Lingshu Solver

Quality 67 / 100needs work

6 tools, about 2,269 tokens to load them all · tool set 08bce887ad87 · tools last changed 2026-10-07 · checked 2026-10-19 10:20 UTC

Tool changes

• 2026-10-07geometryadded

  Deterministic 1D/2D/3D geometry: distances, intersections, areas, volumes, angles, convex hull, point-in-polygon, rotations. Closed-form (not iterative), exact up to floating-point rounding, identical output for identical input. Use it instead of doing geometry yourself. Pass {op, ...args} with op one of: 1D: dist1,midpoint1,divide_point,divide_ratio,harmonic_conjugate,interval_length,interval_midpoint,interval_intersect,interval_union,interval_hull,interval_overlap_length,interval_contains,point_between | 2D: dist2,midpoint2,lerp2,line_from_points,point_line_distance,point_segment_distance,project_point_line,line_intersect,line_intersect_points,segment_intersect,segment_length,angle_3points,angle_vectors,line_angle,triangle_area,triangle_centroid,triangle_incenter,polygon_area,polygon_perimeter,polygon_centroid,point_in_polygon,convex_hull,polygon_is_convex,circle_from_3points,point_circle_position,circle_line_intersect,circle_circle_intersect,circle_measure,sector_area,rotate_point,reflect_point_line,scale_point,parallel_through,perpendicular_through,triangle_circumcenter,triangle_orthocenter,triangle_excenters,triangle_five_centers,euler_line,triangle_nine_point_circle,triangle_euler_inequality,triangle_medians,triangle_altitudes,triangle_bisector_lengths,cevian_concurrent,menelaus_collinear,power_of_point,radical_axis,polar_of_point,pole_of_line,ptolemy,miquel_point,napoleon_triangles,pick_theorem,cocircular_check,minimum_enclosing_circle,circumcircle | 3D: dist3,midpoint3,lerp3,plane_from_3points,point_plane_distance,project_point_plane,reflect_point_plane,coplanar,point_line_distance3,project_point_line3,line_plane_intersect,line_line_relation,plane_plane_intersect,tetra_volume,polygon_area3,face_normal,mesh_volume,sphere_from_4points,sphere_line_intersect,sphere_plane_intersect,sphere_measure,angle_vectors3,angle_line_plane,angle_plane_plane,rotate_axis,cross3,triple_product,tetrahedron_geometry,monge_point | any: distance,midpoint,lerp,norm,normalize,dot,cross,project,reject,translate,centroid,bbox,diameter,stewart_theorem,law_of_cosines,law_of_cosines_sas,law_of_sines,solve_triangle,heron_area,brahmagupta,golden_ratio,regular_polygon,regular_tetrahedron,newton_polytope,tropical_degree_bound,tropical_system_bound,regular_subdivision,bernstein_bound,tropical_bezout_bound,sphere_equation,polynomial_equation. The remaining args are passed flat and depend on op (p, q, a, b, c, d, r, poly, pts, angle, lambda, center, axis, segment, a1,b1,c1,a2,b2,c2, ...). Send an unknown op to receive the full catalog with every signature. READ trust.trustLevel: exact = safe to use directly; definitely_none = computed proof that there is NO intersection, safe to state as a conclusion; degenerate = the INPUT is degenerate (parallel / collinear / coplanar / coincident), do NOT invent a value — report the degeneracy instead.

• 2026-10-07verifychangeddescriptionmeaning changed
  before

  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.

  after · 27% of words in common

  Check whether a claimed answer is actually correct — call this on any number you computed yourself before passing it downstream. verdict=verified means it is a certified real root; verdict=refuted_or_unverified means it is NOT, and nearestCertifiedRoot then carries the correct value so you can self-correct in the same turn. Deterministic and reproducible.

• 2026-10-07poly_rootschangeddescription
  before

  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.

  after · 65% of words in common

  All real roots of a polynomial, each individually Krawczyk-certified with a strict error box. Coefficients are highest degree first: [1,-2,-5,6] means x^3-2x^2-5x+6. Use it instead of letting a language model estimate roots. Complex roots are not returned (real only).

• 2026-10-07solvechangeddescriptionmeaning changed
  before

  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.

  after · 31% of words in common

  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.

