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 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.

Input Schema

TableJSON 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

TableJSON Schema

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

Schema Changelog

Changes observed during successful MCP inspections.

AddedSep 14, 2026

TDQS

A4.7/5.0

Behavior5/5

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

Annotations establish read-only, idempotent, non-destructive behavior, and the description adds substantial operational detail: every row is parser-validated, the link requires all rows to be 'ok', and the response contains text plus structured row results. It also discloses preview behavior and that no image is attached, which goes well beyond the annotations.

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

Conciseness4/5

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

The description is front-loaded with the core action and key constraint, then moves logically through row types, syntax guidance, and return behavior. It is long and includes a broad syntax menu that partly duplicates the referenced syntax resource, but the information is dense and relevant for a complex graph language.

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?

For a complex tool with one parameter, validation semantics, and structured output, the description covers input expectations, validation consequences, output fields, preview limitations, and the editing alternative. Since an output schema exists, it does not need to document return structure exhaustively, but it still explains the important return semantics.

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

Parameters5/5

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

Although schema coverage is 100%, the description adds important meaning to the single equations parameter: it must be the complete graph in display order, unchanged rows must be included when editing, and strings must not be joined with semicolons. It also explains what kinds of strings are valid, which the schema does not cover.

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?

The description opens with a specific verb and resource: 'Build an equation.io graph link' and adds that it validates rows with the app's parser. It also distinguishes this from decode_graph_url when editing an existing graph. An agent can identify the tool's job without opening sibling schemas.

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?

The description gives clear usage context: pass the complete graph, include unchanged rows when editing, and consult decode_graph_url for existing graphs. It also directs agents to read the syntax resource before non-trivial use. It does not explicitly compare against show_graph, so it stops short of full alternative routing.

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

All Equation.io tools Inspect

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