261,480 tools. Last updated 2026-07-05 13:08
"namespace:app.vercel.wc-predict-zeta" matching MCP tools:
- Append a new row to a workspace's table surface. The data field is a JSON object with column-name keys. Status column accepts: drafted, queued, sealed, active, blocked. Works on any workspace; columns auto-seed on the first row if the table surface is empty. Multi-surface workspaces accept `surface_slug` to target a specific sheet (use `list_surfaces` to enumerate); omit it to fall through to the workspace's primary table surface. **Unmapped data fields:** Keys in `data` that don't match any existing column are still STORED on the row (nothing is dropped), but they won't render in the table UI until the column exists. The response carries an `unmapped_fields` array listing those keys plus a human-readable `warning` so an agent can decide whether to surface them, call `add_column`, or retry with `auto_create_columns: true`. **Auto-create columns:** Pass `auto_create_columns: true` to have the server append a fresh text column for every unmapped key in one atomic step (humanised label from the key, type `text`). The response then includes `created_columns: ColumnDef[]` with the new column metadata. Use this when you're appending machine-emitted rows whose shape you can't predict ahead of time; leave it omitted (default false) when you want explicit schema control.Connector
- Run a read-only SQL query in the project and return the result. Prefer this tool over `execute_sql` if possible. This tool is restricted to only `SELECT` statements. `INSERT`, `UPDATE`, and `DELETE` statements and stored procedures aren't allowed. If the query doesn't include a `SELECT` statement, an error is returned. For information on creating queries, see the [GoogleSQL documentation](https://cloud.google.com/bigquery/docs/reference/standard-sql/query-syntax). Example Queries: -- Count the number of penguins in each island. SELECT island, COUNT(*) AS population FROM bigquery-public-data.ml_datasets.penguins GROUP BY island -- Evaluate a bigquery ML Model. SELECT * FROM ML.EVALUATE(MODEL `my_dataset.my_model`) -- Evaluate BigQuery ML model on custom data SELECT * FROM ML.EVALUATE(MODEL `my_dataset.my_model`, (SELECT * FROM `my_dataset.my_table`)) -- Predict using BigQuery ML model: SELECT * FROM ML.PREDICT(MODEL `my_dataset.my_model`, (SELECT * FROM `my_dataset.my_table`)) -- Forecast data using AI.FORECAST SELECT * FROM AI.FORECAST(TABLE `project.dataset.my_table`, data_col => 'num_trips', timestamp_col => 'date', id_cols => ['usertype'], horizon => 30) Queries executed using the `execute_sql_readonly` tool will have the job label `goog-mcp-server: true` automatically set. Queries are charged to the project specified in the `projectId` field.Connector
- List Cassandra prediction verticals available via predict(domain, entity), with what each predicts and its data sources.Connector
- Forecast the next `horizon` readings of a canonical telemetry series using TimesFM (Google's time-series foundation model). Returns a point forecast plus quantile uncertainty bands (q0.1 … q0.9) — no per-machine training required. The kernel already normalizes raw OEM telemetry into canonical FCS fields; this predicts where a field is headed next. Args: time_series historical canonical values, oldest→newest (≥16 recommended) canonical_field the FCS field the series represents (e.g. "spindle_load_pct"), carried through for labeling/provenance horizon number of steps to predict (1–256, default 24) frequency accepted for forward-compat; TimesFM 2.5 auto-detects cadence USE WHEN: a user wants to know where a metric is trending — "what will spindle load look like over the next 2 hours", "project coolant temperature", "forecast throughput". For threshold/failure questions use predict_breach or remaining_life instead. PREMIUM (Pro tier) — runs ML inference (~$0.05/call once metered billing is active).Connector
