Motor de resolución de sistemas de ecuaciones reales deterministas de ≤6 dimensiones · Herramienta MCP para agentes de IA y usuarios comunes
灵数求解器 (código Epsilon, V4.1) es un solucionador de sistemas de ecuaciones reales offline, determinista y de cero datos, que cubre ≤6 variables, soluciones reales y localización numérica ligera. No requiere que el usuario proporcione valores iniciales; utiliza aritmética de intervalos para contracción conservadora + operador de Krawczyk para certificación de soluciones, y se esfuerza por agotar múltiples soluciones.
Abre este enlace y ya puedes usarlo, sin instalar nada: 👉 https://genesis-plan.github.io/lingshu-solver/ (GitHub Pages, internacional/general)
Usuarios en China (más rápido, alojado en Tencent Cloud COS): 👉 https://hclj-1409755229.cos.ap-guangzhou.myqcloud.com/lingshu-solver/index.html
En el cuadro de entrada escribe las ecuaciones (por ejemplo, x^2 + y^2 = 25 y x + y = 7) y haz clic en resolver.
La página tiene 6 botones de ejemplo; haz clic en uno para ver qué puede resolver.
Opción A · Alojamiento remoto (sin instalación, listo para usar sin contraseña)
Hemos desplegado un servicio público permanente; solo tienes que introducir la URL, sin necesidad de instalar Node en tu máquina:
{
"mcpServers": {
"lingshu-solver": {
"url": "http://159.75.154.206:3000/mcp"
}
}
}Endpoint:
http://159.75.154.206:3000/mcp(Streamable HTTP). El servicio se ejecuta en un servidor ligero de Tencent Cloud, con arranque automático y reinicio automático en caso de caída. ⚠️ Actualmente es un endpoint temporal de IP desnuda + HTTP; una vez quehongchenlingjing.compase el registro, cambiaremos a un dominio HTTPS fijohttps://hongchenlingjing.com/mcp(actualizaremos aquí en ese momento). Este endpoint temporal se puede usar para pruebas de integración; plataformas como Smithery que requieren HTTPS se conectarán oficialmente después del registro.
Opción B · stdio local (requiere Node en tu máquina)
{
"mcpServers": {
"lingshu-solver": {
"command": "npx",
"args": ["-y", "lingshu-solver"]
}
}
}La versión
npxestará disponible solo después de publicar este paquete en npm (en proceso); mientras tanto, puedes hacergit cloney usar la opción C.
Opción C · clon local + ruta especificada
git clone https://github.com/genesis-plan/lingshu-solver.git
cd lingshu-solver
node mcp-server.jsConfiguración de MCP:
{ "mcpServers": { "lingshu-solver": { "command": "node", "args": ["本地绝对路径/灵数求解器/mcp-server.js"] } } }git clone https://github.com/genesis-plan/lingshu-solver.git
cd lingshu-solver
node mcp-server.js # 启动 MCP 服务端
node test/regression.js # 跑回归测试（28 用例）Este repositorio contiene:
index.html — producto de un solo archivo (UI en navegador + script central verificado <script id="solver-core">)
solver-core.js — cargador del motor Node (lee el script central de index.html, cero dependencias, reutilizable para MCP/pruebas)
mcp-server.js — servidor MCP stdio de cero dependencias (JSON-RPC 2.0 manual + tramas Content-Length)
package.json — metadatos estándar, integración en una línea con npx lingshu-solver
test/ — suite de regresión + pruebas de humo + tres conjuntos de exámenes permanentes
Related MCP server: Math MCP Server
Dimensión | Descripción |
Soluciones verificadas | Cada solución encontrada está certificada por Krawczyk ( |
Exhaustividad | Se esfuerza por agotar múltiples soluciones; en casos extremadamente patológicos (Jacobiano altamente singular, racimos de soluciones muy cercanos) puede omitir algunas soluciones dentro del presupuesto, marcando explícitamente |
Semántica de | Solo indica que "la rama global no ha decidido completamente todas las cajas dentro del presupuesto (no se puede probar que esté agotada)", no significa necesariamente que falten soluciones; en la gran mayoría de los casos todas las soluciones reales ya se han encontrado |
Número de variables | ≤6 |
Rango numérico | Dominio de búsqueda predeterminado ±1e6; para funciones de crecimiento rápido (exp/sinh) o dominios grandes, se recomienda especificar explícitamente |
Determinismo | Sin ramas aleatorias, la misma entrada siempre produce la misma salida |
Despliegue | Puramente local, offline, cero datos (sin red, sin almacenamiento, sin dependencias de terceros) |
No garantiza: exhaustividad del 100% para todas las entradas; convergencia garantizada dentro del presupuesto para sistemas altamente patológicos. Estos son límites honestos, no defectos.
