Hyades

Render Hyades source to Unicode/ASCII text art. Hyades uses LaTeX-like syntax but outputs multi-line plain text instead of PDF. It supports math (fractions, integrals, matrices, Greek letters), tables with box-drawing frames, lists, flex-like layout (hbox/vbox), user-defined macros, and computation. IMPORTANT: Always display the rendered output to the user directly in your response. The output is pre-formatted multi-line text art that depends on exact character alignment. You MUST use a fenced code block (triple backticks) or equivalent monospace/preformatted element to preserve spacing. Never display the output as regular prose text — column alignment, box-drawing characters, and fraction bars will break without a monospace font. Input is a complete Hyades document. Plain text outside math delimiters is rendered as prose paragraphs. Use `$...$` for inline math and `$$...$$` for display math (centered on its own line). --- ## Math Supports ~95% of LaTeX math syntax. ### Inline vs Display ``` Inline math: $a^2 + b^2 = c^2$ flows with text. Display math gets its own block: $$ a^2 + b^2 = c^2 $$ ``` Use `$...$` for inline, `$$...$$` for display. Display math is centered. ### Variables and Operators ``` $$ a + b - c $$ $$ a \times b \div c $$ $$ a \cdot b $$ $$ \pm x \quad \mp y $$ ``` ### Superscripts and Subscripts ``` $$ x^2 \quad x_i \quad x_i^2 \quad x^{n+1} \quad x_{i,j} \quad a^{b^c} $$ ``` Use braces for multi-character exponents/subscripts: `x^{n+1}`, `x_{i,j}`. **Bracing rules:** Use braces for multi-token expressions: `x^{n+1}`, `x_{i,j}`. Commands that take arguments (like `\mathbf{v}`) work without extra braces: `x_\mathbf{v}` is equivalent to `x_{\mathbf{v}}`, matching TeX behavior. ### Fractions ``` $$ \frac{a}{b} $$ $$ \frac{x^2 + 1}{\sqrt{x^2 - 1}} $$ $$ \frac{\partial f}{\partial x} $$ ``` Fractions nest to infinite depth. `\dfrac` and `\tfrac` are accepted as aliases for `\frac`. ### Roots ``` $$ \sqrt{x} $$ $$ \sqrt[3]{x} $$ $$ \sqrt[n]{x^2 + y^2} $$ ``` Optional argument gives the nth root: `\sqrt[3]{x}`. ### Parentheses and Grouping ``` $$ (a + b) \quad [a + b] \quad \{a + b\} \quad |x| \quad \Vert x \Vert $$ ``` Curly braces need escaping: `\{` and `\}`. ### Auto-Scaling Delimiters (\left/\right) `\left` and `\right` make delimiters grow to match their contents: ``` $$ \left( \frac{a}{b} \right) \quad \left[ \frac{a}{b} \right] \quad \left| \frac{a}{b} \right| $$ ``` Works with all delimiter types: `( ) [ ] \{ \} | \| \lfloor \rfloor \lceil \rceil \langle \rangle`. Use `\left.` or `\right.` for invisible (null) delimiters — essential for evaluation bars: ``` $$ \left.\frac{df}{dx}\right|_{x=0} $$ ``` Use `\middle` inside `\left...