- Predict the VAS (Viewability Attention Score) a specific creative would achieve at a given moment, based on historical data and causal modeling. Uses the CausalPredictionService which: 1. Embeds the moment description to find historically similar moments 2. If >= 5 similar moments exist with the same creative, uses weighted-average prediction 3. If insufficient data, falls back to Gemini generative prediction 4. Always decomposes the prediction into causal factors WHEN TO USE: - Evaluating whether a creative will perform well in a specific context - A/B testing creative placement hypotheses before committing budget - Understanding which causal factors drive VAS for a creative - Comparing expected performance across different moment types RETURNS: - prediction: { predictedVAS (0-1), confidence (0-1), method ('historical'|'model'), sampleSize } - causal_factors: { audienceMatch, contextMatch, attentionState, socialPotential } (each 0-1) - metadata: { creative_id, moment_description } - suggested_next_queries: Follow-up queries EXAMPLE: User: "How would a coffee ad perform at a transit station during morning rush?" predict_moment_quality({ moment_description: "transit venue, morning commute, 12 viewers, high attention, mostly 25-34 age range", creative_id: "coffee-brand-morning-30s" })Connector
- Statistically validated leading indicator signals evaluated against live supply chain data. Each signal is a Granger-causal relationship tested at p<=0.01 with directional accuracy >=55%. Signals predict commodity price movements, manufacturing shifts, and macroeconomic changes 1 week to 6 months ahead. Returns ACTIVE (threshold crossed — act now), WATCH (approaching threshold — prepare), or CLEAR status for each signal. 58 signals across 3 tiers organized by predictor group (GDI pillars, SMI regions, cross-index spreads). Used by commodity traders for forward-looking positioning, procurement teams for buy/defer timing, and hedge funds for alternative data signals.Connector
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- Flicense-qualityCmaintenanceProvides XGBoost-based directional predictions (UP/DOWN) for EURUSD and GBPUSD forex pairs via MCP tools, including feature extraction and signal generation.Last updated

ZetaChain CLIofficial
Alicense-qualityCmaintenanceEnables building and interacting with ZetaChain universal applications across multiple blockchains (EVM, Solana, Bitcoin, Sui, TON). Supports scaffolding projects, querying cross-chain data, managing balances, and executing cross-chain calls through natural language.Last updated1026ISC
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Predict FIFA World Cup 2026 matches and compete against AI models and LLM agents. Submit predictions, check the leaderboard, and list upcoming matches.
Cassandra prediction hub: one MCP door over govcon forecasts (recompete, contractor signals).
- Statistically validated leading indicator signals evaluated against live supply chain data. Each signal is a Granger-causal relationship tested at p<=0.01 with directional accuracy >=55%. Signals predict commodity price movements, manufacturing shifts, and macroeconomic changes 1 week to 6 months ahead. Returns ACTIVE (threshold crossed — act now), WATCH (approaching threshold — prepare), or CLEAR status for each signal. 58 signals across 3 tiers organized by predictor group (GDI pillars, SMI regions, cross-index spreads). Used by commodity traders for forward-looking positioning, procurement teams for buy/defer timing, and hedge funds for alternative data signals.Connector
- KILLER ANALYSIS: given a target KPI + multiple candidate indicators, rank which candidates best predict the target by correlation strength. Perfect for "what moves my KPI?" questions. Returns ranked list with r, p-value, R² for each candidate. Maximum 30 candidates per call.Connector
