinant / augmented-matrix / system blocks, and the linear-algebra vocabulary | | `geometry.tex` | angles, vectors, coordinate systems, the `<draw>` figures and axes — then the trigonometric circle and the six solids in cabinet projection | | `statistics-probability.tex` | counting, probability and expectation, variance, distributions and density — then weighted trees, the two laws, and the five figures of descriptive statistics | Compile any of them with `lualatex <file>.tex` from the `examples/` folder. --- ## Project layout ``` scholatex.cls LaTeX class: options, packages, reads & injects the body scholatex.lua transpiler core: tags, text, control flow, aliases scholatex-style.lua attribute resolution (colours, styles, sizes, alignment…) scholatex-math.lua the $…$ math mini-language (operators, integrals, functions, trig) scholatex-util.lua parsing primitives (groups, brace balance, comma split) scholatex-table.lua the <table> block scholatex-img.lua the <img> tag scholatex-box.lua the <box> and <row> blocks scholatex-grid.lua the <grid> named-area layout block scholatex-section.lua the <section>/<subsection>/<subsubsection> blocks scholatex-list.lua the <list:STYLE> block scholatex-matrix.lua the <matrix>/<det>/<bmatrix> and <system> blocks scholatex-vartab.lua the <fn> object and the <vartab> table scholatex-signtab.lua the <signtab> sign table scholatex-plot.lua the <plot> curve: areas, cobwebs, probability laws scholatex-tree.lua the <tree> weighted probability tree scholatex-stats.lua the <stats> descriptive-statistics figures scholatex-numberline.lua the <numberline> graduated line, declared or solved scholatex-affine.lua exact sign analysis of affine factors (rational zeros) scholatex-figure.lua the <draw> block: figures, points, segments, trigcircle scholatex-solid.lua space geometry in cabinet projection (solid …) scholatex-toc.lua the <tableofcontents> tag examples/ eight commented showcase documents ``` New tags register themselves via `scholatex.register_tag` / `scholatex.register_block`; a name clash raises an error rather than silently overwriting, so modules stay independent. --- ## Diagnostics Errors point at the source line, e.g. `scholatex: line 12: unknown tag attribute: 'xyz'`. Defining an alias whose name is a built-in (`let section = …`) prints a warning: the built-in always wins, so the alias would be silently dead — pick a different name. --- ## What's new ### 2.5 The lycée release: the last nine figures and tables of the French secondary curriculum, so a worksheet from seconde to terminale never leaves the tag language. - **Sign tables `<signtab>`** — automatic (`<signtab f>` computes rows, exact zeros and forbidden values from the factored expression) or manual (one row per factor, `0` at a boundary zero, `||` at a forbidden value; a sign change without either is a compile error). - **Weighted probability trees `<tree>`** — declarative branches, `!B` for the complement, symbolic probabilities accepted, single branches auto-completed with their complement, `products:on` for the leaf products (exact when numeric). - **Areas in `<plot>`** — `area:{a,b}` under a curve, `between:g` between two curves. - **Cobwebs** — `cobweb:{u0, n}` draws the staircase of u(n+1) = f(u(n)) with the bisector, iterates computed. - **Probability laws** — `<plot normal:{mu,sigma}>` and `<plot binomial:{n,p}>` without an `<fn>` object; `area:` highlights P(a ≤ X ≤ b) on both. - **The `<fn>` equation form** — `<fn f(x) = (x+2)(x-3)>` registers itself under its left-hand name; the declaration reads like the exercise. - **Data variables** — `let notes = {Mathematiques = 15.5, ...}` then `<stats kind:bars data:notes>`; multi-line `let` tables accepted. - **Statistics `<stats>`** — bars (a dictionary of frequencies, numeric or categorical), histogram (density, honest with unequal classes), pie, boxplot (French quartiles), scatter with a computed least-squares `fit:on`. - **Trigonometric circle** — `<draw>trigcircle`, remarkable angles in principal measure by default, `step:{pi/12}` and `range:{0, pi/2}` for a chosen graduation or a first-quadrant close-up, `values:on` for the cos/sin projections. - **Number line `<numberline>`** — declared interval sets (included/excluded endpoints, `union`, infinite bounds, isolated points) or a solved inequality (block form), the set computed exactly. - **Space geometry** — `solid cube/cuboid/pyramid/cylinder/cone/sphere` in perspective cavalière, hidden edges computed from face orientation, solids laid side by side. ### 2.4 - **Analytic geometry in `<draw>`: the `axes:` mode** — `<draw axes:{xmin,xmax,ymin,ymax}>` draws a graduated cartesian frame and reads every line as a coordinate directive rather than a construction. One unit stays one centimetre and the drawing is clipped to the window. A block without `axes:` keeps the 2.3 construction behaviour unchanged. - `point NAME (x,y)` places and labels a point, available to later lines by name. - `vector u (x,y)` draws a free