{
  "title": "Finite difference table explorer",
  "human_url": "https://happytails.ai/en/calculators/finite-difference-table-explorer/",
  "agent_url": "https://happytails.ai/agents/en/calculators/finite-difference-table-explorer/",
  "language": "en",
  "markdown_url": "https://happytails.ai/en/calculators/finite-difference-table-explorer.md",
  "content": "Finite difference table explorer\nBuild a full difference table and test whether equally spaced samples fit a proposed polynomial degree.\nHow can we improve this tool?\nReport a problem or share an idea.\nPlease leave out private information. Your message and the tool name go to our team via PostHog.\nHow to use Finite difference table explorer\nPaste the sample values in their original order.\nSet the starting x, equal spacing and proposed maximum polynomial degree.\nInspect every difference and the consistency result, then download the complete table.\nUseful next steps\nContinued fraction explorer\nHow to use it\nBuild a full difference table and test whether equally spaced samples fit a proposed polynomial degree.\nLimits and assumptions\nEnter 2 to 64 equally spaced values, with at most 20,000 input characters. Values may be exact decimals, scientific notation or integer fractions within 120 digits per part and exponents from −120 to 120. Choose degree 0 to 20 and nonzero spacing. A degree-d consistency check needs at least d + 2 points. Exact arithmetic does not silently tolerate measurement rounding. Conditional next values are shown only for consistent samples; finite samples never prove the generating rule.\nKeep the exact values\nDownload JSON for the calculation, CSV for the complete table and the method note. Processing stays on your device.",
  "content_format": "text/plain",
  "visibility": "public",
  "links": [
    {
      "name": "Continued fraction explorer",
      "url": "https://happytails.ai/en/calculators/continued-fraction-explorer/"
    }
  ],
  "tool": {
    "id": "finite-difference-table-explorer",
    "category": "calculators",
    "built": true,
    "requirements": "Enter 2 to 64 equally spaced values, with at most 20,000 input characters. Values may be exact decimals, scientific notation or integer fractions within 120 digits per part and exponents from −120 to 120. Choose degree 0 to 20 and nonzero spacing. A degree-d consistency check needs at least d + 2 points. Exact arithmetic does not silently tolerate measurement rounding. Conditional next values are shown only for consistent samples; finite samples never prove the generating rule.",
    "implementation": {
      "fields": [
        {
          "key": "degree",
          "label": "Proposed maximum polynomial degree",
          "value": 2,
          "type": "number",
          "min": 0,
          "max": 20,
          "step": 1
        },
        {
          "key": "start",
          "label": "Starting x",
          "value": "0",
          "type": "text"
        },
        {
          "key": "spacing",
          "label": "Sample spacing",
          "value": "1",
          "type": "text"
        }
      ],
      "live": true,
      "background": true,
      "presentation": "metrics",
      "inputMaxLength": 20000,
      "inputErrorCode": "SEQ_SIZE",
      "note": "Enter 2 to 64 equally spaced values separated by whitespace, commas or semicolons. Decimals and integer fractions are exact; use decimal points. Check a proposed degree and inspect every difference. Exact tables are limited to 200,000 digit characters. A finite sample does not prove a generating rule.",
      "experience": {
        "automatic": true,
        "single": false,
        "inputMaxLength": 20000,
        "inputMode": "text",
        "label": "Equally spaced sample values",
        "placeholder": "0 1 4 9 16",
        "help": "Enter equally spaced sample values in order. Use decimal points, or exact fractions such as 1/3. Results update as you type. Up to 20,000 characters.",
        "action": null
      },
      "mode": "automatic",
      "interactive": false
    },
    "execution": "Browser interface",
    "api": null,
    "browser_agent": {
      "supported": true,
      "name": "run_current_tool",
      "discovery": "WebMCP on the human page in a supporting browser",
      "verification": "See audit/API-AUDIT.md; availability is not verification"
    }
  },
  "markdown": "# Finite difference table explorer\n\n- Human page: https://happytails.ai/en/calculators/finite-difference-table-explorer/\n- Markdown: https://happytails.ai/en/calculators/finite-difference-table-explorer.md\n- Structured JSON: https://happytails.ai/agents/en/calculators/finite-difference-table-explorer/index.json\n- Visibility: public\n\n## Tool capabilities\n\n| Property | Value |\n| --- | --- |\n| Tool ID | `finite-difference-table-explorer` |\n| Category | calculators |\n| Implementation | Registered implementation. Registration alone is not a production-quality guarantee. |\n| Browser execution | Automatic updates after valid input or file selection. |\n| Browser processing | Browser; see tool notes for network behavior. |\n| HTTP API | Not callable through HTTP. |\n| Browser-agent interface | run_current_tool |\n\n### Implementation notes\n\nEnter 2 to 64 equally spaced values separated by whitespace, commas or semicolons. Decimals and integer fractions are exact; use decimal points. Check a proposed degree and inspect every difference. Exact tables are limited to 200,000 digit characters. A finite sample does not prove a generating rule.\n\n### Inputs and settings\n\nText input: Equally spaced sample values.\n\nExample or placeholder shown in the interface (not a validated fixture):\n\n```text\n0 1 4 9 16\n```\n\nEnter equally spaced sample values in order. Use decimal points, or exact fractions such as 1/3. Results update as you type. Up to 20,000 characters.