# Equation.io

> Create interactive 2D and 3D graphs with validated equations, shareable links, and PNG previews.

- name: io.equation/equation
- version: 1.0.1
- connection class: R0 (autonomous)
- trust: 95/100
- quality: 88/100 (good)
- owner: not claimed
- descriptor: https://api.protogrid.dev/v1/servers/io.equation%2Fequation
- tools: https://api.protogrid.dev/v1/servers/io.equation%2Fequation/tools

**An agent can connect right now, no human step.** Remote endpoint, no authentication, reachable on the last probe.

## Connection (mcpServers)

```json
{
  "mcpServers": {
    "equation": {
      "type": "http",
      "url": "https://equation.io/mcp"
    }
  }
}
```


## Trust

- hygiene: 100
- liveness: 99
- freshness: 100
- provenance: 85
- drivers: +repository +dns-namespace +website +reachable +uptime-97% +updated-18d-ago
- Derived from observable signals (official registry feed and our own credential-free probes); no code audit performed.

## Quality 88/100 (good)

### protocol: 75 (weight 25)

- warn `protocol.modern`: newest supported version is 2025-06-18; 2026-07-28 not supported, older versions are deprecated until 2027-07-28
- n/a `protocol.stateless`: only applies to 2026-07-28 servers
- pass `protocol.transport`: streamable HTTP
- n/a `protocol.list_ttl`: only applies to 2026-07-28 servers

### authorization: n/a (weight 15)

- n/a `auth.prm`, `auth.as_metadata`, `auth.cimd`: no remote uses OAuth
- n/a `auth.secret_in_url`: no templated URL

### tool hygiene: 93 (weight 30)

- pass `tools.descriptions`: every tool has a description
- warn `tools.description_length`: 1 tools have descriptions over 1,024 characters, which crowds the context
- pass `tools.schemas`: every tool has an object input schema
- pass `tools.annotations`: 3 of 3 tools declare readOnlyHint or destructiveHint
- pass `tools.directory_hints`: every tool declares readOnlyHint, destructiveHint, idempotentHint and openWorldHint
- pass `tools.token_cost`: about 900 tokens to load every tool
- pass `tools.api_dump`: tools are not a one-to-one API dump

### stability: 100 (weight 15)

- pass `stability.changes`: 5 tool changes in 30 days
- pass `stability.rug_pull`: no tool changed its meaning under the same name

### dependencies: n/a (weight 15)

- n/a `deps.known_vulns`, `deps.mcp_sdk_version`, `deps.resolvable`: no npm or PyPI package

- tools: 3, about 900 tokens to load them all
- tool set hash: ee828bc763d704b508516d5a0cbf1f8e
- tools last changed: 2026-10-18T12:28:03.189Z
- badge: [![protogrid quality](https://protogrid.dev/badge/io.equation/equation.svg)](https://protogrid.dev/servers/io.equation/equation)
- Checks run on what our credential-free, read-only probes observe; tools are never called and no code audit is performed.

