Burs-IA Utils

Resolver sistema lineal

linear-system-solve

Read-onlyIdempotent

Resuelve un sistema de ecuaciones lineales Ax = b (hasta 20 incógnitas). Cuándo: un resultado numérico tiene que ser exacto o reproducible y no estimado. No para: resolver ax² + bx + c = 0 con raíces reales o complejas, discriminante y vértice (quadratic-solve). Efectos secundarios: ninguno (solo lectura, sin red, sin estado guardado). Determinista: la misma entrada da la misma salida. Límites: entrada JSON de hasta 64 KB, 1 s por llamada, resultado de hasta 1 MB.

EN: Solves a square system of linear equations Ax = b (up to 20 unknowns) by Gauss-Jordan elimination with partial pivoting. When: a numeric result has to be exact or reproducible instead of estimated. Not for: solving ax² + bx + c = 0, returning real or complex roots, the discriminant and the vertex (quadratic-solve). Side effects: none (read-only, no network access, no stored state). Deterministic: the same input gives the same output. Limits: JSON input up to 64 KB, 1 s per call, result up to 1 MB.

Input Schema

Name	Required	Description	Default
`a`	Yes	Matrix as array of rows (array of array; required; at least 1 items; up to 20 items).
`b`	Yes	Right-hand side (array of number; required; at least 1 items; up to 20 items).

Output Schema

Name	Required	Description	Default
`x`	No

Schema Changelog

Changes observed during successful MCP inspections.

Changed2 schema fields changedNov 2, 2026

addedInput schema / properties / a / examples

Added value: +[
+  [
+    [
+      2,
+      1
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+    [
+      1,
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+  ]
+]

addedInput schema / properties / b / examples

Added value: +[
+  [
+    3,
+    5
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+]

First observedNov 1, 2026

TDQS

A4.5/5.0

Behavior4/5

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

Annotations already declare readOnly, idempotent, closed-world and non-destructive, so 'side effects: none (read-only, no network access)' largely restates them. The description does add genuinely new behavior: determinism, plus concrete limits (64 KB JSON input, 1 s per call, 1 MB result) that no annotation conveys. It stops short of noting failure behavior for singular or inconsistent systems, which is the main residual gap for this tool.

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?

Labels are well front-loaded (Cuándo / No para / Efectos secundarios / Límites), and each section is short. However, the Spanish block is repeated verbatim in English, roughly doubling length with zero added information for an agent reading both. The structure is good; the duplication is unearned.

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?

Covers purpose, when/when-not, side-effect profile, determinism and resource limits, and an output schema exists so return values need no prose. For a two-parameter pure computation tool, nothing an agent needs 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.

Parameters4/5

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

Schema coverage is 100%, so baseline is 3, but the description adds constraints the schema cannot express: the system must be square, so A is n×n and must be dimensionally consistent with b — the schema only enforces 1–20 items per row and per array. That is meaningful clarification beyond the schema text.

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 ('Solves a square system of linear equations Ax = b') plus method and scope ('Gauss-Jordan elimination with partial pivoting', 'up to 20 unknowns'). The 'square' qualifier and method name distinguish it from matrix-inverse, matrix-determinant and quadratic-solve, which the description also names explicitly.

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

Usage Guidelines5/5

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

Uses explicit 'When:' and 'Not for:' clauses, naming the alternative (quadratic-solve) and the exact problem class it handles (ax² + bx + c = 0, discriminant, vertex). The selection condition ('exact or reproducible instead of estimated') is stated outright, leaving nothing to inference.

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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