- Use the app's AI gateway: chat, embeddings, list models, read/update config, read usage. Actions: - chat { app_id, messages, model?, temperature?, max_tokens? } Synchronous (no streaming). Returns the full assistant response. Default model is the app's configured default, or "openai/gpt-4o-mini". - embed { app_id, input (string | string[]), model?, encoding_format? } Returns OpenAI-shaped embedding response. - list_models { app_id } Returns { models: AiModel[] } — discover what the app can call. - get_config { app_id } Returns { defaultModel, allowedModels, maxTokensPerRequest, ... } - update_config { app_id, config } Set defaultModel, allowedModels, maxTokensPerRequest (1–100000), or rotate BYOK. - get_usage { app_id, startDate?, endDate? } Aggregate token counts and costs over a window. - submit_video { app_id, model, prompt, duration?, resolution?, aspect_ratio?, generate_audio?, seed? } Submits an async video-generation job. Returns { job_id, status, polling_url }. Poll the returned URL until status is "completed". - poll_video { app_id, job_id } Returns current { status, model, content_urls?, error?, created_at }. When status is "completed", content_urls contains absolute URLs (same origin as the polling_url) that the caller can fetch() directly using the same Authorization header. Use this to drive your own polling loop. - start_meeting { app_id, meeting_url, transcript?, recording?, metadata?, bot_name?, automatic_leave? } Spawn a meeting bot that joins a Zoom/Meet/Teams/Webex call. recording: "mp4" (default), "audio_only", or false. transcript defaults to true. bot_name (1–64 chars) sets the display name attendees see; defaults to "Butterbase Notetaker". automatic_leave: per-bot overrides for the auto-leave timers (in seconds, positive ints, max 86400). Any sub-field omitted inherits the provider default. - waiting_room_timeout_sec — leave if still in the waiting room after N seconds - no_one_joined_timeout_sec — leave if no participants joined within N seconds - everyone_left_timeout_sec — leave N seconds after the last participant leaves - in_call_not_recording_timeout_sec — leave if in-call but not recording for N seconds Example: automatic_leave: { waiting_room_timeout_sec: 900 } makes the bot give up after 15 min in the waiting room. Returns { id, status, botName, ... }. Save id to call get_meeting / stop_meeting later. - get_meeting { app_id, meeting_id } Current status + recordingUrl / transcriptUrl (populated when artifacts are ready). - list_meetings { app_id, status?, limit?, cursor? } Page through this app's bots. status filters to a lifecycle phase (joining / waiting_room / in_call / recording / ended / done / fatal). - stop_meeting { app_id, meeting_id } Force the bot to leave the call. Returns 204 / no body on success. - estimate_meeting { app_id, duration_minutes, transcript? } Predict the USD charge for a hypothetical session at this duration. - configure_meetings_webhook { app_id, forward_url, rotate_secret? } Upsert the app's meetings webhook forward URL. When rotate_secret is true (or no row exists), generates a new signing secret (wsec_…) and returns it once — store it immediately. The secret is the HMAC-SHA256 key that signs every forwarded event for THIS app — see the "meetings" topic in butterbase_docs for verification details. Returns { ok, app_id, forward_url, secret } where secret is null when not rotated. - usage_meetings { app_id } Returns the last 100 rows from actor_usage_logs for the app. Each row has { id, dimension, seconds, usd_charged, created_at }. This tool wraps the same /v1/:app_id/chat/completions, /embeddings, /ai/config, /ai/models, /ai/usage routes the SDK uses. The "chat" action sets stream: false; for streamed deltas, drive the SDK from inside a function or DO.Connector
- Predict whether — and when — a canonical series will cross a threshold. This is the parametric-insurance primitive: it answers "will this machine's <field> exceed <threshold> within the forecast window, and how soon?". Returns will_breach, estimated_steps_to_breach, a confidence, and a quantile-derived breach_window {earliest, latest}. Every result carries a deterministic data_hash so the prediction is cryptographically provable. Pass a caller-owned `mint_id` to write a MINT audit event tying the prediction to a specific machine; add `settle=true` to anchor it on-chain (Solana) for an insurance-grade, tamper-evident record. Args: time_series historical canonical values, oldest→newest (≥16 recommended) threshold the value to test for a crossing (e.g. 95.0 for 95% load) canonical_field FCS field the series represents (e.g. "spindle_load_pct") direction "above" (default) or "below" — which side is the breach horizon steps to look ahead (1–256, default 96) mint_id caller-owned machine to anchor provenance to (optional) settle if true and mint_id is owned, anchor on-chain (costs a fee) USE WHEN: a user asks if/when a limit will be hit — "will spindle load breach 95% this shift", "is coolant temp going to exceed 35°C", "alert me before pressure drops below 2 bar". PREMIUM (Pro tier), ~$0.05/call.Connector