vector from the origin; `vector AB` the bound vector between two placed points. A named vector is remembered: `vector s = u+v` (or `u-v`) draws the sum or difference, labelled with the expression along the arrow; `from:` moves any vector's tail (a placed point, a literal pair, or `~u` for the tip of a drawn vector) and `style:` restyles the copy (`style:dashed-gray`, `style:Blue`) — the parallelogram and triangle rules read on a single frame. - `line` by equation (`y = 2x-1`, `x = -3`, the general `2x+3y = 6`) or `line through A B`. - `circle center:A radius:r` (centre a placed point or a literal pair) or by equation `circle x^2+y^2 = 4`; a named circle carries a `tangent to:C at:P` at a point on it. - `region` shades the half-plane of a linear inequality (`<`, `>`), the boundary dashed. - **Parametric and polar curves in `<plot>`: the `kind:` field** — `kind:parametric` reads `expr:{x(t), y(t)}` over `t:{a, b}`; `kind:polar` reads `expr:{r(theta)}` over `theta:{a, b}`, drawn as `(r cos theta, r sin theta)`. Bounds accept `pi`. Conics follow from the parametrisation (ellipse `{a cos(t), b sin(t)}`, parabola `{t, t^2}`, hyperbola `{a cosh(t), b sinh(t)}`) — no separate conic directive. A `<plot>` without `kind:` is the function graph, unchanged. ### 2.3 - **Figure drawing: the `<draw>` block** — a plane figure is described, not hand-placed. Name the shape and give its measurements; the coordinates are computed trigonometrically and emitted as hard numbers. One drawing unit is one centimetre, so `side:5` draws a 5 cm side. - **Triangles** by any classical definition — `equilateral`, `isosceles`, `right` (right angle at the first point, or `right:X`), three sides `sides:(a,b,c)`, two sides and the included angle `sides:(a,b) angle:t`, two angles and a side `angles:(A,B) side:c`, or three sides named one by one (`AB:3 BC:4 CA:5`). - **Quadrilaterals** — `square`, `rectangle`, `rhombus`, `parallelogram`, `trapezoid`, and `kite` (two pairs of adjacent equal sides, the rhombus being the case where both pairs are equal). - **Regular polygons** by name from the pentagon up (`pentagon`, `hexagon`, `octagon`), or `polygon` with as many points as given. - **Circles** by centre and `radius:r` or `diameter:d` (the radius optionally a placed segment, `radius:AB`); `circle ABC` is the circumscribed circle of three placed points, with `inscribed` for the incircle. - **Coding and measurement** — `marks:on` codes equal sides and right angles; `measures:cm` / `measures:mm` labels each side with its length. Both are opt-in. When a figure has two pairs of equal sides of different lengths (kite, rectangle, parallelogram), the pairs are told apart by their tick count — a single tick on one pair, a double tick on the other — so a kite never reads as a rhombus. - **Composite figures** — several figures in one block share their points; a figure repeating a point is grafted onto it, and a figure sharing an edge deduces that edge's length and is flipped to the far side so the pieces abut. A shared edge is labelled once and ticked once, not twice. - **Multi-character point names** — besides the glued single letters (`triangle ABC`), a parenthesised comma-separated list names multi-character points: `triangle (O, A0, B0)`. - **Loops, interpolation and rotation inside `<draw>`** — the same `for VARIABLE in FROM..TO { … }` loops as the rest of the language; `#k` and `#{expr}` interpolate point names and measurements; `rotate:θ` turns a figure about its first point, `scale:F` multiplies every coordinate of the picture by F leaving the text size alone (default 1, any `<draw>` form), and `labels:off` hides the vertex names — enough to fan, rosette or step figures round a centre. - **Low-level primitives `point` and `line`** — `point(P)` places a dot at coordinates declared with `let P = {x, y}`; `line(A, B)` draws a segment between two points (names or literal `{x, y}` pairs), taking `measures:` like a figure side. As each coordinate is an ordinary expression, a loop can compute endpoints — the building block for free-form drawings. - **Examples** — a new `geometry` showcase covers the inline geometry vocabulary and the full `<draw>` block. ### 2.2 - **Probability and statistics** — the blackboard operators `PP(...)` ℙ and `EE(...)` 𝔼 (with `PP(A mid B)` for a conditional), spread (`var`, `std`, `cov`), distributions (`normal`, `poisson`, `binomial`), and the distribution/density functions (`repart`, `densite`). - **Counting** — the binomial coefficient `C(n, k)` and arrangement `A(n, k)`, recognised by their two arguments so a one-argument `C(t)` stays a function; the factorial `factorial(n)` or `n!