Equation.io

Create a graph link

encode_graph_url

Read-onlyIdempotent

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.

Input Schema

Name	Required	Description	Default
`equations`	Yes	Every equation in the graph, in display order. One equation or definition per string — do not join rows with ";" (inside quoted text a ";" is data, and kept).

Output Schema

Name	Required	Description
`url`	Yes	Graph URL using a #-fragment.
`rows`	Yes
`valid`	Yes
`preview`	No	Static preview availability and limitations.
`share_url`	Yes	Shareable /g/ graph URL.
`preview_omits`	No

Schema Changelog

Changes observed during successful MCP inspections.

Changed1 schema field changedOct 18, 2026

changedOutput schema / required

Previous value: -[
-  "valid",
-  "url",
-  "share_url",
-  "preview",
-  "rows"
-]New value: +[
+  "valid",
+  "url",
+  "share_url",
+  "rows"
+]

First observedSep 14, 2026

TDQS

A4.5/5.0

Behavior5/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Adds substantial behavior beyond the annotations: rows are parser-validated, the link is usable only when every row is 'ok', the response is text + structured data with no image attached, and share_url vs url semantics are spelled out. These are exactly the traits annotations cannot carry.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness3/5

Is the description appropriately sized, front-loaded, and free of redundancy?

Front-loaded correctly and organized, but roughly 300 words for a single-parameter tool includes a long enumeration of row types the description itself concedes is 'a menu, not the syntax' and then redirects to the resource. Useful for capability discovery, yet borderline padding for the size.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness5/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

An output schema exists so return values needn't be explained, and the description still names the rows status shape, both URL forms, and the no-image caveat. Nothing an agent needs to call this correctly is missing.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters4/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema coverage is 100%, so baseline is 3, but the description goes beyond it: 'include unchanged rows too' for edits, the display-order requirement, and the explicit warning not to join rows with ';' while noting a quoted ';' is data. That is real added meaning over the schema.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

Opens with a specific verb+resource ('Build an equation.io graph link') and immediately distinguishes itself from the sibling decode_graph_url by naming it for the edit-existing case. An agent can tell encode from decode without opening either schema.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines4/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

Gives a clear use context (editing an existing graph → include unchanged rows, see decode_graph_url) and a prerequisite (read the syntax resource before a first non-trivial graph). It does not address the other sibling show_graph, so the routing picture is not fully closed.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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