- Analyze the user's CLOSED deals (won + lost) to surface which attributes actually predict wins. Computes win rate per attribute value WITH sample size, and ranks attributes by the spread between their best- and worst-converting values — the data version of the win-rate-by-signal motion. By default cuts by source, type, and owner; pass `attributes` to add any field present on the deals (e.g. segment, competitor, size). Values below `minSample` (default 5) are suppressed as noise. Accepts loosely-typed deal records; needs an `outcome` of won/lost (aliases: outcome/status). Returns the ranked attributes with per-value win rates and the reallocation takeaway. Operates only on supplied deals. Use when the user asks 'which sources/signals convert best', 'why are we winning/losing', or pastes closed-won and closed-lost deals.Connector
- Flag anomalies in a time series WITHOUT running a full forecast — z-score + IQR outlier detection plus trend and rate-of-change (accelerating/steady/ decelerating). No TimesFM inference, so it's faster and cheaper than predict and works on short series (≥4 points). Cross-references the canonical field's known/derived normal range when one is available. Args: values the series to scan (≥4 points) canonical_field FCS field the series represents (enables normal-range context) sensitivity z-score threshold (default 2.0 ≈ 95%); higher = fewer flags Returns anomaly_count, per-anomaly detail (index, value, z_score, deviation, severity: critical/warning/minor), summary statistics, and an attestation hash. USE WHEN: real-time monitoring or a spot check — "is this reading abnormal", "any outliers in the last hour", "flag spikes in vibration". For 'where is it headed' use predict; for 'will it cross X' use predict_breach. PREMIUM (Pro tier) — $0.02/call (no ML inference).Connector
- Predict the next-step value of 4 environmental scalars at a cell — `indices.ndvi`, `modis.lst_day_8day`, `modis.lst_night_8day`, `cams.pm25` — using a small learned dynamics MLP. Reads up to K=6 most-recent attested lags per band, runs them through an ONNX dynamics head (~200k params, CPU-fast), and returns a per-band {value, confidence, n_real_lags, via}. The receipt's `model` block carries `model_id`, `version`, `blake2b_hex` (model_cid), training/validation provenance, a top-level `skill_vs_persistence` block, and `honesty_warnings` — flagging `untrained_baseline` when the artifact is the zero-init sentinel and `NEGATIVE_SKILL` when the learned model is worse than persistence on real held-out NDVI. When the model does not beat persistence, bands with a real lag are returned from that lag tagged `via:persistence_fallback_negative_skill` (bands with no real lag fall back to labelled climatology). Distinct from v1 (`emem_jepa_predict`) which returns a single NDVI scalar via closed-form coefficients. When to use: Use when you want a short-horizon forecast of NDVI / land-surface temperature / PM2.5 at a cell grounded in its attested history. Returns 422 with a `/v1/backfill` hint when the cell lacks enough cached lags. Always read the receipt's `model.honesty_warnings` — `untrained_baseline` means the trivial 'predict last vintage' baseline (treat as no-op), and `NEGATIVE_SKILL` means the served values are the persistence fallback, not a learned improvement. Check each band's `via` field to see whether its value came from the learned model, persistence, or climatology.Connector
- Report how well the kernel's predictions have matched reality: total and evaluated prediction counts, breach-prediction accuracy %, forecast mean absolute error, and accuracy broken down by canonical field. FREE — this is a trust signal. Check it BEFORE deciding to pay for a prediction: "87% breach accuracy across 500 predictions" is the best evidence that the paid forecast is worth buying. Accuracy improves over time as more predictions are tracked and verified against actuals (each is logged with a tamper-evident hash). USE WHEN: a user (or you, on their behalf) wants to gauge how much to trust the forecasts before spending on predict / predict_breach / machine_intelligence.Connector
