Lingshu Solver

{'type': 'object', 'required': ['message'], 'properties': {'context': {'type': 'string', 'description': 'Optional context: the triggering scenario or input characteristics.'}, 'message': {'type': 'string', 'description': 'What you hit, what you expected, and what you actually got.'}}}

{'type': 'object', 'required': [], 'properties': {'channel': {'type': 'string', 'description': 'Payment channel: currently fixed to corporate-static (corporate bank collection). Leave empty.'}, 'orderId': {'type': 'string', 'description': 'For self-reporting: the order id returned by a previous pay call, shaped like LS-YYYYMMDD-xxxxxx.'}, 'selfReportNote': {'type': 'string', 'description': 'Optional payment note (payer, channel, time), kept only for reconciliation, up to 200 characters.'}, 'selfReportPaid': {'type': 'boolean', 'description': 'For self-reporting: set true after paying to declare that this order was paid. The server does not verify and credits the order amount and releases it immediately (honor system); the credit is marked amountVerified:false / creditedBy:self_report so it can be reconciled against bank statements afterwards.'}}}

{'type': 'object', 'required': ['coefficients'], 'properties': {'tolerance': {'type': 'number', 'description': 'Tolerance used to decide a root (optional; internal precision is used by default).'}, 'coefficients': {'type': 'array', 'items': {'type': 'number'}, 'description': 'Polynomial coefficients, highest degree first. [1,-2,-5,6] means x^3-2x^2-5x+6.'}}}

{'type': 'object', 'required': ['equations'], 'properties': {'domain': {'type': 'object', 'description': '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': {'type': 'object', 'description': 'Advanced options (optional), e.g. {budget:500000, maxDepth:28}'}, 'fastMode': {'type': 'boolean', 'description': 'Fast mode (default false).'}, 'equations': {'type': 'array', 'items': {'type': 'string'}, 'description': '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': {'type': 'boolean', 'description': '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': {'type': 'array', 'items': {'type': 'string'}, 'description': 'Variable names (optional). If omitted they are auto-detected from the equation text, in order of appearance. Maximum 6.'}}}

{'type': 'object', 'required': ['equation', 'candidate'], 'properties': {'equation': {'type': 'string', 'description': 'A single equation containing an equals sign, e.g. "x^2 = 4".'}, 'candidate': {'oneOf': [{'type': 'number'}, {'type': 'object'}, {'type': 'array'}], 'description': 'The claimed answer: a number (single variable, default variable x), {variable:value} for multiple variables, or an array in variables order.'}, 'tolerance': {'type': 'number', 'description': 'Neighbourhood radius (optional, default 1e-3) within which a matching certified root is searched.'}, 'variables': {'type': 'array', 'items': {'type': 'string'}, 'description': 'Variable names (required for multiple variables or array candidates), e.g. ["x","y"].'}}}