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lingshu-solver

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solve

Computes deterministic, reproducible numeric solutions for systems of real equations. Acts as a non-hallucinating math backend for AI agents.

Instructions

Deterministic solver for systems of real equations. This is not a language model: no randomness, and identical input always returns an identical, reproducible result. Use it when you need a verifiable, reproducible numeric answer for algebraic equations or common transcendentals (sin/cos/tan/log/exp/sqrt/abs); it works well as a non-hallucinating math backend for an AI agent. Not suitable for symbolic algebra, closed-form proofs, initial-value ODEs, or mandatory integer equality. INPUT: equations (array of strings containing an equals sign, e.g. ["x^2+y^2=25","x+y=7"]); supported operators + - * / ^ sqrt log sin cos tan exp abs, with in-text domain constraints such as x in [-30,30]; variables (optional, auto-detected, max 6); domain (optional, e.g. {"x":[-30,30]}), defaulting to +/-1e6 per variable. HARD LIMITS: at most 6 variables; 1 to 64 equations and the equation count must be at least the variable count; up to 100KB of equation text per call; output is fixed at 6 decimal places and is not configurable. OUTPUT (JSON): resultType is empty (no real solutions, proven), finite (finite verified solutions) or infinite (infinite solution set, only the recommended nearest-to-origin solution is given); summary; solutions[] with values[] (6-decimal numbers), tier (proven means Krawczyk-certified, otherwise likely or candidate), certified, text; residual and other internals under internals; recommended holds the compact nearest-to-origin structure. truncated=true means the global branch-and-bound did not finish inside the budget; it does not necessarily mean solutions were missed and in most cases every real solution was found; narrow the domain or raise options.budget and retry if you need a completeness guarantee. Errors return error.type (invalid_input or internal_error). If something looks wrong, call give_feedback rather than guessing. The same input always produces the exact same output, so caching and retries are safe. PAYMENT: this endpoint is free to use. Pass honorPaid:true to declare personal or evaluation use and the call is served with no verification and no balance deduction; payment is voluntary and never enforced.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
domainNoExplicit search domain (optional), e.g. {"x":[-30,30],"y":[-30,30]}. Recommended for near-infinite solution sets or fast-growing functions such as exp or sinh; without it the default +/-1e6 may fail to prune and set truncated.
optionsNoAdvanced options (optional), e.g. {budget:500000, maxDepth:28}
fastModeNoFast mode (default false).
equationsYesArray of equation strings, e.g. ["x^2 + y^2 = 25", "x + y = 7"]. Supports + - * / ^ sqrt log sin cos tan exp abs, plus in-text domain constraints such as x in [-30,30].
variablesNoVariable names (optional). If omitted they are auto-detected from the equation text, in order of appearance. Maximum 6.

Schema Changelog

Changes observed during successful MCP inspections.

  1. Changed5 schema fields changedv1.0.22
    • changedInput schema / properties / domain / description
      Previous value: -"显式搜索域（可选）。形如 {\"x\":[-30,30],\"y\":[-30,30]}。对\"有限解·部分\"演示或快增长函数（exp/sinh）建议显式给定，否则默认 ±1e6 可能剪枝失效并触发 truncated。"New value: +"Explicit search domain (optional), e.g. {\"x\":[-30,30],\"y\":[-30,30]}. Recommended for near-infinite solution sets or fast-growing functions such as exp or sinh; without it the default +/-1e6 may fail to prune and set truncated."
    • changedInput schema / properties / equations / description
      Previous value: -"方程字符串数组，如 [\"x^2 + y^2 = 25\", \"x + y = 7\"]。支持 + - * / ^ sqrt log sin cos tan exp abs，以及 in-text 域约束 \"x ∈ [-30,30]\"。"New value: +"Array of equation strings, e.g. [\"x^2 + y^2 = 25\", \"x + y = 7\"]. Supports + - * / ^ sqrt log sin cos tan exp abs, plus in-text domain constraints such as x in [-30,30]."
    • changedInput schema / properties / fastMode / description
      Previous value: -"快速模式（默认 false）"New value: +"Fast mode (default false)."
    • changedInput schema / properties / options / description
      Previous value: -"高级选项（可选），如 {budget:500000, maxDepth:28}"New value: +"Advanced options (optional), e.g. {budget:500000, maxDepth:28}"
    • changedInput schema / properties / variables / description
      Previous value: -"变量名数组（可选）。不填则由方程文本自动识别，顺序按出现。最多 6 个。"New value: +"Variable names (optional). If omitted they are auto-detected from the equation text, in order of appearance. Maximum 6."
  2. First observedv1.0.2

TDQS

A4.8/5.0
Behavior5/5

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

No annotations are supplied, so the description carries full burden and does so richly: determinism/reproducibility ('identical input always returns an identical output, so caching and retries are safe'), hard limits, error taxonomy (invalid_input/internal_error), truncated semantics, and payment behavior. This is exactly the behavioral disclosure a mutation-free but complex tool needs.

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 purpose, then INPUT/HARD LIMITS/OUTPUT/PAYMENT headers that make scanning easy; each block is substantive rather than filler. It is long, and the OUTPUT block is verbose because no output schema exists, but the payment paragraph is the only portion that could be trimmed.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness5/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

With no output schema and nested options/domain objects, the description supplies the return contract itself (resultType enum, solutions[].tier/certified, truncated, error.type), so an agent knows what it will get back. Nothing material is missing for correct invocation or interpretation.

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 coverage is already 100%, so the schema handles per-parameter meaning; the description still adds constraints the schema does not encode (max 6 variables, 1-64 equations, equation count >= variable count, 100KB cap, 6-decimal fixed output, domain defaulting to +/1e6). It stops short of explaining options.budget/maxDepth or fastMode, which the schema also leaves thin.

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 ('deterministic solver for systems of real equations') and immediately separates itself from siblings by naming what it is not: not symbolic algebra, not an ODE solver, not a language model. An agent can distinguish it from poly_roots/verify without opening any schema.

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

Usage Guidelines5/5

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

Explicitly frames when to use it ('verifiable, reproducible numeric answer for algebraic equations or common transcendentals') and when not ('Not suitable for symbolic algebra, closed-form proofs, initial-value ODEs, or mandatory integer equality'), plus it routes failures to give_feedback. This is the full when/when-not/alternative pattern.

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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