- Return step-by-step instructions for setting up x402 USDC autopay for this MCP server. Use this if a paid tool returned a 402 error or you're onboarding a new agent that needs to pay for API calls. Free.Connector
- Predict times across 5K / 10K / Half / Marathon from a known race result, using the Riegel exponent (1.06) and age-graded performance scores against IAAF world records. Source: ham.run race predictor. Pass useMyData:true to overlay age + sex from the connected athlete profile.Connector
- List all paid endpoints exposed by this MCP server with their prices and live status. Free — no wallet required. Use this first to discover what tools are available.Connector
- Return ready-to-paste configuration snippets for installing this MCP server in Claude Code, Cursor, Cline, Continue.dev, Windsurf, and Zed. Free.Connector
- Predict what the audience will look like at a screen at a specific time. WHEN TO USE: - Planning campaigns for specific time slots - Estimating audience composition before buying - Comparing audience at different times of day Uses historical audience data to predict typical audience patterns. RETURNS: - predicted_face_count: Expected number of viewers - predicted_attention: Expected attention score - typical_income: Most common income level at that time - typical_lifestyle: Most common lifestyle segment at that time - confidence: Prediction confidence (0-1, based on sample count) - sample_count: Number of historical data points used EXAMPLE: User: "What's the typical audience at this screen on Monday at 3pm?" get_audience_forecast({ screen_id: "507f1f77bcf86cd799439011", hour: 15, day: 1, lookback_days: 30 })Connector
- 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 ``` $$ \overset{n}{=} $$ $$ \underset{x}{y} $$ $$ \stackrel{\text{def}}{=} $$ ``` `\overset{top}{base}` places annotation above base; `\underset{bot}{base}` below. `\stackrel` is an alias for `\overset`. ### Overbrace and Underbrace ``` $$ \overbrace{a + b + c}^{3 \text{ terms}} $$ $$ \underbrace{x + y + z}_{n \text{ terms}} $$ ``` ### Primes ``` $$ f'(x) \quad f''(x) \quad f'''(x) \quad f^{(n)}(x) $$ ``` ### Math Fonts `\mathbf{v}` → bold, `\mathbb{R}` → blackboard bold (ℕℤℚℝℂ), `\mathcal{L}` → calligraphic, `\mathfrak{R}` → Fraktur (𝔄𝔅ℭ), `\mathsf{A}` → sans-serif (𝖠𝖡𝖢), `\mathscr{A}` → script (same as \mathcal), `\boldsymbol{\alpha}` → bold (works with Greek: 𝛂𝛃, and symbols: `\boldsymbol{\nabla}` → 𝛁, `\boldsymbol{\partial}` → 𝛛) ### Dots and Ellipses `\ldots` (low dots, for commas), `\cdots` (centered, for operators), `\vdots` (vertical), `\ddots` (diagonal, for matrices) ### Summation ``` $$ \sum_{i=1}^{n} x_i $$ ``` `\Sum` and `\SUM` give progressively larger variants. ### Products ``` $$ \prod_{i=1}^{n} x_i $$ ``` `\Prod` and `\PROD` give larger variants. ### Integrals ``` $$ \int_a^b f(x) \, dx $$ $$ \iint f(x,y) \, dx\,dy $$ $$ \oint_C f(z) \, dz $$ ``` Also: `\iiint`, `\oiint`. Larger variants: `\Int`, `\INT`, etc. ### Limits `\lim` places its subscript directly below: ``` $$ \lim_{x \to 0} \frac{\sin x}{x} = 1 $$ $$ \max_{x \in [0,1]} f(x) $$ $$ \argmax_{\theta} L(\theta) $$ ``` ### Calculus Operators ``` $$ \frac{dy}{dx} \quad \frac{d^2y}{dx^2} \quad \frac{\partial f}{\partial x} $$ $$ \nabla f \quad \nabla \cdot \mathbf{F} \quad \nabla \times \mathbf{F} \quad \nabla^2 f $$ ``` ### Matrices Six types with different delimiters. `&` separates columns, `\\` or `;` separates rows. LaTeX-style `\begin{pmatrix}...\end{pmatrix}` also works for all matrix types. ``` $$ \pmatrix{a & b \\ c & d} $$ % (parentheses) $$ \bmatrix{a & b \\ c & d} $$ % [brackets] $$ \Bmatrix{a & b \\ c & d} $$ % {braces} $$ \vmatrix{a & b \\ c & d} $$ % |bars| (determinants) $$ \Vmatrix{a & b \\ c & d} $$ % ‖double bars‖ (norms) $$ \matrix{a & b \\ c & d} $$ % no delimiters ``` ### Cases (Piecewise Functions) ``` $$f(x) = \cases{ x & \text{if } x > 0 \\ 0 & \text{if } x = 0 \\ -x & \text{if } x < 0 }$$ ``` ### Aligned Equations `&` marks the alignment point: ``` $$\aligned{ f(x) &= x^2 + 2x + 1 \\ &= (x + 1)^2 }$$ ``` Use `\intertext{...