\n\n| Setting | Meaning | Control type | Default | Constraints |\n| --- | --- | --- | --- | --- |\n| `degree` | Proposed maximum polynomial degree | number | 2 | min=0 max=20 step=1 |\n| `start` | Starting x | text | \"0\" |  |\n| `spacing` | Sample spacing | text | \"1\" |  |\n\n### Browser-agent workflow\n\n1. Open the human page in a browser that supports WebMCP.\n2. Discover the interface exposed by that page; use its actual schema.\n3. Select files on the page first when the tool requires files.\n4. Call `run_current_tool` with valid input and settings.\n5. Inspect the returned result or error and the displayed output. Retrieve files from the displayed download links.\n\nCalls do not automatically copy or download results. Browser permissions still apply. Interface availability alone is not proof of successful execution.\n\n### Planning specification\n\nEnter 2 to 64 equally spaced values, with at most 20,000 input characters. Values may be exact decimals, scientific notation or integer fractions within 120 digits per part and exponents from −120 to 120. Choose degree 0 to 20 and nonzero spacing. A degree-d consistency check needs at least d + 2 points. Exact arithmetic does not silently tolerate measurement rounding. Conditional next values are shown only for consistent samples; finite samples never prove the generating rule.\n\nThis describes intended requirements. Use the implementation notes, interface schema and observed output to determine current support.\n\n### Complete machine-readable capability record\n\n```json\n{\n  \"id\": \"finite-difference-table-explorer\",\n  \"category\": \"calculators\",\n  \"built\": true,\n  \"requirements\": \"Enter 2 to 64 equally spaced values, with at most 20,000 input characters. Values may be exact decimals, scientific notation or integer fractions within 120 digits per part and exponents from −120 to 120. Choose degree 0 to 20 and nonzero spacing. A degree-d consistency check needs at least d + 2 points. Exact arithmetic does not silently tolerate measurement rounding. Conditional next values are shown only for consistent samples; finite samples never prove the generating rule.\",\n  \"implementation\": {\n    \"fields\": [\n      {\n        \"key\": \"degree\",\n        \"label\": \"Proposed maximum polynomial degree\",\n        \"value\": 2,\n        \"type\": \"number\",\n        \"min\": 0,\n        \"max\": 20,\n        \"step\": 1\n      },\n      {\n        \"key\": \"start\",\n        \"label\": \"Starting x\",\n        \"value\": \"0\",\n        \"type\": \"text\"\n      },\n      {\n        \"key\": \"spacing\",\n        \"label\": \"Sample spacing\",\n        \"value\": \"1\",\n        \"type\": \"text\"\n      }\n    ],\n    \"live\": true,\n    \"background\": true,\n    \"presentation\": \"metrics\",\n    \"inputMaxLength\": 20000,\n    \"inputErrorCode\": \"SEQ_SIZE\",\n    \"note\": \"Enter 2 to 64 equally spaced values separated by whitespace, commas or semicolons. Decimals and integer fractions are exact; use decimal points. Check a proposed degree and inspect every difference. Exact tables are limited to 200,000 digit characters. A finite sample does not prove a generating rule.\",\n    \"experience\": {\n      \"automatic\": true,\n      \"single\": false,\n      \"inputMaxLength\": 20000,\n      \"inputMode\": \"text\",\n      \"label\": \"Equally spaced sample values\",\n      \"placeholder\": \"0 1 4 9 16\",\n      \"help\": \"Enter equally spaced sample values in order. Use decimal points, or exact fractions such as 1/3. Results update as you type. Up to 20,000 characters.\",\n      \"action\": null\n    },\n    \"mode\": \"automatic\",\n    \"interactive\": false\n  },\n  \"execution\": \"Browser interface\",\n  \"api\": null,\n  \"browser_agent\": {\n    \"supported\": true,\n    \"name\": \"run_current_tool\",\n    \"discovery\": \"WebMCP on the human page in a supporting browser\",\n    \"verification\": \"See audit/API-AUDIT.md; availability is not verification\"\n  }\n}\n```\n\n## Page guide\n\nBuild a full difference table and test whether equally spaced samples fit a proposed polynomial degree.\n\nHow can we improve this tool?\n\nReport a problem or share an idea.\n\nPlease leave out private information. Your message and the tool name go to our team via PostHog.\n\n### How to use Finite difference table explorer\n\n1. Paste the sample values in their original order.\n2. Set the starting x, equal spacing and proposed maximum polynomial degree.\n3. Inspect every difference and the consistency result, then download the complete table.\n\n## Useful next steps\n\n- [Continued fraction explorer](https://happytails.ai/en/calculators/continued-fraction-explorer/) ([Markdown](https://happytails.ai/en/calculators/continued-fraction-explorer.md))\n\n## How to use it\n\nBuild a full difference table and test whether equally spaced samples fit a proposed polynomial degree.\n\n### Limits and assumptions\n\nEnter 2 to 64 equally spaced values, with at most 20,000 input characters. Values may be exact decimals, scientific notation or integer fractions within 120 digits per part and exponents from −120 to 120. Choose degree 0 to 20 and nonzero spacing. A degree-d consistency check needs at least d + 2 points. Exact arithmetic does not silently tolerate measurement rounding. Conditional next values are shown only for consistent samples; finite samples never prove the generating rule.\n\n### Keep the exact values\n\nDownload JSON for the calculation, CSV for the complete table and the method note. Processing stays on your device.\n"
}