ScorpTech x402 API

Equation Solve

equation_solve

Read-onlyIdempotent

Solve equations exactly where possible. Polynomials of any degree up to 100: exact rational roots, exact surd forms for quadratic factors ("(3 + √5)/2", complex "(-1 + i√3)/2"), multiplicities via square-free factorisation, and high-precision numeric roots (Aberth–Ehrlich + Newton polishing) for the rest. Any other single-variable equation ("cos(x) = x", "2^x = x^2 + 1", "ln(x) + x = 5") is solved numerically over a range with sign scanning + Brent's method, rejecting poles. Systems of linear equations ("2x + 3y = 7", "x - y = 1") are solved with exact rational Gaussian elimination, reporting unique, none, or infinitely many solutions in parametric form. Price: $0.002 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/equation-solve

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": "equation_solve"
  }
}

Input Schema

Name	Required	Description	Default
`max`	No	Numeric mode: search range end
`min`	No	Numeric mode: search range start
`angle`	No		rad
`equation`	No	One equation, e.g. "x^2 - 5x + 6 = 0" (no "=" means "= 0")
`variable`	No	Variable to solve for (auto-detected)
`equations`	No	Linear system, e.g. ["2x + 3y = 7", "x - y = 1"]

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

A4.3/5.0

Behavior5/5

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

Annotations already cover safety (readOnly, idempotent, non-destructive), and the description adds real behavioral context beyond them: the exact algorithms used, the numeric-mode search range and pole rejection, the guaranteed failure/precision boundary (numeric fallback for non-polynomials), and the per-call cost of $0.002 USDC plus the HTTPS mirror endpoint. Cost and payment mechanism are exactly the kind of trait an agent cannot get from the schema or annotations.

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?

Front-loaded with the core capability, then mode-by-mode detail, then pricing — a sensible order with no filler sentences. It is dense with parentheticals and algorithm names (Aberth–Ehrlich, Brent) that are informative but lengthen an already long block.

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?

With no output schema, the description carries the return-value burden and does describe what comes back: rational roots, surd forms, complex roots, multiplicities, and unique/none/parametric solution classifications. It does not specify the response structure or precision controls, and leaves the angle parameter unaddressed — minor gaps for a 6-param tool.

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 83%, so the schema largely documents equation, variable, equations, min and max, and the description reinforces range-based numeric solving. However, the 'angle' enum (rad/deg) is undocumented in both the schema description and the description text, leaving trig-equation unit handling unexplained. Baseline 3 is appropriate for high-coverage schemas with one unaddressed parameter.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

States a specific verb+resource ('Solve equations') and then enumerates the three concrete problem classes it handles — polynomials up to degree 100, general single-variable equations, and linear systems — with example inputs for each. An agent can tell exactly what this tool does and does not compute, and no sibling in the list (poly_eval, poly_mul, matrix_ops) overlaps on solving.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines4/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

The three modes are each tied to a condition: polynomial input → exact/surd/multiplicity handling, any other single-variable equation → numeric over a range, a list of equations → Gaussian elimination. That is clear routing guidance for the primary decision. It stops short of naming alternatives (e.g. use poly_eval for mere evaluation) or stating exclusions/multi-variable nonlinear limits.

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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