}` inside aligned to insert prose between rows. Intertext is left-aligned at the document margin while equations remain centered: ``` $$\aligned{ x &= a \\ \intertext{where} a &= b + c }$$ ``` `\tag` works on aligned blocks — the tag is right-justified and vertically centered: ``` $$\aligned{ f(x) &= x^2 + 2x + 1 \\ &= (x + 1)^2 } \tag{7}$$ ``` ### Boxed ``` $$ \boxed{E = mc^2} $$ ``` Draws a box-drawing frame around the content. ### Phantom ``` $$ a + \phantom{bbb} + c $$ ``` Invisible placeholder — renders as whitespace with the same dimensions as the content. ### Smash ``` $$ \sqrt{\smash{y^3}} $$ ``` `\smash{content}` renders content but collapses its height to a single line (the baseline row). Used to prevent tall content from affecting surrounding constructs like roots or delimiters. ### Substack ``` $$ \sum_{\substack{i=1 \\ j>0}} x_{ij} $$ ``` Stacks multiple lines vertically (for multi-line subscripts/superscripts). ### Tag ``` $$ E = mc^2 \tag{1} $$ ``` Equation tag rendered as `(text)`. ### Number Theory ``` $$ a \equiv b \pmod{n} $$ $$ a \bmod n \quad a \mid b $$ $$ \binom{n}{k} $$ ``` ### Style Commands (No-ops) `\displaystyle`, `\textstyle`, `\scriptstyle`, `\scriptscriptstyle` are accepted but transparent (Hyades has no math size concept). `\notag` and `\nonumber` are also silently ignored. This allows pasting LaTeX source that uses these commands without errors. ### Math Spacing `\!` (negative thin), `\,` (thin), `\:` (medium), `\;` (thick), `\quad` (1em), `\qquad` (2em) ### Atom-Type Overrides (\mathord, \mathbin, \mathrel) Override the default spacing category of a symbol. Analogous to TeX's `{=}` idiom for suppressing operator spacing, but explicit and readable: ``` $a \mathord{=} b$ %% "a=b" — = treated as ordinary symbol (no spacing) $a = b$ %% "a = b" — default relation spacing $f \mathrel{:} A \to B$ %% "f : A → B" — : treated as relation (symmetric spacing) $a : b$ %% "a: b" — default punctuation spacing $a \mathbin{\triangle} b$ %% "a △ b" — triangle with binary operator spacing ``` - `\mathord{X}`: Suppress spacing — X renders as an ordinary symbol with no surrounding gaps. Use this instead of TeX's `{=}` or `{}=` idiom which does not work in Hyades. - `\mathbin{X}`: Force binary operator spacing (gap on both sides). - `\mathrel{X}`: Force relation spacing (gap on both sides). ### Binary Operators `\oplus`, `\otimes`, `\odot`, `\circ`, `\bullet`, `\star`, `\dagger`, `\ddagger` ### Geometry `\angle`, `\triangle`, `\perp`, `\parallel` ### Famous Equations (all valid input) ``` $$ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $$ %% Quadratic formula $$ e^{i\pi} + 1 = 0 $$ %% Euler's identity $$ f(x) = \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{(x-\mu)^2}{2\sigma^2}} $$ %% Normal distribution $$ \fn{Attention}(Q, K, V) = \fn{softmax}\left(\frac{QK^\top}{\sqrt{d_k}}\right) V $$ %% Attention mechanism $$ e^x = \sum_{n=0}^{\infty} \frac{x^n}{n!} $$ %% Taylor series $$ \int_{-\infty}^{\infty} e^{-x^2} dx = \sqrt{\pi} $$ %% Gaussian integral $$ P(A|B) = \frac{P(B|A) P(A)}{P(B)} $$ %% Bayes' theorem $$ \nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t} $$ %% Maxwell's equation $$ i\hbar \frac{\partial}{\partial t} \Psi = \hat{H} \Psi $$ %% Schrodinger equation $$ \fn{softmax}(x_i) = \frac{e^{x_i}}{\sum_j e^{x_j}} $$ %% Softmax ``` --- ## Text Formatting ``` \textbf{bold text} \textit{italic text} \texttt{monospace text} \textbf{\textit{bold italic}} ``` Nesting `\textbf` and `\textit` produces bold-italic text. Inline math `$...$` inside `\textit` or `\textbf` is rendered as math (not styled as text): ``` \textit{Let $f(x) = x^2$ be a function} ``` ### Verbatim (No Processing) ``` \verb|raw \commands { } are preserved| ``` ### Special Characters `\textbackslash` → \, `\textdollar` → $, `\textpercent` → %, `\textampersand` → &, `\texthash` → # ### Text Spacing Commands `\ ` (backslash-space) — explicit inter-word space. Useful after abbreviations: `i.e.