Scientific Calculator

Taylor Series Calculator

calculator_taylor

Read-only

Taylor/Maclaurin series expansion around a point up to a given order.

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": {
      "expression": "<expression>"
    },
    "name": "calculator_taylor"
  }
}

Input Schema

Name	Required	Description	Default
`order`	No	Highest power / order (default 5).
`point`	No	Expansion point (default 0).
`variable`	No	Variable (default x).	x
`expression`	Yes	Function to expand.

Output Schema

Name	Required	Description	Default
`order`	No
`result`	Yes
`expression`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

First observedOct 23, 2026

TDQS

B3.4/5.0

Behavior3/5

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

Annotations already establish that this is a read-only, non-destructive, closed-world computation, so the safety profile is clear. The description adds no further behavioral context such as convergence limitations, precision, or computational cost, but it does not contradict the annotations.

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 a single efficient sentence that front-loads the operation and scope. There is no filler or irrelevant detail.

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?

Given full schema coverage, an output schema, and annotations that cover safety, the description is sufficient to identify and call the tool. It could be stronger by clarifying when this tool should be chosen over related calculus/expansion siblings.

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 coverage is 100%, so all four parameters are already documented in the input schema. The description only restates the concepts of expansion point and order, adding little beyond the schema's own parameter descriptions.

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 names a specific operation (Taylor/Maclaurin series expansion) and its scope (around a point, up to an order). It is clear what the tool does, but it does not explicitly distinguish itself from nearby siblings such as calculator_derivative, calculator_expand, or calculator_limit.

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?

The description gives no guidance on when to use this tool versus alternatives. With many sibling calculators covering derivatives, limits, and expansion, an agent has to infer the intended selection context.

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

All Scientific Calculator tools Inspect

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