ScorpTech x402 Tools

Vandermonde

vandermonde

Read-onlyIdempotent

The Vandermonde convolution. The sum of C(m, k)*C(n, r-k) equals C(m+n, r). For m = 3, n = 3, and r = 2 the value is 15. m and n run from 0 to 256, and r must not pass m+n. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/vandermonde

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": {
      "m": "<m>",
      "n": "<n>",
      "r": "<r>"
    },
    "name": "vandermonde"
  }
}

Input Schema

Name	Required	Description	Default
`m`	Yes
`n`	Yes
`r`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

A3.7/5.0

Behavior4/5

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

The description adds substantial context beyond the annotations: a per-call price, x402/Solana payment requirement, and an alternate HTTPS endpoint. It also states a cross-parameter validity rule ('r must not pass m+n') that is not encoded in the schema, which is valuable behavioral information for a paid remote tool.

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 compact and front-loads the mathematical definition, then the example, constraints, and payment details. Every sentence contributes, though the formula notation ('C(m, k)*C(n, r-k)') could be slightly clearer.

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 read-only arithmetic function with no output schema, the description supplies the computed identity, an example result, domain bounds, the r constraint, and payment/transport details. It is nearly complete, lacking only explicit parameter-role descriptions and any statement of the return format.

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 0%, so the description must compensate. It gives the parameter domains and one critical relational constraint (r ≤ m+n), plus a worked example, but it largely restates the m/n ranges already in the schema and never explicitly defines the individual roles of m, n, and r beyond the formula.

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 mathematical operation (Vandermonde convolution) and gives its combinatorial identity, so an agent knows exactly what is computed. It does not distinguish itself from nearby siblings such as binom or multichoose, leaving that differentiation to the name and formula.

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?

Usage is implied by the identity and the boundary rule 'r must not pass m+n', but there is no explicit guidance on when to call this instead of binom or multichoose. The reader must infer the appropriate context from the domain.

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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