\ $f$` renders without extra sentence spacing. `\@` — marks the next period as sentence-ending (silently consumed). `\,` — thin space (works in both text and math mode). --- ## Paragraphs and Line Breaking Text flows into paragraphs automatically. A single newline is a space; a blank line starts a new paragraph. ### Line-Breaking Modes ``` \linebreaker{greedy} % Default. Fast, good results. \linebreaker{knuth} % TeX-style optimal. Minimizes ugliness. \linebreaker{raggedright} % Left-aligned, no justification. ``` ### Hyphenation `\sethyphenate{true}` / `\sethyphenate{false}` --- ## Tables Tables use `\table` with nested `\row` and `\col`: ``` \table[width:40, frame:single, pad:{l:1,r:1}]{ \row[frame:{b:double}]{ \col{Name} \col{Value} } \row{ \col{Alpha} \col{0.05} } \row{ \col{Beta} \col{0.95} } } ``` ### Table Properties | Property | Values | Default | |----------|--------|---------| | `width` / `w` | number, `auto` | parent width | | `frame` / `f` | `none`, `dotted`, `single`, `rounded`, `double`, `bold` | `single` | | `border` | same as frame (outer edges only) | unset | | `pad` / `p` | number or `{t:N, b:N, l:N, r:N}` | 0 | | `align` / `a` | `l`/`left`, `c`/`center`, `r`/`right` | `l` | | `valign` / `va` | `t`/`top`, `m`/`middle`, `b`/`bottom` | `t` | Row properties: `frame`, `pad`, `align`, `valign`, `height`. Column properties: `width`, `align`, `valign`, `frame`, `pad`, `span`, `reset`. Frame styles: `none` (space), `dotted` (┄┆), `single` (─│), `rounded` (╭╮╰╯ corners), `double` (═║), `bold` (━┃) Compound edges: `frame:{t:double, b:single, l:none, r:none}`, `pad:{l:1, r:1}` Properties cascade: table → column (down rows) → row → cell. IMPORTANT: When a row overrides a property (e.g. `frame:{b:double}`), that override is inherited by ALL subsequent rows. To stop it, the next row must explicitly reset it (e.g. `frame:{b:single}`). The `border` property on the table level controls the outer edges and cannot be overridden by row or column `frame`. --- ## Lists ``` \fancylist{ - First item - Second item with longer text that wraps to the next line - Third item - Nested child - Grandchild } ``` Three nesting levels supported. Uses ●/○ bullets in Unicode, - in ASCII. --- ## Layout Primitives Flex-like box model for spatial control. ### Box Types ``` \begin[width]{hbox} % horizontal (side by side) \child[width][align]{content} \end{hbox} \begin[top|middle|bottom]{hbox} % hbox with vertical alignment \child[width][align]{content} \end{hbox} \begin[width]{vbox} % vertical (stacked) \child[width][align]{content} \end{vbox} ``` Child width: fixed number, `auto` (fill remaining), `intrinsic` (natural width), or omitted (equal share). When multiple children omit width, they split the remaining space equally (after fixed-width children). Horizontal alignment: `left`, `center`, `right`. Vertical alignment for hbox: set on `\begin` bracket — `top` (default), `middle`, `bottom`. Width inheritance: boxes without an explicit width inherit their parent's width. `\setwidth{N}` sets the document-level width. ### Rules ``` \hrule[width]{left_cap}{fill_char}{right_cap} \vrule[height]{top}{fill}{bottom} \intersect_rules{...} % fix junction characters at rule crossings ``` Width/height can be a number or `auto`. An `auto`-width `\hrule` in a vbox stretches to the box width. An `auto`-height `\vrule` in an hbox stretches to match the tallest sibling. `\intersect_rules` scans all cells, checks neighboring line arms, and replaces with correct junction glyphs (┌ ┬ ┐ ├ ┼ ┤ └ ┴ ┘). Handles single, double, bold, and mixed styles. ### Measuring Content ``` \measure<content_name,width_var,height_var>{content to measure} ``` Renders content invisibly, stores it under `content_name` (retrieve with `\recall<content_name>`), and stores the measured width and height into integer variables. ### Spacing `\vskip{N}` (N blank lines), `\hskip{N}` (N spaces) ### Common Layout Patterns Two-column with gutter: ``` \begin{hbox} \child{Left column} \child[2]{} \child{Right column} \end{hbox} ``` Centering via auto spacers: ``` \begin{hbox} \child[auto]{} \child[intrinsic]{Centered content} \child[auto]{} \end{hbox} ``` Indentation: ``` \begin{hbox} \child[4]{} \child[auto]{Indented content} \end{hbox} ``` --- ## User-Defined Macros ``` \macro<\greet{name}>{Hello, ${name}!