• 2026-10-02paychangeddescription, input schemameaning changed
  before

  Create a real payment order for this or future solving. Returns the order id, a dedicated key, and a structured payment intent. The payment channel is a corporate static collection code (UnionPay aggregate QR) settling into a corporate bank account; no payment-platform merchant API is used. AFTER PAYING: call this tool again with orderId and selfReportPaid:true and the order is credited and released immediately, with no manual check and no waiting for reconciliation, because this service runs on an honor system. If the server has no payment method configured the order is still created but payIntent.payTo is null; use honorPaid:true or contact the operator instead.

  after · 37% of words in common

  Optional voluntary-support only. The hosted endpoint is no per-call charge today (metering off) (metering off: no credential required, no call limit, no per-call charge), so no payment is needed at all. This tool records a support contribution of any amount: the channel is a corporate static collection code (UnionPay aggregate QR) settling into a corporate bank account, and no payment-platform merchant API is used. AFTER PAYING: nothing to do — there is no self-crediting step and no waiting for reconciliation; the operator reconciles against the corporate bank statement, and any positive amount counts as support, not a bill. If the server has no payment method configured the order is still created but payIntent.payTo is null; in that case just keep calling the endpoint with no credential at all.

• 2026-10-02solvechangeddescription
  before

  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 <key>；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。

  after · 92% of words in common

  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.

• 2026-10-01paychangeddescription, input schemameaning changed
  before

  对公收款：为本次/后续求解创建一笔真实付费订单（¥0.01/次），返回订单号、专属 key 与结构化付款意图（payIntent）。统一收款入口 = 工银e支付银联聚合码（支持支付宝/微信/银联扫码），钱落公司对公户，不接任何支付平台商户 API。【付款后自助入账·推荐】付款完成后再调一次本工具并传 orderId + selfReportPaid:true，即**立即入账、立即放行**，不需要任何人工核对、不需要等对账 —— 本服务按信任制运转（同一道门 honorPaid 本来就免费，所以「声明已付款」不会多出任何损失，只是把诚实付款的人从「等入账」里解放出来）。若服务端未配置收款方式（LS_PAY_TO 为空），订单仍可创建但 payIntent.payTo 为 null，此时请改用 honorPaid:true 或联系作者。

  after · 11% of words in common

  Create a real payment order for this or future solving. Returns the order id, a dedicated key, and a structured payment intent. The payment channel is a corporate static collection code (UnionPay aggregate QR) settling into a corporate bank account; no payment-platform merchant API is used. AFTER PAYING: call this tool again with orderId and selfReportPaid:true and the order is credited and released immediately, with no manual check and no waiting for reconciliation, because this service runs on an honor system. If the server has no payment method configured the order is still created but payIntent.payTo is null; use honorPaid:true or contact the operator instead.

• 2026-10-01verifychangeddescription, input schemameaning changed
  before

  核验一个「声称的答案」到底对不对——这是「LLM 猜了 2.1、真根是精确 2」的检查。输入方程 + 候选值/点（数字，或 {变量:值}，或按 variables 顺序的数组），本工具在候选点邻域内调用同一套认证内核：若找到与之匹配的认证根 → 返回 verified + 误差盒；若找不到 → 返回 refuted 并附上最近的认证根（让 Agent 立刻看到正确值）。确定性、非 LLM、结果可复现。★ 计费边界（Agent 必读）：与 solve 同规则 —— honorPaid:true 即信任制免费放行；否则走付费通道（GET /pricing）。

  after · 9% of words in common

  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.

• 2026-10-01poly_rootschangeddescription, input schemameaning changed
  before

  多项式全部实根，逐个 Krawczyk 认证（带严格误差盒）。输入系数「最高次在前」，如 [1,-2,-5,6] 表示 x³−2x²−5x+6。确定性、可复现、可证明正确；复数根不返回（本品只做实数）。给 AI Agent 当「可靠的多项式求根件」——不会再像通用 LLM 那样把根算错或半对。★ 计费边界（Agent 必读）：与 solve 同规则 —— honorPaid:true 即信任制免费放行；否则走付费通道（GET /pricing）。

  after · 15% of words in common

  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.

• 2026-10-01give_feedbackchangeddescription, input schemameaning changed
  before

  AI 智能体在调用 solve 遇到卡点、错误、或认为结果有问题时，主动回报。回报内容仅落本地 feedback.log，不会外传。帮助作者持续改进。

  after · 6% of words in common

  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.

Showing the latest 10. Full history: list_changes · trend: quality JSON.

Checks run on what our credential-free, read-only probes observe; tools are never called and no code audit is performed. How it is computed.