Multiply two integers using the Common-Base Multiplication Method: x=N+a, y=N+b, xy=N^2+N(a+b)+ab. Returns the chosen base, offsets, terms, and exact result.
| Name | Required | Description | Default |
|---|---|---|---|
| x | Yes | First integer | |
| y | Yes | Second integer | |
| base | Yes | Common base N. If omitted by a client, use a convenient nearby base such as a multiple of 10. |
Changes observed during successful MCP inspections.
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations exist, so the description bears the full burden. It discloses the algorithmic behavior via the formula and names what is returned (base, offsets, terms, result), but says nothing about edge cases, negative integers, or error conditions. Adequate but incomplete for a computation tool.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Is the description appropriately sized, front-loaded, and free of redundancy?
Two compact sentences that lead with the purpose and pack the formula and return contents efficiently. Slightly dense but no wasted words.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
With no output schema, the description usefully enumerates the return contents (base, offsets, terms, exact result), which is the key missing piece. The method and parameters are covered, though edge-case behavior remains unstated.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema coverage is 100%, so all three parameters are already documented. The description reinforces the meaning of N, a, b through the formula, adding marginal value, but does not add syntax or constraint detail beyond the schema. Baseline 3 applies.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Does the description clearly state what the tool does and how it differs from similar tools?
States a specific verb and resource ('Multiply two integers') and names the exact method used, fully distinguishing it from siblings like prime_analyze and generate_java_algorithm. An agent can identify the operation without opening the schema.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Does the description explain when to use this tool, when not to, or what alternatives exist?
The description explains what the tool does but gives no guidance on when to choose it over a plain multiplication or the sibling analytical tools. No exclusions, prerequisites, or alternative-selection criteria are provided.
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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