{ "openapi": "3.1.1", "info": { "title": "Graphing Calculator API", "version": "1.0.0", "summary": "Plot up to 6 functions or parametric curves with roots, extrema, intersections and SVG/PNG export.", "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://graphingcalculator.usefulweb.site" } ], "paths": { "/api/v1/calculate": { "post": { "operationId": "calculate", "summary": "Plot up to 6 functions or parametric curves with roots, extrema, intersections and SVG/PNG export.", "description": "Graphs y = f(x) for up to six functions (or parametric curves x(t), y(t)) over the range you choose, lists the roots, local minima and maxima and the intersection points numerically, prints a table of values and offers the graph as SVG and PNG downloads.\n\nMethodology:\n- Each function is parsed by the shared CAS core and evaluated in double precision at 600 points; jumps across vertical asymptotes are broken instead of joined, and extreme values are clipped unless you set y min/max.\n- Roots: sign changes on a 4,000-point grid refined by bisection, plus touching roots (local minima of |f| that reach zero). Poles are excluded because |f| must be tiny at a root.\n- Extrema: the derivative is computed symbolically and its roots are found the same way; each critical point is classified by comparing neighbouring values (inflection points are skipped).\n- Intersections: roots of f_i − f_j for every pair of functions. All of these are numeric approximations (about 10 significant digits) and only cover the plotted range.\n- The graph is an accessible SVG (title, description, data table); the PNG is rasterised from the same SVG with ImageMagick.", "tags": [ "math" ], "x-mcp-tool": "graphing_calculator", "requestBody": { "required": true, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/GraphingCalculatorInput" }, "examples": { "example1": { "summary": "Sine and a parabola", "value": { "functions": "y = sin(x)\ny = x^2/4 - 1", "xMin": -5, "xMax": 5 } }, "example2": { "summary": "Cubic with roots and extrema", "value": { "functions": "x^3 - 3x", "xMin": -3, "xMax": 3, "tableStep": 0.5 } }, "example3": { "summary": "Parametric circle and Lissajous curve", "value": { "mode": "parametric", "functions": "cos(t), sin(t)\nsin(3t), cos(2t)", "tMin": 0, "tMax": 6.283185307179586, "png": false } }, "example4": { "summary": "Rational function with asymptotes", "value": { "functions": "1/(x - 1)\nx/2", "xMin": -4, "xMax": 4, "yMin": -6, "yMax": 6, "png": false } } } } } }, "responses": { "200": { "description": "Calculation result envelope.", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/GraphingCalculatorResult" } } } }, "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" } } } } } }, "GraphingCalculatorInput": { "type": "object", "additionalProperties": false, "properties": { "mode": { "title": "Graph type", "type": "string", "enum": [ "functions", "parametric" ], "default": "functions" }, "functions": { "title": "Functions (one per line)", "description": "Functions: \"y = x^2 - 2\" or just \"x^2 - 2\". Parametric: \"cos(t), sin(t)\" per line. Up to 6 lines.", "type": "string", "maxLength": 3000 }, "xMin": { "title": "x min", "type": "number", "default": -10 }, "xMax": { "title": "x max", "type": "number", "default": 10 }, "yMin": { "title": "y min", "description": "Optional; automatic (asymptotes are clipped) when empty.", "type": "number" }, "yMax": { "title": "y max", "description": "Optional.", "type": "number" }, "tMin": { "title": "t min (parametric)", "type": "number", "default": 0 }, "tMax": { "title": "t max (parametric)", "description": "Default 2π.", "type": "number", "default": 6.283185307179586 }, "tableStep": { "title": "Table step", "description": "Optional step for the table of values (default: a tenth of the range; at most 41 rows).", "type": "number", "minimum": 0 }, "analyze": { "title": "Find roots, extrema and intersections", "type": "boolean", "default": true }, "png": { "title": "Also create a PNG download", "type": "boolean", "default": true } }, "required": [ "functions" ] }, "GraphingCalculatorResult": { "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": [ "mode", "domain", "curves", "intersections", "table", "svg", "png" ], "properties": { "mode": { "type": "string", "enum": [ "functions", "parametric" ] }, "domain": { "type": "object", "additionalProperties": false, "required": [ "min", "max", "variable" ], "properties": { "min": { "type": "number" }, "max": { "type": "number" }, "variable": { "type": "string" } } }, "curves": { "type": "array", "items": { "type": "object", "additionalProperties": false, "required": [ "index", "input", "expression", "latex", "derivative", "roots", "extrema", "yIntercept" ], "properties": { "index": { "type": "integer" }, "input": { "type": "string" }, "expression": { "type": "string" }, "latex": { "type": "string" }, "derivative": { "type": [ "string", "null" ] }, "roots": { "type": "array", "items": { "type": "number" } }, "extrema": { "type": "array", "items": { "type": "object", "additionalProperties": false, "required": [ "x", "y", "kind" ], "properties": { "x": { "type": "number" }, "y": { "type": "number" }, "kind": { "type": "string", "enum": [ "minimum", "maximum" ] } } } }, "yIntercept": { "type": [ "number", "null" ] } } } }, "intersections": { "type": "array", "items": { "type": "object", "additionalProperties": false, "required": [ "a", "b", "x", "y" ], "properties": { "a": { "type": "integer" }, "b": { "type": "integer" }, "x": { "type": "number" }, "y": { "type": "number" } } } }, "table": { "type": "object", "additionalProperties": false, "required": [ "columns", "rows" ], "properties": { "columns": { "type": "array", "items": { "type": "string" } }, "rows": { "type": "array", "items": { "type": "array", "items": { "type": [ "number", "null" ] } } } } }, "svg": { "type": "object", "additionalProperties": false, "required": [ "artifactId", "filename", "mime", "bytes", "sha256", "path" ], "properties": { "artifactId": { "type": "string" }, "filename": { "type": "string" }, "mime": { "type": "string" }, "bytes": { "type": "integer" }, "sha256": { "type": "string" }, "path": { "type": "string", "description": "Download path on the same site (valid for about 2 hours)." } } }, "png": { "type": [ "object", "null" ], "additionalProperties": false, "required": [ "artifactId", "filename", "mime", "bytes", "sha256", "path" ], "properties": { "artifactId": { "type": "string" }, "filename": { "type": "string" }, "mime": { "type": "string" }, "bytes": { "type": "integer" }, "sha256": { "type": "string" }, "path": { "type": "string", "description": "Download path on the same site (valid for about 2 hours)." } } } } }, "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" } } } } } } } }