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nikhilxnarula

sagemath-mcp

Analyze

analyze

Run all graph checks at once and return a summary. Prioritizes quick checks, skips irrelevant ones with reasons, and answers open-ended graph questions.

Instructions

Run every check at once and return one summary of the graph.

Cheap checks first; checks that do not apply are skipped with a reason (b-invariance needs a brick, for instance). Prefer this for open-ended questions such as "what can you tell me about this graph?" or "is this a near-bipartite essentially-4-edge-connected cubic brick?".

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
kmaxNolargest cyclic cut size to search for.
graphYesa graph6 string or a registry name.
max_orderNovertex-count ceiling for the exhaustive cyclic-cut search.

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault

No arguments

Schema Changelog

Changes observed during successful MCP inspections.

  1. First observedv0.1.0

TDQS

A4.3/5.0
Behavior4/5

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

With no annotations, the description carries the behavioral burden and does disclose useful traits: cheap checks run first, inapplicable checks are skipped with a reason, and the result is a single summary. It does not discuss side effects or error handling, but for a read-only analysis tool this is reasonable.

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

Conciseness5/5

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

The description is compact, front-loaded with the core purpose, and every sentence adds value. The examples and the note about cheap checks and skipping are placed effectively without redundancy.

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?

Given the output schema exists, parameter schema is fully covered, and the description explains when to use the tool and what behavior to expect, nothing essential is missing for an agent to call it correctly.

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

Parameters3/5

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

Schema coverage is 100%, so the schema already documents all three parameters. The description adds no additional parameter-level meaning beyond what the schema provides, so the baseline 3 is appropriate.

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 action ('Run every check at once') and resource ('the graph'), and clearly differentiates itself from the sibling check tools by being the aggregate summary tool. The examples further clarify its role as a broad analysis entry point.

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 prefer this tool for open-ended questions and gives two concrete example queries. It does not explicitly state when to use a specific sibling tool instead, but the guidance is clear enough for an agent to select it appropriately.

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