{ "openapi": "3.1.1", "info": { "title": "Math Workbench API", "version": "1.0.0", "summary": "Simplify, factor, differentiate, integrate, solve, take limits, series and plots in one box.", "description": "Every endpoint performs the same calculation as the human page and returns inputs, result, units, assumptions, sources, warnings and computedAt. MCP endpoint: /mcp." }, "servers": [ { "url": "https://mathworkbench.usefulweb.site" } ], "paths": { "/api/v1/calculate": { "post": { "operationId": "calculate", "summary": "Simplify, factor, differentiate, integrate, solve, take limits, series and plots in one box.", "description": "A small computer algebra system: type commands such as \"integrate x*e^x from 0 to 1\", \"derivative sin(x)^2\", \"solve x^2 - 5x + 6 = 0\", \"limit sin(x)/x as x -> 0\" or \"series cos(x) at 0 order 6\". Results are exact (fractions, roots, π) where possible, and the tool says clearly when it falls back to a numeric answer.\n\nMethodology:\n- Input is tokenised and parsed with a Pratt parser that understands implicit multiplication (2x, 3(x+1), x sin x), powers of functions (sin^2(x)), |x| and the usual functions; log means the natural logarithm, log10/log2 are explicit.\n- All numbers are exact fractions (BigInt rationals); expressions are kept in a canonical form (like terms collected, powers merged, exact values of roots and special angles).\n- Derivatives use the sum, product, power and chain rules. Integrals use a table of standard forms, linearity, substitution, integration by parts, partial fractions and the e^(ax)·sin(bx) formula; every antiderivative is verified by differentiating it numerically at several points.\n- Definite integrals use F(b) − F(a) when an antiderivative exists and the integrand has no singularity inside the interval, cross-checked by adaptive Simpson (or tanh–sinh quadrature for endpoint singularities and infinite ranges); otherwise the numeric value is shown and labelled as such.\n- Limits try direct substitution, then L’Hôpital’s rule on 0/0 and ∞/∞ quotients, degree comparison at infinity, and finally numeric one-sided evaluation with extrapolation (marked as numeric).\n- Equations: linear, quadratic, rational, radical and higher polynomial equations (rational root theorem, then Durand–Kerner for the rest); systems of linear equations by exact Gaussian elimination.\n\nA compact computer algebra system, not a full replacement for Mathematica or SymPy: some simplifications (e.g. most trigonometric identities) are not applied, and numeric fallbacks are approximations.", "tags": [ "math" ], "x-mcp-tool": "math_workbench", "requestBody": { "required": true, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/MathWorkbenchInput" }, "examples": { "example1": { "summary": "Definite integral by parts", "value": { "query": "integrate x*e^x from 0 to 1" } }, "example2": { "summary": "Second derivative", "value": { "query": "d^2/dx^2 sin(x)^2" } }, "example3": { "summary": "Solve a quadratic", "value": { "query": "solve 2x^2 + 3x - 4 = 0" } }, "example4": { "summary": "Classic limit", "value": { "query": "limit (1 - cos(x))/x^2 as x -> 0" } }, "example5": { "summary": "Taylor series", "value": { "query": "series ln(1+x) at 0 order 5" } }, "example6": { "summary": "Factor a polynomial", "value": { "query": "factor x^4 - 5x^2 + 4" } }, "example7": { "summary": "Plot two functions", "value": { "query": "plot sin(x), x - x^3/6 from -4 to 4" } }, "example8": { "summary": "Integral without elementary antiderivative", "value": { "query": "integrate e^(-x^2) from 0 to 2" } } } } } }, "responses": { "200": { "description": "Calculation result envelope.", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/MathWorkbenchResult" } } } }, "400": { "description": "Malformed JSON body.", "content": { "application/problem+json": { "schema": { "$ref": "#/components/schemas/Problem" } } } }, "422": { "description": "Invalid input (see errors[]).", "content": { "application/problem+json": { "schema": { "$ref": "#/components/schemas/Problem" } } } }, "429": { "description": "Rate limit exceeded (see Retry-After).", "content": { "application/problem+json": { "schema": { "$ref": "#/components/schemas/Problem" } } } } } } }, "/api/v1/tool": { "get": { "operationId": "getToolDefinition", "summary": "Inputs, output schema and examples for this tool", "responses": { "200": { "description": "Tool definition.", "content": { "application/json": { "schema": { "type": "object" } } } } } } } }, "components": { "schemas": { "Problem": { "type": "object", "description": "RFC 9457 problem details. 