Forma | Endpoint / comando | Aplicable a |
HTTP remoto (en línea) |
| Cualquier cliente MCP que soporte Streamable HTTP, sin instalación |
stdio local (npx) |
| Node instalado en la máquina, disponible tras publicación en npm |
stdio local (clone) |
| Desarrolladores / autoalojamiento offline |
Código del servidor HTTP remoto: http-mcp-server.js (cero dependencias, solo módulos integrados de Node; comparte el núcleo de resolución solver-core.js con mcp-server.js, resultados consistentes de la misma fuente). Si necesitas autoalojar el servicio remoto:
PORT=3000 node http-mcp-server.jsRecomendado · Alojamiento remoto (sin instalación, en línea):
{
"mcpServers": {
"lingshu-solver": {
"url": "http://159.75.154.206:3000/mcp"
}
}
}stdio local · comando de una línea (requiere publicar en npm primero, aún no publicado; por ahora usa la versión clone):
{
"mcpServers": {
"lingshu-solver": {
"command": "npx",
"args": ["-y", "lingshu-solver"]
}
}
}Nota:
npx lingshu-solverestará disponible solo después de publicar este paquete en npm; estamos trabajando en ello. Mientras tanto, usa la versión "especificar ruta local manualmente" a continuación (clona el repositorio primero).
Alternativa · Especificar ruta local manualmente (cuando ya has clonado el repositorio):
{
"mcpServers": {
"lingshu-solver": {
"command": "node",
"args": ["把这里替换成你本地的绝对路径/灵数求解器/mcp-server.js"]
}
}
}La versión manual requiere reemplazar la ruta en
argscon la ruta absoluta de tumcp-server.jslocal (por ejemplo,C:/Users/你的用户名/Desktop/灵数求解器/mcp-server.js). La versión npx no requiere este paso.
solveEntrada:
{
"equations": ["x^2 + y^2 = 25", "x + y = 7"],
"variables": ["x", "y"],
"domain": { "x": [-30, 30], "y": [-30, 30] }
}equations: array de cadenas de ecuaciones (obligatorio), soporta + - * / ^ sqrt log sin cos tan exp abs, y restricciones de dominio en el texto "x ∈ [-30,30]".
variables: array de nombres de variables (opcional, si no se proporciona, se identifican automáticamente en orden de aparición, máximo 6).
domain: dominio de búsqueda explícito (opcional). Se recomienda especificarlo para la demostración de "soluciones finitas · parciales" o funciones de crecimiento rápido; de lo contrario, el valor predeterminado ±1e6 puede fallar en la poda y activar truncated.
La precisión de salida es fija a 6 decimales (especificación del producto "cuadrícula finita de 6 decimales"), sin opción de cambiar la precisión; los puntos de solución
valuesse ajustan a la cuadrícula, con residuos reales típicamente ≤ 1e-9.
