Scientific Calculator

Polynomial Solver

calculator_polynomial

Read-only

Find roots from coefficients (highest degree first) or an equation. Degree 1–10.

Tool call template

This tool declares no required parameters. Add optional parameters from the input schema as needed.

{
  "id": 1,
  "jsonrpc": "2.0",
  "method": "tools/call",
  "params": {
    "arguments": {},
    "name": "calculator_polynomial"
  }
}

Input Schema

Name	Required	Description
`equation`	No	Polynomial equation.
`variable`	No	Variable name.
`coefficients`	No	Coeffs highest degree first, e.g. [1,-5,6].

Output Schema

Name	Required	Description	Default
`roots`	No
`degree`	No
`expression`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

First observedOct 23, 2026

TDQS

A3.5/5.0

Behavior3/5

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

Annotations already mark this as read-only, non-destructive, and closed-world, so the safety profile is covered. The description adds the degree limit and input modes, but it does not mention complex-root handling, precision, or error behavior.

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?

The description is two compact sentences with the main action front-loaded and no wasted wording. It fits the tool well and is easy to scan.

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?

Given the output schema and annotations, much is already structured. Still, with zero required parameters, the description should clarify that the caller must supply either coefficients or an equation, and it should better distinguish this tool from sibling equation/root solvers.

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%, so the schema already documents equation, variable, and coefficients. The description reinforces coefficient ordering and the degree range, but it does not clarify whether equation and coefficients are mutually exclusive or that at least one input path is needed.

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: "Find roots" for a polynomial, with two accepted input forms and a degree range. It is clear, but it does not explicitly distinguish this from sibling tools like calculator_quadratic_equation, calculator_cubic_equation, or calculator_root_finder.

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?

It tells the agent that roots can be found from coefficients or an equation, and it sets a degree 1–10 boundary. However, it gives no explicit guidance on when to use this tool instead of sibling root-finding or equation-solving tools, and it does not state exclusions.

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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