422 responses include per-field `errors`.", "required": [ "type", "title", "status", "detail" ], "properties": { "type": { "type": "string" }, "title": { "type": "string" }, "status": { "type": "integer" }, "detail": { "type": "string" }, "code": { "type": "string" }, "errors": { "type": "array", "items": { "type": "object", "required": [ "field", "message" ], "properties": { "field": { "type": "string" }, "message": { "type": "string" } } } } } }, "MathWorkbenchInput": { "type": "object", "additionalProperties": false, "properties": { "query": { "title": "Command", "description": "Commands: simplify, expand, factor, derivative (or d/dx), integrate [from a to b], solve, limit … as x -> a, evaluate … at x = 2, series … at a order n, plot f, g from a to b. Use * or juxtaposition for products (2x), ^ for powers, sqrt(), ln(), log10(), sin(), e, pi.", "type": "string", "maxLength": 2000 } }, "required": [ "query" ] }, "MathWorkbenchResult": { "type": "object", "additionalProperties": false, "required": [ "schemaVersion", "tool", "computedAt", "inputs", "summary", "result", "units", "assumptions", "sources", "warnings", "presentation", "links" ], "properties": { "schemaVersion": { "type": "string", "const": "1.0" }, "tool": { "type": "object", "additionalProperties": false, "required": [ "id", "name", "version" ], "properties": { "id": { "type": "string" }, "name": { "type": "string" }, "version": { "type": "string" } } }, "computedAt": { "type": "string", "format": "date-time" }, "inputs": { "type": "object", "description": "Normalised inputs actually used, including applied defaults." }, "summary": { "type": "string" }, "result": { "type": "object", "additionalProperties": false, "required": [ "command", "input", "variable", "result", "latex", "numeric", "symbolic", "method", "steps", "items", "notes" ], "properties": { "command": { "type": "string", "enum": [ "simplify", "expand", "factor", "derivative", "integrate", "solve", "limit", "evaluate", "series", "plot" ] }, "input": { "type": "string", "description": "The parsed input in canonical plain-text form." }, "variable": { "type": [ "string", "null" ] }, "result": { "type": [ "string", "null" ], "description": "Main result as plain text (null when nothing could be computed)." }, "latex": { "type": [ "string", "null" ], "description": "Main result as LaTeX." }, "numeric": { "type": [ "number", "null" ], "description": "Decimal value when the result is a single real number." }, "symbolic": { "type": "boolean", "description": "True when the result is exact/symbolic, false for numeric approximations." }, "method": { "type": "string" }, "steps": { "type": "array", "items": { "type": "string" } }, "items": { "type": "array", "items": { "type": "object", "additionalProperties": false, "required": [ "label", "text", "latex", "numeric" ], "properties": { "label": { "type": "string" }, "text": { "type": "string" }, "latex": { "type": [ "string", "null" ] }, "numeric": { "type": [ "number", "null" ] } } } }, "notes": { "type": "array", "items": { "type": "string" } } } }, "units": { "type": "object", "additionalProperties": { "type": "string" } }, "assumptions": { "type": "array", "items": { "type": "string" } }, "sources": { "type": "array", "items": { "type": "object", "additionalProperties": false, "required": [ "title" ], "properties": { "title": { "type": "string" }, "url": { "type": "string" }, "publisher": { "type": "string" }, "retrievedAt": { "type": "string" }, "note": { "type": "string" } } } }, "warnings": { "type": "array", "items": { "type": "string" } }, "presentation": { "type": "array", "items": { "type": "object" }, "description": "Display blocks used by the human page (same data)." }, "links": { "type": "object", "additionalProperties": false, "required": [ "human", "api", "openapi", "methodology" ], "properties": { "human": { "type": "string", "format": "uri" }, "api": { "type": "string", "format": "uri" }, "openapi": { "type": "string", "format": "uri" }, "methodology": { "type": "string", "format": "uri" } } } } } } } }