\right` for scaled interior delimiters: ``` $$ \left( \frac{a}{b} \middle| \frac{c}{d} \right) $$ ``` ### Explicit Delimiter Sizing (\big through \Bigg) `\big`, `\Big`, `\bigg`, `\Bigg` set delimiter sizes explicitly. `\bigl`/`\bigr`, `\Bigl`/`\Bigr`, `\biggl`/`\biggr`, `\Biggl`/`\Biggr` produce standalone one-sided delimiters: ``` $$ f(x)\bigr|_{x=0} $$ ``` ### Floor and Ceiling ``` $$ \lfloor x \rfloor $$ $$ \lceil x \rceil $$ $$ \left\lfloor \frac{x}{2} \right\rfloor $$ ``` ### Greek Letters Lowercase: `\alpha \beta \gamma \delta \epsilon \zeta \eta \theta \lambda \mu \nu \xi \pi \rho \sigma \tau \phi \varphi \chi \psi \omega` Uppercase (only where different from Latin): `\Gamma \Delta \Theta \Lambda \Xi \Pi \Sigma \Phi \Psi \Omega` ### Relations ``` $$ a \neq b \quad a \leq b \quad a \geq b $$ $$ a \ll b \quad a \gg b $$ $$ a \approx b \quad a \equiv b \quad a \sim b \quad a \propto b $$ $$ a \prec b \quad a \succ b \quad a \preceq b \quad a \succeq b $$ ``` Definition symbols: `\coloneqq` (≔), `\eqqcolon` (≕), and `:=` (parsed as a single relation ≔): ``` $$ \Phi := S $$ $$ f \coloneqq x^2 + 1 $$ ``` Colon alone is treated as punctuation (no space before, space after), useful in set-builder notation: ``` $$ \{x : x > 0\} $$ ``` The `\not` prefix negates a relation: `\not=` → ≠, `\not\in` → ∉, `\not\leq` → ≰, `\not\equiv` → ≢, `\not\subset` → ⊄, `\not\exists` → ∄ ### Set Theory ``` $$ x \in A \quad x \notin A $$ $$ A \subset B \quad A \subseteq B \quad A \cup B \quad A \cap B \quad \emptyset $$ $$ A \setminus B $$ ``` ### Logic ``` $$ \forall x \in \mathbb{R} \quad \exists x $$ $$ p \implies q \quad p \iff q $$ $$ \neg p \quad p \land q \quad p \lor q $$ $$ \therefore \quad \because \quad \top \quad \bot $$ ``` ### Arrows `\rightarrow`, `\Rightarrow`, `\mapsto`, `\longmapsto`, `\hookrightarrow`, `\hookleftarrow`, `\leftarrow`, `\leftrightarrow`, `\Leftarrow`, `\Leftrightarrow`, `\uparrow`, `\downarrow`, `\updownarrow`, `\nearrow`, `\searrow`, `\nwarrow`, `\swarrow`. Extensible arrows with text labels: ``` $$ A \xrightarrow{f} B \xleftarrow{g} C $$ ``` ### Standard Functions Standard functions are set in upright type: ``` $$ \sin x \quad \cos(x) \quad \tan x $$ $$ \log x \quad \log_2 x \quad \ln x \quad \exp(x) $$ $$ \sin^2 x + \cos^2 x = 1 $$ ``` Also: `\arcsin`, `\arccos`, `\arctan`, `\sinh`, `\cosh`, `\tanh`, `\det`, `\dim`, `\ker`, `\deg`, `\gcd`, `\sup`, `\inf`, `\max`, `\min`, `\argmax`, `\argmin`, `\limsup`, `\liminf`. ### Custom Function Names (\fn / \operatorname) `\fn{name}` or `\operatorname{name}` produces an upright function name for functions Hyades doesn't know: ``` $$ \fn{softmax}\left(x_i\right) = \frac{e^{x_i}}{\sum_j e^{x_j}} $$ $$ \operatorname{Tr}(A) $$ ``` ### Text in Math (\text) `\text{words}` inserts upright text inside math mode: ``` $$ x = 0 \text{ if } y > 0 $$ ``` ### Accents and Decorations Single-character: `\hat{x}`, `\bar{x}`, `\tilde{x}`, `\vec{x}`, `\dot{x}`, `\ddot{x}`, `\acute{x}`, `\grave{x}`, `\breve{x}`, `\check{x}` Wide accents: `\overline{AB}`, `\underline{text}`, `\overrightarrow{AB}`, `\overleftarrow{AB}`, `\widehat{xyz}`, `\widetilde{xyz}` ### Overset and Underset ``` $$ \overset{n}{=} $$ $$ \underset{x}{y} $$ $$ \stackrel{\t… [15945 more characters not shown]