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axiomatic-mcp

Official
by Axiomatic-AI

AxPDE_parse_pde

Parses natural-language or LaTeX PDE descriptions into a structured SymPy spec. Produces compile-checked input for downstream PDE derivation and verification.

Instructions

Parse a natural-language or LaTeX PDE description into a structured SymPy spec: the differential operator(s) as operator code, plus domain, boundary conditions, variables, and unknowns. Each operator is compile-checked before returning. The spec feeds directly into derive_source and verify_solution. This does NOT choose a manufactured solution or write a solver.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
descriptionYesNatural-language or LaTeX description of the PDE problem, including the equation, the domain, and the boundary conditions. E.g. "The 1D heat equation u_t = u_xx on [0,1] for t in [0,1], with homogeneous Dirichlet boundary conditions u(0,t) = u(1,t) = 0."

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault
specNoThe structured artifact. Feed spec.equations / variables / domain / boundary_conditions onward.
errorNo
successYesWhether parsing produced a usable spec.
compile_resultsNoPer-equation compile check, e.g. {"pde": {"compiled": true}}.

Schema Changelog

Changes observed during successful MCP inspections.

  1. Addedv0.1.20

TDQS

A4/5.0
Behavior3/5

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

With no annotations provided, the description carries the full burden of behavioral disclosure. It mentions that each operator is compile-checked before returning, which is a valuable behavior. However, it does not disclose potential failure modes, whether the operation is stateless, or any side effects. For a parsing tool, this is moderately transparent but leaves some behavioral aspects unstated.

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 two sentences, with the core purpose front-loaded in the first sentence, followed by output components and downstream use, and then an exclusion in the second sentence. Every sentence adds value with no redundancy. It is efficient and well-structured.

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

Completeness4/5

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

The description covers the tool's purpose, input requirements, output components, compile-check behavior, downstream integration, and what it does not do. An output schema exists, so return values are not needed in the description. It is nearly complete for a single-parameter tool; minor gaps like error handling or edge-case behavior are not critical.

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?

The schema covers 100% of parameters, and the schema's own description of the 'description' parameter is highly detailed, including a concrete example. The tool description adds context about the output structure but does not add new meaning to the parameter beyond what the schema already provides. Baseline of 3 is appropriate since the schema does the heavy lifting.

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 states a specific verb ('parse') and resource ('natural-language or LaTeX PDE description into a structured SymPy spec'), and enumerates the output components (operator code, domain, boundary conditions, variables, unknowns). It also explicitly distinguishes itself from siblings by noting it does not choose a manufactured solution or write a solver, which differentiates it from derive_source and verify_solution.

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 provides clear usage context by stating the spec feeds directly into derive_source and verify_solution, implying it should be used as a preprocessing step for those tools. It also gives an explicit exclusion ('does NOT choose a manufactured solution or write a solver'), which helps prevent misuse. However, it does not explicitly mention when not to use it in favor of other tools, such as when a structured spec already exists.

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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