SooTool

geometry.matrix_solve

Read-onlyIdempotent

Solve square linear systems Ax = b from Decimal-string matrices and vectors, returning float64 solution vectors. Use for n×n equation sets; singular or mismatched inputs raise errors.

Instructions

연립일차방정식 Ax = b 의 해 x 를 numpy.linalg.solve(float64)로 구한다. A 는 n×n Decimal 문자열 2차원 리스트, b 는 길이 n 리스트. 해는 float64 repr 문자열이며 정밀도는 약 15자리다. 특이행렬이거나 b 의 길이가 n 과 다르면 오류. 비정방(과결정, 부족결정) 시스템은 지원하지 않는다.

Input Schema

Name	Required	Description	Default
`A`	Yes
`b`	Yes

Output Schema

Name	Required	Description
`x`	Yes
`_meta`	No	서버가 붙이는 영수증(integrity), 엔진, 힌트
`trace`	Yes	계산 근거(tool, formula, inputs, steps, output)

Schema Changelog

Changes observed during successful MCP inspections.

First observedv0.3.0Oct 29, 2026

TDQS

A4.5/5.0

Behavior4/5

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

Annotations already cover the read-only, idempotent, closed-world profile, and the description adds real behavioral detail beyond them: the float64 conversion of Decimal string inputs, ~15-digit precision, and the exact failure modes (singular matrix, length mismatch). It does not say how errors are surfaced (exception vs. error payload), which is the remaining gap.

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?

Four tight sentences, front-loaded with the operation and its numeric backend, then input types, then output precision, then error/limitation cases. No filler.

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?

Return type is also covered by an output schema, yet the description still states the result is a float64 repr string with ~15-digit precision. Combined with the documented inputs and error conditions, an agent has everything needed to call it and interpret failures.

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

Parameters4/5

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

Schema coverage is 0% (bare 'A'/'b' titles), but the description compensates well: A is an n×n two-dimensional list of Decimal strings, b is a length-n list, and both are required. It leaves the exact accepted string format for decimals implicit, so a small gap remains.

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 ('연립일차방정식 Ax = b 의 해 x 를 ... 구한다') and pins the implementation to numpy.linalg.solve(float64). It also excludes non-square systems, which cleanly separates it from siblings like geometry.matrix_inverse and geometry.matrix_determinant that operate on the same matrices.

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?

Gives clear preconditions (A must be n×n, b must have length n, matrix must be non-singular) and explicit non-support for overdetermined/underdetermined systems. It does not name an alternative tool to use instead when those conditions fail, so it stops short of full when/when-not routing.

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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