### Tool changes

- 2026-10-18 `encode_graph_url` changed (description, outputSchema)
  - before: Build an equation.io graph link, validating every row with the app's parser. Pass the COMPLETE graph in "equations": a flat array of strings, one equation or definition per string, in display order — when editing an existing graph (see decode_graph_url), include unchanged rows too. Rows can be: equations and inequalities in x,y (curves, regions; z makes it 3D), bare expressions in x, y (scalar fields — a curve is written y = f(x); complex plots via w), points (rows report "draggable"), parametric tuples in u,v — and definitions: "a = 2" (a draggable slider), "f(x) = x^3 - a x", coordinate fields like "r = sqrt(x^2+y^2)" for polar. t animates. Also derivatives d/dx, integrals int[a..b] f dx, sums sum[n=1..N], domain()/conformal()/iter() for complex plots, rgb()/hsl()/oklch() color fields, y' = … slope fields, random variables "X ~ Normal(m, s)"/"P(0<X<2)"/"E(X^2)", and "view(x = -5..5, y = -2..2)"/"camera(theta, phi)" framing rows. That is a menu, not the syntax: before your first non-trivial graph, read the "syntax" MCP resource (also at https://equation.io/llms.txt). The result returns text and structured data only. "rows" gives each equation's validation result: status "ok" with its kind, or "error" with the parser message. The link is usable only once every row is "ok". Give users the share_url (it unfurls to a preview card in chat apps); url is the equivalent #-fragment form. "preview" and "preview_omits" describe the share link's simplified static preview (t = 0, 3D as wireframes), which draws less than the interactive app. No image is attached to the tool response.
  - after: Build an equation.io graph link, validating every row with the app's parser. Pass the COMPLETE graph in "equations": a flat array of strings, one equation or definition per string, in display order — when editing an existing graph (see decode_graph_url), include unchanged rows too. Rows can be: equations and inequalities in x,y (curves, regions; z makes it 3D), bare expressions in x, y (scalar fields — a curve is written y = f(x); complex plots via w), points (rows report "draggable"), parametric tuples in u,v — and definitions: "a = 2" (a draggable slider), "f(x) = x^3 - a x", coordinate fields like "r = sqrt(x^2+y^2)" for polar. t animates. Also derivatives d/dx, integrals int[a..b] f dx, sums sum[n=1..N], domain()/conformal()/iter() for complex plots, rgb()/hsl()/oklch() color fields, y' = … slope fields, random variables "X ~ Normal(m, s)"/"P(0<X<2)"/"E(X^2)", and "view(x = -5..5, y = -2..2)"/"camera(theta, phi)" framing rows. That is a menu, not the syntax: before your first non-trivial graph, read the "syntax" MCP resource (also at https://equation.io/llms.txt). The result returns text and structured data only. "rows" gives each equation's validation result: status "ok" with its kind, or "error" with the parser message. The link is usable only once every row is "ok". Give users the share_url (it unfurls to a link card in chat apps); url is the equivalent #-fragment form. No image is attached to the tool response.
- 2026-10-02 `show_graph` changed (annotations)
- 2026-10-02 `decode_graph_url` changed (annotations)
- 2026-10-02 `encode_graph_url` changed (annotations)
- 2026-09-27 `encode_graph_url` changed (description)
  - before: Build an equation.io graph link, validating every row with the app's parser. Pass the COMPLETE graph in "equations": a flat array of strings, one equation or definition per string, in display order — when editing an existing graph (see decode_graph_url), include unchanged rows too. Rows can be: equations and inequalities in x,y (curves, regions; z makes it 3D), bare expressions (scalar fields; complex plots via w), points (rows report "draggable"), parametric tuples in u,v — and definitions: "a = 2" (a draggable slider), "f(x) = x^3 - a x", coordinate fields like "r = sqrt(x^2+y^2)" for polar. t animates. Also derivatives d/dx, integrals int[a..b] f dx, sums sum[n=1..N], domain()/conformal()/iter() for complex plots, rgb()/hsl()/oklch() color fields, y' = … slope fields, random variables "X ~ Normal(m, s)"/"P(0<X<2)"/"E(X^2)", and "view(x = -5..5, y = -2..2)"/"camera(theta, phi)" framing rows. That is a menu, not the syntax: before your first non-trivial graph, read the "syntax" MCP resource (also at https://equation.io/llms.txt). The result returns text and structured data only. "rows" gives each equation's validation result: status "ok" with its kind, or "error" with the parser message. The link is usable only once every row is "ok". Give users the share_url (it unfurls to a preview card in chat apps); url is the equivalent #-fragment form. "preview" and "preview_omits" describe the share link's simplified static preview (t = 0, 3D as wireframes), which draws less than the interactive app. No image is attached to the tool response.
  - after: Build an equation.io graph link, validating every row with the app's parser. Pass the COMPLETE graph in "equations": a flat array of strings, one equation or definition per string, in display order — when editing an existing graph (see decode_graph_url), include unchanged rows too. Rows can be: equations and inequalities in x,y (curves, regions; z makes it 3D), bare expressions in x, y (scalar fields — a curve is written y = f(x); complex plots via w), points (rows report "draggable"), parametric tuples in u,v — and definitions: "a = 2" (a draggable slider), "f(x) = x^3 - a x", coordinate fields like "r = sqrt(x^2+y^2)" for polar. t animates. Also derivatives d/dx, integrals int[a..b] f dx, sums sum[n=1..N], domain()/conformal()/iter() for complex plots, rgb()/hsl()/oklch() color fields, y' = … slope fields, random variables "X ~ Normal(m, s)"/"P(0<X<2)"/"E(X^2)", and "view(x = -5..5, y = -2..2)"/"camera(theta, phi)" framing rows. That is a menu, not the syntax: before your first non-trivial graph, read the "syntax" MCP resource (also at https://equation.io/llms.txt). The result returns text and structured data only. "rows" gives each equation's validation result: status "ok" with its kind, or "error" with the parser message. The link is usable only once every row is "ok". Give users the share_url (it unfurls to a preview card in chat apps); url is the equivalent #-fragment form. "preview" and "preview_omits" describe the share link's simplified static preview (t = 0, 3D as wireframes), which draws less than the interactive app. No image is attached to the tool response.