`. - **Linear-algebra vocabulary** — `ker`, `im`, `rank`, `span`, `tr`, `com`, `eigen` (the spectrum), `adj`, with `transpose(A)` → Aᵀ and `inv(A)` → A⁻¹. - **Vector analysis** — `grad`, `div`, `curl`, the Laplacian `lap(f)` Δf, the directional derivative `dirderiv(f, u)`, the Landau notations `bigO`/`litO`, the transforms `laplace`/`fourier` and their inverses, and the surface/volume integrals `surfint`/`volint`/`flux`. - **Number theory and helpers** — `euler` φ, `mobius` μ, congruence `a equiv b mod n`, plus `lcm`, `sign`, `card`, `powerset`, the integer interval `range(1, n)` ⟦1, n⟧, the keyword `mid` for a spaced bar, and the templates `taylor`, `jacobian`, `hessian`. - **Fixes** — a parenthesised group over a fraction now grows to full height (`(a/b)^2`); higher-order differentials `d^2y/dx^2` set the upright d throughout; plot tick numbers stay readable where a curve crosses an axis, and the axis arrow clears the last graduation. - **Examples by domain** — the maths showcase now mirrors the manual's four categories: `basics`, `algebra`, `analysis` (which holds the function studies) and `probability`. ### 2.1 - **Mathematical vocabulary** — number sets in blackboard bold (`NN` `ZZ` `DD` `QQ` `RR` `CC`, plus `PP` `KK` `HH` `FF` `EE` `UU`), quantifiers and connectives (`forall` `exists` `and` `or` `lnot` `neg`), implication and equivalence as words or arrows (`=>`/`implies`, `<=>`/`iff`), set relations (`in` `subset` `cup` `cap` `setminus` `emptyset` …), the integer part (`floor` `ceil` `round`), and accents (`bar`/`conj` for the conjugate-mean-closure overline, `not` for logical negation, `hat` `tilde`). - **Negation with a single `!`** — `!` in front of a relation or quantifier negates it with the proper struck-through glyph: `!in` ∉, `!exists` ∄, `!subset` ⊄, `!subseteq` ⊈, `!equiv` ≢. `!=` stays "not equal". - **Limit arrow** — `arrow(n to +inf)` sets a long right arrow with its condition underneath, for the "uₙ → l" phrasing in running maths. - **Colours are CamelCase only** *(breaking change)* — the lowercase keywords (`red`, `navy`, …) are removed; write the CamelCase form (`Red`, `Navy`). One rule for all 151 colours. A lowercase colour now raises an error that names the CamelCase replacement. - **Function studies** — three new tags for analysis: `<fn>` builds a function object (name, formula, abscissas, derivative signs, variation), `<vartab>` renders its variation table, `<plot>` draws its curve (via pgfplots, with pole handling). The table comes in four shapes — full (f″, f′, f), classic (f′, f), convexity (f″, f), or a plain value table (f) — since the two derivative lines are independent and optional. - **Section numbering styles** — `num`, `roman`, `ROMAN`, `alpha`, `ALPHA` set the counter style of a heading level on its own, with no inherited prefix; the default stays hierarchical. - **Examples reorganised** — the showcase set is now `text-style`, `containers`, `math-language`, `math-analysis`, `math-algebra` and `functions` (the old single `03-math` is split by topic). ### 2.0 - **New escape rules** *(breaking change)* — to print a special character, double it: `<<` `>>` `{{` `}}` `##` give a literal `<` `>` `{` `}` `#`. A backslash is now an ordinary character (so `C:\Users` just works); it is no longer an escape. The old `\<` `\>` `\{` `\}` `\#` forms no longer apply. - **Line break is a tag** *(breaking change)* — use `<nextline>` (in text and table cells) instead of the old `\\`. In running text a blank line already starts a new paragraph, so `<nextline>` is only for a break without a paragraph change. ### 1.2 - **Script/fraction precedence fix** — `^` and `_` now bind tighter than `/`, so `x^2/y` renders as the fraction of `x^2` over `y` (and `1/i^2` as `1` over `i^2`), matching ordinary mathematical reading - **Automatic spacing for tall lines** — consecutive lines containing fractions or integrals no longer touch; TeX inserts just enough air where needed, leaving ordinary text unchanged ### 1.1 - **Maths expansion** — full integral family (`int`, multiple integrals with Fubini ordering, `contourint`, `pvint`, `meanint`), upright functions and trigonometry, Leibniz and partial derivatives with ISO 80000-2 upright differentials - **Operators in display style** — `sum`, `prod`, `lim` keep fractions full-size and place limits under the word - **Full colour parity** — all 151 xcolor svgnames colours recognised, grouped by family in the [reference](#colour-reference) - **Cross-platform install** — documented `tlmgr` and manual paths for macOS, Linux and Windows --- ## Acknowledgments `scholatex` is built on excellent LaTeX packages: - [tcolorbox](https://ctan.org/pkg/tcolorbox) — framed boxes and posters - [tabularray](https://ctan.org/pkg/tabularray) — reliable 2-D table layout - [unicode-math](https://ctan.org/pkg/unicode-math) — OpenType maths - [fontspec](https://ctan.org/pkg/fontspec) — system fonts in LuaLaTeX - [xcolor](https://ctan.org/pkg/xcolor) — the svgnames colour palette --- ## License Copyright © 2026 Gérard Dubard. `scholatex` is free software: you can redistribute it and/or modify it under the terms of the **GNU General Public License version 3** (or later) as published by the Free Software Foundation. See the [`LICENSE`](LICENSE) file for the full text. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.