Graph Paper

Look up a math capability

lookup_math_capability

Read-only

Needs sign-in: Look up whether the Compute Engine can do something before you claim it. Pass a concept keyword (e.g. "prime factorization", "eigenvalues") or a LaTeX trigger (e.g. "\gcd", "\int"). Multiple keywords are OR-matched, so listing a few synonyms casts a wider net (e.g. "modulo floor divide remainder") rather than narrowing the search. The result lists matching registered operators, each with its canonical name and whether it is actually evaluable. Trust the result: if nothing evaluable matches, the capability is NOT available — say so rather than inventing a function.

Tool call template

Replace each placeholder with a value matching the input schema. Only required parameters are included; add optional parameters as needed.

{
  "id": 1,
  "jsonrpc": "2.0",
  "method": "tools/call",
  "params": {
    "arguments": {
      "query": "<query>"
    },
    "name": "lookup_math_capability"
  }
}

Input Schema

Name	Required	Description	Default
`query`	Yes	One or more concept keywords (OR-matched) or a LaTeX trigger to search for.

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 24, 2026

TDQS

A4.5/5.0

Behavior4/5

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

Annotations only declare readOnlyHint and openWorldHint, so the description carries the real weight: it discloses the sign-in requirement, the OR-matching semantics, and that results include an evaluability flag. It stops short of describing error modes or what an empty result looks like beyond the guidance to trust it.

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?

Front-loads the auth note and purpose, and every sentence carries information about behavior or correct usage. Slightly dense with stacked parenthetical examples, but nothing is redundant.

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?

Complete for a single-parameter lookup with no output schema: the description explains both the input construction and the shape of the result (matching operators, canonical names, evaluability). Nothing an agent needs in order to call it correctly is missing.

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?

Schema coverage is 100%, so the baseline is 3, but the description adds genuine meaning beyond the schema: LaTeX-trigger queries, concrete keyword examples, and the non-obvious heuristic that multiple synonyms widen rather than narrow the search. That materially changes how an agent constructs the query.

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?

States a specific verb and resource ("Look up whether the Compute Engine can do something") and implicitly contrasts with evaluate_math by framing it as a pre-check before claiming a capability. An agent can distinguish it from the evaluation siblings without reading the 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?

Explicitly says to use it "before you claim it" and tells the agent what to do when no match is found ("say so rather than inventing a function"). It gives clear usage context but never names the sibling tools (evaluate_math, explain) it should be chosen over.

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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