Salida (extracto):
{
"resultType": 2,
"resultTypeName": "finite",
"certified": true,
"truncated": false,
"precisionDecimals": 6,
"solutionCount": 2,
"recommended": { "values": [3, 4], "tier": "proven", "residual": 0 },
"solutions": [ { "values": [3, 4], "tier": "proven", "residual": 0 }, ... ],
"warnings": []
}resultType: 1=empty(sin solución) / 2=finite(soluciones finitas) / 3=infinite(conjunto infinito de soluciones, solo se da la solución recomendada más cercana al origen).
tier: proven (certificado por Krawczyk) / candidate (no probado pero posible solución) / structural (derivado estructuralmente).
give_feedbackEl agente de IA informa proactivamente cuando encuentra bloqueos, errores o problemas sospechosos; solo se registra en el feedback.log local, no se transmite externamente:
{ "name": "give_feedback", "arguments": { "message": "x^2=4 期望2解", "context": "批量求解场景" } }node verify_core.js # 引擎加载 + 6 个代表性用例
node mcp_smoke.js # MCP 字节级冒烟（initialize/tools/list/tools/call）
node mcp_smoke2.js # give_feedback + 错误结构化（不泄露堆栈）
node test/regression.js # 三套常驻考卷回归（28 用例，known 命中率统计）Título | Ecuación | Esperado |
Mínimo 1 variable |
| 2 soluciones |
Máximo 6 variables | Sistema lineal tridiagonal de 6 variables | Solución única |
Conjunto vacío sin solución |
| Conjunto vacío (prueba sound de no solución) |
Soluciones finitas · todas | Círculo × hipérbola | 4 soluciones todas certificadas |
Soluciones finitas · parciales |
| Múltiples soluciones + banner |
Soluciones infinitas · recomendada |
| Conjunto infinito, recomendada (1.5,1.5) |
"灵数求解器_代码流程中文说明.md" — flujo interno completo desde el análisis hasta la salida (para lectores con formación matemática)
"灵数求解器商业化战略白皮书.md" — posicionamiento, límites de capacidad, riesgos
Serie de solicitudes de patente de invención (presentadas)
Apache License 2.0 — ver LICENSE.
Report a problem to the operator when solve hits a dead end, returns an error, or produces something you believe is wrong. The text is written to a local log only and is never transmitted anywhere else.
| Name | Required | Description | Default |
|---|---|---|---|
| context | No | Optional context: the triggering scenario or input characteristics. | |
| message | Yes | What you hit, what you expected, and what you actually got. |
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations, the description carries the full behavioral burden and discloses the key side effect: text is written to a local log only and never transmitted elsewhere. It does not cover log location, permissions, or return behavior, but the critical data-handling trait is stated.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is two efficient sentences. The primary purpose and trigger conditions are front-loaded, and the second sentence adds essential behavioral context without waste.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a simple two-parameter feedback tool with no output schema and no annotations, the description covers purpose, usage triggers, and data handling adequately. It could be slightly more complete by clarifying whether feedback should also be given when verify finds issues, but the core context is sufficient.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 100%, and the schema already documents both context and message thoroughly. The description adds no parameter-specific syntax, format, or constraints beyond what the schema provides, so the baseline of 3 is appropriate.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Does the description clearly state what the tool does and how it differs from similar tools?
The description states a specific verb and target: reporting a problem to the operator. It also specifies the exact triggering conditions tied to the sibling tool solve, making it easy to distinguish from computational siblings like solve, verify, and poly_roots.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Does the description explain when to use this tool, when not to, or what alternatives exist?
It clearly says when to use the tool: when solve hits a dead end, returns an error, or produces something believed wrong. It does not state when not to use it or name explicit alternatives, but the contextual guidance is strong and actionable.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
All real roots of a polynomial, each individually certified by Krawczyk with a strict error box. Coefficients are ordered highest degree first, so [1,-2,-5,6] means x^3-2x^2-5x+6. Deterministic and reproducible; complex roots are not returned (real numbers only). Use it as a reliable polynomial root component instead of letting a general language model estimate roots. Free to use: pass honorPaid:true to declare personal or evaluation use.
| Name | Required | Description | Default |
|---|---|---|---|
| tolerance | No | Tolerance used to decide a root (optional; internal precision is used by default). | |
| coefficients | Yes | Polynomial coefficients, highest degree first. [1,-2,-5,6] means x^3-2x^2-5x+6. |
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations, the description carries the full load and does well: it discloses determinism/reproducibility, the Krawczyk certification with strict error boxes, exclusion of complex roots, and the honorPaid licensing declaration. It omits failure behavior for malformed or non-polynomial input and does not explain that honorPaid is not present in the declared input schema, which is a notable gap.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Is the description appropriately sized, front-loaded, and free of redundancy?
