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Scientific Calculator

by ai.saifs
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Matrix Rank

calculator_rank
Read-only

Rank of a square or rectangular matrix.

Tool call template

Replace each placeholder with a value matching the input schema. Only required parameters are included; add optional parameters as needed.

{
  "id": 1,
  "jsonrpc": "2.0",
  "method": "tools/call",
  "params": {
    "arguments": {
      "matrix": "<matrix>"
    },
    "name": "calculator_rank"
  }
}

Input Schema

NameRequiredDescriptionDefault
matrixYesMatrix.

Output Schema

NameRequiredDescriptionDefault
rankYes
resultYes

Schema Changelog

Changes observed during successful MCP inspections.

  1. First observed

TDQS

C2.9/5.0
Behavior2/5

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

Annotations already declare this a safe, closed-world read operation, so the description's only added behavioral detail is that rectangular matrices are accepted. It says nothing about numerical tolerance, behavior on empty or non-numeric input, or cost for large matrices.

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?

One short, front-loaded sentence with no waste, but it is thin to the point of under-specification rather than tightly informative.

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

Completeness3/5

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

An output schema exists so return values need not be explained, and the tool is simple, but for a tool whose only parameter is documented as 'Matrix.' the description could have stated that the input is an array of numeric rows. Adequate, not complete.

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?

Single parameter with 100% schema coverage, so the baseline is 3. The description adds no meaning beyond the schema, which itself only labels the parameter 'Matrix.' — but the schema carries the formal definition and an example.

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?

States a specific mathematical operation (rank) on a specific resource (square or rectangular matrix), which is enough to separate it from siblings like calculator_determinant, calculator_matrix_inverse and calculator_transpose. It lacks an explicit verb ('computes the rank of'), but the intent is unambiguous.

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 versus calculator_determinant, calculator_eigenvalues or calculator_matrix_inverse, which are the obvious alternatives for matrix analysis. No mention of inputs it rejects or conditions under which rank is the right call.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

All Scientific Calculator toolsInspect
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