} \greet{World} % → Hello, World! \macro<\fullname{first}{last}>{${first} ${last}} \fullname{John}{Doe} % → John Doe % Optional parameters with defaults \macro<\heading[char=-]{title}>{ ${title} \hrule[20]{}{${char}}{} } \heading{Default} % uses - \heading[char:=]{Custom} % uses = ``` --- ## Document Settings ``` \setwidth{80} % Output width in columns (default: 80) \setunicode{true} % Use Unicode symbols (default: true) \setmathitalic{true} % Italicize math variables (default: true) \linebreaker{greedy} % Line-breaking algorithm \sethyphenate{true} % Enable hyphenation \setparskip{1} % Blank lines between paragraphs \setmathabove{1} % Blank lines above display math (default: 0) \setmathbelow{1} % Blank lines below display math (default: 0) ``` --- ## Computation Variables, loops, and conditionals are available. ### Variables and Arithmetic ``` \let<x>{10} \let<y>{20} \let<sum>{\add{\valueof<x>,\valueof<y>}} Result: \valueof<sum> % → Result: 30 ``` ### Conditionals ``` \let<n>{42} \if{\gt{\valueof<n>,0}}{positive}\else{non-positive} ``` ### Loops ``` \let<i>{1} \begin{loop} \exit_when{\gt{\valueof<i>,5}} \valueof<i>\hskip{1} \inc<i> \end{loop} % Output: 1 2 3 4 5 ``` ### Content Storage `\assign<name>{content}` stores text, `\recall<name>` retrieves it. `\let`/`\valueof` is for integers; `\assign`/`\recall` is for text. ### Lambdas ``` \lambda<double>[x]{\mul{\recall<x>,2}} \recall<double>[5] % → 10 ``` ### Arrays ``` \let<nums[]>{[10, 20, 30]} \valueof<nums>[0] % → 10 \len<nums> % → 3 \push<nums>{40} % append ``` --- ## Quick Reference ### Math Mode | Input | Output | |-------|--------| | `$x^2$` | x² | | `$x_i$` | xᵢ | | `$\frac{a}{b}$` | a/b (stacked) | | `$\sqrt{x}$` | √x | | `$\sum_{i=1}^n$` | Σ with limits | | `$\int_a^b$` | ∫ with limits | | `$\prod_{i=1}^n$` | ∏ with limits | | `$\lim_{x \to 0}$` | lim with subscript below | | `$\limsup_{n}$` | lim sup with subscript below | | `$\liminf_{n}$` | lim inf with subscript below | | `$\alpha, \beta, \gamma$` | α, β, γ | | `$\mathbb{R}$` | ℝ | | `$\mathbf{v}$` | 𝐯 | | `$\leq, \geq, \neq$` | ≤, ≥, ≠ | | `$\in, \forall, \exists$` | ∈, ∀, ∃ | | `$\rightarrow, \Rightarrow$` | →, ⇒ | | `$\infty, \partial, \nabla$` | ∞, ∂, ∇ | | `$f'(x)$` | 𝑓′(𝑥) | | `$\binom{n}{k}$` | binomial coefficient | | `$\lfloor x \rfloor$` | ⌊x⌋ | | `$\fn{name}$` | custom function name | | `$\operatorname{name}$` | same as \fn | | `$\text{words}$` | upright text in math | | `$\ll, \gg$` | ≪, ≫ | | `$\mathord{=}$` | suppress operator spacing | | `$\mathbin{:}$` | force binary operator spacing | | `$\mathrel{:}$` | force relation spacing | | `$\prec, \succ$` | ≺, ≻ | | `$\neg, \land, \lor$` | ¬, ∧, ∨ | | `$\subseteq, \setminus$` | ⊆, ∖ | | `$\mid$` | ∣ (divides) | | `$\therefore, \because$` | ∴, ∵ | | `$\wp, \imath, \jmath$` | ℘, ı, ȷ | | `$\Box$` | □ | | `$\not=$` | ≠ (\not prefix negates relations) | | `$\left.\right\|$` | invisible delimiter (evaluation bar) | | `$\overset{n}{=}$` | annotation above base | | `$\underset{x}{y}$` | annotation below base | | `$\boxed{x}$` | framed box around content | | `$\phantom{x}$` | invisible spacer | | `$\smash{x}$` | collapse height to baseline | | `$\xrightarrow{f}$` | extensible arrow with label | | `$\substack{a \\ b}$` | stacked lines | | `$\mathfrak{R}$` | Fraktur (𝔄𝔅ℭ) | | `$\mathsf{A}$` | sans-serif (𝖠𝖡𝖢) | | `$\boldsymbol{\alpha}$` | bold Greek (𝛂𝛃) | | `$\coloneqq$` | ≔ (definition) | | `$\eqqcolon$` | ≕ (reverse definition) | | `$a := b$` | ≔ (combined relation) | ### Text Commands | Command | Effect | |---------|--------| | `\textbf{x}` | **bold** | | `\textit{x}` | *italic* | | `\texttt{x}` | monospace | | `\verb\|x\|` | verbatim | | `\hrule` | horizontal line | | `\vskip{N}` | N blank lines | | `\hskip{N}` | N spaces | ### Table Syntax ``` \table[width:W, frame:STYLE, pad:{l:L,r:R}, border:STYLE, align:A]{ \row[frame:{b:STYLE}]{ \col[width:N, align:A]{content} } } ``` ### Layout Syntax ``` \begin[width]{vbox} \child[width][h_align]{content} \end{vbox} \begin[top|middle|bottom]{hbox} \child[width][h_align]{content} \end{hbox} ``` ### Settings ``` \setwidth{N} \setunicode{true|false} \setmathitalic{true} \linebreaker{greedy|knuth|raggedright} \sethyphenate{true} \setparskip{N} \setmathabove{N} \setmathbelow{N} ```Connector