Burs-IA Utils

Determinante de matriz

matrix-determinant

Read-onlyIdempotent

Calcula el determinante de una matriz cuadrada (hasta 20×20). Cuándo: un resultado numérico tiene que ser exacto o reproducible y no estimado. No para: calcular la inversa de una matriz cuadrada (matrix-inverse). 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: Computes the determinant of a square matrix (up to 20×20) by LU decomposition with partial pivoting. When: a numeric result has to be exact or reproducible instead of estimated. Not for: computing the inverse of a square matrix (matrix-inverse). 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
`matrix`	Yes	Matrix as array of rows (array of array; required; at least 1 items; up to 20 items).

Output Schema

Name	Required	Description	Default
`determinant`	No

Schema Changelog

Changes observed during successful MCP inspections.

Changed1 schema field changedNov 2, 2026

addedInput schema / properties / matrix / examples

Added value: +[
+  [
+    [
+      1,
+      2
+    ],
+    [
+      3,
+      4
+    ]
+  ]
+]

First observedNov 1, 2026

TDQS

A4.6/5.0

Behavior4/5

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

Annotations already declare readOnlyHint=true, idempotentHint=true, openWorldHint=false and destructiveHint=false, so the 'no side effects' sentence largely repeats structured data. However, the description adds genuine context beyond annotations: the LU/partial-pivoting algorithm, determinism guarantee, and concrete limits (64 KB input, 1 s per call, 1 MB result).

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

Conciseness4/5

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

Well front-loaded: purpose, when, when-not, effects, determinism, limits, each in a labelled clause. The only waste is the full ES/EN duplication, which doubles length without adding information an agent lacks in one language.

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?

For a single-parameter pure-computation tool with an output schema and rich annotations, everything needed to call it correctly is present: input shape, limits, determinism, and the sibling to use for a different operation. The output schema covers the return value, so the description need not.

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 description coverage is 100% and the matrix parameter is fully documented with bounds, so the baseline is 3. The description adds the 64 KB JSON-input ceiling and the 20×20 row/column shape constraint, giving an agent extra guardrails beyond the schema.

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 (computes the determinant of a square matrix), plus the size bound (up to 20×20) and the algorithm (LU decomposition with partial pivoting). This clearly distinguishes it from sibling matrix tools like matrix-inverse.

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?

Explicitly gives the when ('a numeric result has to be exact or reproducible instead of estimated') and the when-not with a named alternative ('Not for: computing the inverse of a square matrix (matrix-inverse)'). The agent can route without opening either schema.

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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