solve
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.【计费·仅托管远程端点】本端点每次 solve 收费 1 分钱（¥0.01/次），需在请求头携带 Authorization: Bearer ；尚无凭证时请先 GET /pricing 查看价格与付款方式（无需注册账号，凭证即身份）。信任制：solve 入参传 honorPaid:true 即声明「个人/评估用途」并直接放行（不验证、不扣余额）——不付钱也能用，付费属自愿。若结果用于产品/商业/自动化流程，欢迎走付费通道（GET /pricing 取得订单，通过对公账户付款支持作者）；不付也照常能用，本服务不做强制验证。托管端点收款走公司「对公静态收款」，不接任何支付平台商户 API：下单 → 对公转账备注订单号 → 付款后自助入账（再调 pay 传 orderId + selfReportPaid:true 即立即放行，零人工；按 ¥0.01/次）。自助入账不做验证（信任制）：同一道门的 honorPaid 本来就免费 ⇒ 声明已付不会造成额外损失，只是让诚实付款的人不必等对账。本地版（npx -y lingshu-solver）与网页版永久免费、无次数限制、离线不外传 —— 若不便付费请直接用它们。免费调用：initialize / tools/list / give_feedback / GET /credit。
Input Schema
| Name | Required | Description | Default |
|---|---|---|---|
| domain | No | 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. | |
| options | No | Advanced options (optional), e.g. {budget:500000, maxDepth:28} | |
| fastMode | No | Fast mode (default false). | |
| equations | Yes | 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]. | |
| honorPaid | No | 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. | |
| variables | No | Variable names (optional). If omitted they are auto-detected from the equation text, in order of appearance. Maximum 6. |