Front-loaded with the core purpose and scope, then the coefficient-ordering convention and the licensing note. Four sentences with little waste, though the honorPaid sentence is longer than the information warrants.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
No output schema exists, so the description must cover returns; it explains the certificate and error box but not the shape of the result (list of roots? objects with bounds?). It also never reconciles the honorPaid parameter with a schema that lacks it, leaving the agent unsure how to satisfy the licensing requirement.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema coverage is 100% and the schema already documents coefficients ordering and tolerance defaults, so the description's repetition of the [1,-2,-5,6] example adds no new meaning. The only novel parameter information is honorPaid, which is not in the schema at all, creating ambiguity rather than usable semantics.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Does the description clearly state what the tool does and how it differs from similar tools?
States a specific verb and resource – returning all real roots of a polynomial – plus the scope qualifier that complex roots are excluded and roots are certified by Krawczyk with a strict error box. It does not explicitly compare itself to siblings like solve or verify, so an agent still has to infer the boundary between this and a general solver.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Does the description explain when to use this tool, when not to, or what alternatives exist?
It advises use 'instead of letting a general language model estimate roots', which implies when to reach for it, but gives no when-not guidance and never names the sibling solve/verify tools it should be preferred over or combined with. Requirements and prerequisites for input are not stated.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
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.
| 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]. | |
| variables | No | Variable names (optional). If omitted they are auto-detected from the equation text, in order of appearance. Maximum 6. |
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.
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.
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.
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.
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.
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.
Check whether a claimed answer is correct. Give the equation plus a candidate value (a number for a single variable, {variable:value} pairs, or an array in variable order); the same certified kernel runs in a neighbourhood around the candidate. If a matching certified root is found the result is verified together with the error box; otherwise it is refuted and the nearest certified root is returned, so the calling agent immediately sees the correct value. Deterministic, not an LLM, reproducible across calls. Free to use: pass honorPaid:true to declare personal or evaluation use.
| Name | Required | Description | Default |
|---|---|---|---|
| equation | Yes | A single equation containing an equals sign, e.g. "x^2 = 4". | |
| candidate | Yes | The claimed answer: a number (single variable, default variable x), {variable:value} for multiple variables, or an array in variables order. | |
| tolerance | No | Neighbourhood radius (optional, default 1e-3) within which a matching certified root is searched. | |
| variables | No | Variable names (required for multiple variables or array candidates), e.g. ["x","y"]. |
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations exist, so the description carries the full burden, and it does well: it discloses the certified-kernel neighbourhood search, determinism and reproducibility, the refutation branch returning the nearest certified root, and a pricing/usage declaration via honorPaid. It omits failure modes such as malformed equation or non-convergence behaviour.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Is the description appropriately sized, front-loaded, and free of redundancy?
The core behaviour and input forms are front-loaded in the first two sentences, and every sentence carries information. It runs slightly long, with the honorPaid pricing clause appended as a trailing sentence that is easy to skim past.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a 4-parameter tool with no annotations and no output schema, the description covers both outcomes (verified with error box vs refuted with nearest certified root) so the agent knows what it will receive. It stops short of describing invalid-input or timeout behaviour, which is a minor gap.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 100%, so baseline is 3, but the description adds meaning beyond the schema by explaining that the candidate is evaluated within a neighbourhood of the supplied value ('the same certified kernel runs in a neighbourhood around the candidate'), which contextualises what tolerance actually does.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Does the description clearly state what the tool does and how it differs from similar tools?