Full history: https://api.protogrid.dev/v1/servers/io.equation%2Fequation/changes

## Remotes

- https://equation.io/mcp (streamable-http, auth none, reachable true, uptime30d 0.974359)

## Packages

_none_

## Tools (3)

- `decode_graph_url`: Decode an equation.io link (either the #-fragment form or the /g/ share form) into its list of equation rows, so you can edit them and build a new link with encode_graph_url. The rows use the equation.io syntax documented in the "syntax" MCP resource (also at https://equation.io/llms.txt).
- `encode_graph_url`: Build an equation.io graph link, validating every row with the app's parser. Pass the COMPLETE graph in "equations": a flat array of strings, one equation or definition per string, in display order — when editing an existing graph (see decode_graph_url), include unchanged rows too.

Rows can be: equations and inequalities in x,y (curves, regions; z makes it 3D), bare expressions in x, y (scalar fields — a curve is written y = f(x); complex plots via w), points (rows report "draggable"), parametric tuples in u,v — and definitions: "a = 2" (a draggable slider), "f(x) = x^3 - a x", coordinate fields like "r = sqrt(x^2+y^2)" for polar. t animates. Also derivatives d/dx, integrals int[a..b] f dx, sums sum[n=1..N], domain()/conformal()/iter() for complex plots, rgb()/hsl()/oklch() color fields, y' = … slope fields, random variables "X ~ Normal(m, s)"/"P(0<X<2)"/"E(X^2)", and "view(x = -5..5, y = -2..2)"/"camera(theta, phi)" framing rows. That is a menu, not the syntax: before your first non-trivial graph, read the "syntax" MCP resource (also at https://equation.io/llms.txt).

The result returns text and structured data only. "rows" gives each equation's validation result: status "ok" with its kind, or "error" with the parser message. The link is usable only once every row is "ok". Give users the share_url (it unfurls to a link card in chat apps); url is the equivalent #-fragment form. No image is attached to the tool response.
- `show_graph`: Display an interactive equation.io graph inside the conversation, with editable equations, sliders, pan/zoom, and 3D rotation. Use when the user asks to see or explore a graph. Pass the COMPLETE graph as "equations", one equation or definition per string, preserving unchanged rows when editing. For a slider use "a = 2" then "y = a sin(x)". For advanced syntax read the "syntax" resource (https://equation.io/llms.txt). Returns per-row validation and share links; a row with status "error" is not drawn until its text is corrected and the graph resubmitted. Use encode_graph_url for validation or link-only requests (including share-link preview notes). In clients without UI support, provide share_url.