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amichae2

Math MCP Server

by amichae2

lstsq

Compute a least-squares solution to Ax ≈ b, finding the best approximate fit for overdetermined or inconsistent linear systems.

Instructions

Compute a least-squares solution to Ax ≈ b.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
aYes
bYes
methodNogelsd
regularizationNo

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault

No arguments

Behavior2/5

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

With no annotations, the description should disclose behavioral traits. It only states the high-level goal, omitting details like default method, regularization effects, or handling of ill-conditioned systems.

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?

The description is a single concise sentence, but it sacrifices essential detail. It is not verbose but could be restructured to include more context without being lengthy.

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

Completeness2/5

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

Despite having an output schema, the description fails to provide sufficient context for the 4 parameters, especially method and regularization. It is incomplete for a tool of moderate complexity.

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

Parameters2/5

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

Schema has 0% description coverage; the description adds nothing beyond parameter names. It implies a is matrix and b is vector but does not explain method or regularization meanings.

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

Purpose4/5

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

The description clearly states the tool computes a least-squares solution to Ax ≈ b, which is a specific verb and resource. It distinguishes from siblings like curve_fit or solve as a linear algebra operation.

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

Usage Guidelines2/5

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

No guidance on when to use this tool over alternatives (e.g., curve_fit for non-linear, solve for exact). The description lacks context or examples.

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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