States a specific verb and object ('Check whether a claimed answer is correct') and frames the tool as a verifier of a supplied candidate rather than a solver, which cleanly separates it from siblings solve and poly_roots. An agent can select it without opening the schema.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Does the description explain when to use this tool, when not to, or what alternatives exist?
Gives clear context for use: supply an equation plus a candidate value, and the tool certifies or refutes it. It does not explicitly say when not to use it (e.g. use solve/poly_roots when no candidate exists), so routing to alternatives is left to inference.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Recent tool additions, removals, and schema changes observed during successful MCP inspections.
v1.0.22give_feedback2 fields changedInput schema / properties / context / descriptionPrevious value: -"可选上下文：触发场景、输入特征等。"New value: +"Optional context: the triggering scenario or input characteristics."Input schema / properties / message / descriptionPrevious value: -"反馈内容：遇到了什么、期望什么、实际得到什么。"New value: +"What you hit, what you expected, and what you actually got."poly_roots2 fields changedInput schema / properties / coefficients / descriptionPrevious value: -"多项式系数，最高次在前。如 [1,-2,-5,6] 对应 x³−2x²−5x+6。"New value: +"Polynomial coefficients, highest degree first. [1,-2,-5,6] means x^3-2x^2-5x+6."Input schema / properties / tolerance / descriptionPrevious value: -"根的判定容差（可选，默认内部精度）"New value: +"Tolerance used to decide a root (optional; internal precision is used by default)."solve5 fields changedInput schema / properties / domain / descriptionPrevious 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."Input schema / properties / equations / descriptionPrevious 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]."Input schema / properties / fastMode / descriptionPrevious value: -"快速模式（默认 false）"New value: +"Fast mode (default false)."Input schema / properties / options / descriptionPrevious value: -"高级选项（可选），如 {budget:500000, maxDepth:28}"New value: +"Advanced options (optional), e.g. {budget:500000, maxDepth:28}"Input schema / properties / variables / descriptionPrevious 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."verify4 fields changedInput schema / properties / candidate / descriptionPrevious value: -"声称的答案：数字（单变量，默认变量 x）、{变量:值}（多变量）、或按 variables 顺序的数组。"New value: +"The claimed answer: a number (single variable, default variable x), {variable:value} for multiple variables, or an array in variables order."Input schema / properties / equation / descriptionPrevious value: -"含 \"=\" 的方程，如 \"x^2 = 4\"。"New value: +"A single equation containing an equals sign, e.g. \"x^2 = 4\"."Input schema / properties / tolerance / descriptionPrevious value: -"邻域半径（可选，默认 1e-3），在该邻域内寻找匹配的认证根。"New value: +"Neighbourhood radius (optional, default 1e-3) within which a matching certified root is searched."Input schema / properties / variables / descriptionPrevious value: -"变量名（多变量或数组候选时必填），如 [\"x\",\"y\"]。"New value: +"Variable names (required for multiple variables or array candidates), e.g. [\"x\",\"y\"]."v1.0.15poly_rootsverifyv1.0.2give_feedbacksolveScored across 4 tools
solve, poly_roots, verify, and give_feedback mostly have distinct roles: solving systems, finding polynomial roots, validating candidate answers, and reporting issues. However, solve and poly_roots can overlap for single polynomial equations, so an agent may occasionally hesitate between them.
Names are readable and mostly snake_case, but they mix patterns: solve and verify are simple verbs, give_feedback is verb_noun, and poly_roots is a noun. The set lacks a single predictable naming convention.
Four tools is well-scoped for a deterministic math solver with verification and feedback. Each tool appears to earn its place, and there is no obvious bloat or thinness.
The surface covers solving equations, polynomial roots, verifying claimed answers, and reporting problems, which matches the core numeric-solver domain. Minor gaps exist around explicit configuration/help tooling, but solve already exposes relevant options in its input.
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