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Lingshu Solver

by io.github.genesis-plan
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Deterministic (non-LLM) solver for systems of real equations. Use it instead of computing the math yourself whenever a wrong number has a cost. Same input always returns the identical result — no hallucination, no randomness, so caching and retries are safe. Supports algebraic equations and common transcendentals (sin/cos/tan/log/exp/sqrt/abs), max 6 variables, no initial guess needed. READ THE trust BLOCK: it tells you, per result, whether the value is safe to use directly or must be verified first. Pass domain explicitly for exp/sin or large ranges, else truncated may be true. Not for symbolic derivation, initial-value ODEs, or integer constraints. Optional: pass honorPaid:true to declare personal or evaluation use — then it is served free with no key, no balance and no deduction; payment is voluntary and never enforced.

Input 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].
honorPaidNoHonor system: set true to declare this call personal or evaluation use. It is released for free with no verification and no balance deduction. Set false only when this runs inside a product, a commercial pipeline or an automated workflow; payment is voluntary and never enforced.
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. Changed6 schema fields changed
    • 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 / honorPaid / description
      Previous value: -"信任制：声明本次为「个人/评估用途」即放行（不验证、不扣余额）——不付钱也能用。若结果用于产品/商业/自动化流程，欢迎改走付费通道（GET /pricing 取得订单与 key）支持作者；付费属自愿，本服务不做强制验证。"New value: +"Honor system: set true to declare this call personal or evaluation use. It is released for free with no verification and no balance deduction. Set false only when this runs inside a product, a commercial pipeline or an automated workflow; payment is voluntary and never enforced."
    • 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 observed

TDQS

A4.2/5.0
Behavior5/5

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

With no annotations, the description carries the full burden and does so well: it discloses determinism (identical result, safe for caching and retries), capability limits (algebraic + listed transcendentals, max 6 variables, no initial guess), a result-safety signal via the trust block, the truncated-result risk and how domain mitigates it, and the honorPaid payment semantics. This is the behavioral context an agent needs before calling.

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 purpose is front-loaded in the first sentence and the dense single paragraph is largely information-bearing rather than filler. It is longer than typical and somewhat run-on, but for a 6-parameter tool with no output schema and no annotations the length is justified.

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 tool with no output schema and no annotations, the description covers limits, determinism, result-safety via the trust block, domain guidance and the payment flag. It is nearly complete; the only real gap is that the actual shape of the returned result (beyond the trust flag) is not described.

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 baseline is 3. The description goes beyond the schema by advising when to supply domain explicitly ('for exp/sin or large ranges, else truncated may be true'), which is operational guidance the schema only hints at. The meaning of honorPaid is also reinforced at a level the schema alone conveys more tersely.

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?

States a specific verb and resource: a 'Deterministic (non-LLM) solver for systems of real equations', which an agent can immediately place. The exclusions ('Not for symbolic derivation, initial-value ODEs, or integer constraints') help separate it from general math work, but the description never names the obvious sibling poly_roots, so the boundary with that tool is left implicit.

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?

Gives a clear positive trigger ('Use it instead of computing the math yourself whenever a wrong number has a cost') and explicit exclusions (symbolic derivation, IVP ODEs, integer constraints). It also points to the trust block and the domain parameter as conditions. It stops short of naming sibling alternatives such as verify or poly_roots, so it is strong context without full routing.

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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