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Math MCP Learning

by io.github.clouatre-labs
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Matrix Transpose

matrix_transpose
Read-onlyIdempotent

Transpose a matrix (swap rows and columns).

Input Schema

NameRequiredDescriptionDefault
matrixYes2D list of numbers representing the matrix. Each inner list is a row. Example: [[1, 2, 3], [4, 5, 6]]

Output Schema

NameRequiredDescriptionDefault
topicYes
difficultyYes
original_colsYes
original_rowsYes
result_matrixYes

Schema Changelog

Changes observed during successful MCP inspections.

  1. Changed1 schema field changed
    • addedInput schema / properties / matrix / description
      Added value: +"2D list of numbers representing the matrix. Each inner list is a row. Example: [[1, 2, 3], [4, 5, 6]]"
  2. Changed4 schema fields changed
    • removedOutput schema / additionalProperties
      Removed value: -true
    • addedOutput schema / description
      Added value: +"Result of matrix transpose operation."
    • addedOutput schema / properties
      Added value: +{
+  "difficulty": {
+    "type": "string"
+  },
+  "original_cols": {
+    "type": "integer"
+  },
+  "original_rows": {
+    "type": "integer"
+  },
+  "result_matrix": {
+    "items": {
+      "items": {
+        "type": "number"
+      },
+      "type": "array"
+    },
+    "type": "array"
+  },
+  "topic": {
+    "type": "string"
+  }
+}
    • addedOutput schema / required
      Added value: +[
+  "original_rows",
+  "original_cols",
+  "result_matrix",
+  "difficulty",
+  "topic"
+]
  3. Changed2 schema fields changed
    • addedInput schema / additionalProperties
      Added value: +false
    • removedInput schema / properties / matrix / title
      Removed value: -"Matrix"
  4. Changed1 schema field changed
    • addedInput schema / properties / matrix / maxItems
      Added value: +10000
  5. First observed

TDQS

B3.4/5.0
Behavior2/5

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

Annotations already declare readOnlyHint=true and idempotentHint=true, covering the safety and repeatability profile. The description adds no behavioral context beyond that (no shape constraints, no input validation notes), so it contributes almost nothing beyond the structured fields.

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?

A single, front-loaded sentence with zero filler. Every word earns its place.

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?

For a trivial pure-math tool with a complete parameter schema and an output schema, the description is sufficient — an agent needs no return-value or permission detail. It could be marginally stronger with an explicit usage cue, but nothing essential is missing.

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?

Schema description coverage is 100% and the single 'matrix' parameter is fully documented in the schema, including an example. The description adds no additional parameter meaning, so the baseline of 3 applies.

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 states a specific verb and resource ('Transpose a matrix') and adds the mathematical semantics via the parenthetical 'swap rows and columns'. It is clearly distinguishable from siblings like matrix_multiply or matrix_inverse, though it never names those alternatives.

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

Usage Guidelines3/5

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

No explicit when-to-use or when-not-to-use guidance is given. Usage is only implied by the well-known mathematical meaning of 'transpose', which an agent must infer rather than read.

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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