ScorpTech x402 API

Eulerian Poly

eulerian_poly

Read-onlyIdempotent

The Eulerian polynomial A_n(x) = sum A(n, k) * x^k. A_3(2) is 13, A_4(1) is 24, and A_5(0) is 1. n runs from 1 to 20, and x runs from 0 to 10. Past 15 digits the value is a decimal string. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/eulerian-poly

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": {
      "n": "<n>",
      "x": "<x>"
    },
    "name": "eulerian_poly"
  }
}

Input Schema

Name	Required	Description	Default
`n`	Yes
`x`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

A3.8/5.0

Behavior4/5

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

Annotations already establish read-only, idempotent, non-destructive behavior. The description adds useful context beyond that: the $0.001 USDC x402 payment requirement, the HTTPS endpoint alternative, and the output format switch to a decimal string beyond 15 digits. It does not mention rate limits or failure modes, but it exceeds the annotation baseline.

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?

The description is front-loaded with the mathematical definition and examples, then moves to ranges, output format, pricing, and endpoint. Every sentence carries information, though the three examples and payment details make it slightly dense rather than maximally concise.

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 two-parameter mathematical evaluation tool with no output schema, the description covers the operation, valid input bounds, output formatting for large values, payment requirements, and an alternate transport. It is largely complete; a brief note on when to prefer it over sibling Eulerian tools would close the remaining gap.

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 0%, so the description must carry parameter meaning. It does: the formula clarifies that n is the polynomial degree/index and x is the evaluation point, and it restates the valid ranges (n 1–20, x 0–10) with examples like A_3(2)=13. It could explicitly label each parameter, but the formula and examples provide substantial semantic value.

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 mathematical object and operation: computing the Eulerian polynomial A_n(x). The formula and worked examples make the purpose unambiguous. It does not explicitly differentiate itself from sibling tools such as eulerian, eulerian_row, or eulerian_sum, so it falls short of a 5.

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?

The description gives concrete examples and valid input ranges, which imply usage. However, it does not state when to use this tool versus alternatives like eulerian_row or eulerian_sum, nor does it explain any prerequisites beyond the numeric bounds.

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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