Diophantine equation solver

Open Diophantine equation solver on Happytails.ai. This view has the same page content and links, with explicit tool capabilities. Read the processing notes before using a tool.

Tool capabilities

{
  "id": "diophantine-equation-solver",
  "category": "calculators",
  "built": true,
  "requirements": "Supported families are linear a*x + b*y = c and product x*y = n, with integer inputs. Linear equations return the gcd divisibility condition, an exact particular pair and integer direction, including zero-coefficient and all-pairs cases. Product equations enumerate every signed ordered factor pair for |n| ≤ 1000000000000; n=0 has two infinite families. Other named families return unresolved, never a false no-solution claim. This is not a general polynomial equation parser. All processing stays on your device. Paste JSON with dot decimals; quote exact fractions and large integers. Input is limited to 100,000 characters and 100 digits per scalar. Exact results use reduced fractions, with a 1,024-digit and 200,000-step arithmetic bound. Enumeration is limited to 10,000 complete results and 1,000,000 search steps; exceeding a bound returns an error, not a partial answer. Geometry uses floating-point approximations. JSON and typed JSON Pointer CSV retain the complete input, results, constraints and worked steps. Reports are limited to 4,000,000 JSON and 8,000,000 CSV characters. Each calculation uses a disposable worker with a 10-second timeout. Search and sort the first 200 preview rows. Copy result copies the summary. Download JSON or CSV for every result and worked step. Geometry tools also provide a downloadable SVG diagram.",
  "implementation": {
    "fields": [],
    "presentation": "metrics",
    "inputMaxLength": 100000,
    "inputErrorCode": "EXACT_MATH_INPUT",
    "note": "Supported families are linear a*x + b*y = c and product x*y = n, with integer inputs. Linear equations return the gcd divisibility condition, an exact particular pair and integer direction, including zero-coefficient and all-pairs cases. Product equations enumerate every signed ordered factor pair for |n| ≤ 1000000000000; n=0 has two infinite families. Other named families return unresolved, never a false no-solution claim. This is not a general polynomial equation parser. All processing stays on your device. Paste JSON with dot decimals; quote exact fractions and large integers. Input is limited to 100,000 characters and 100 digits per scalar. Exact results use reduced fractions, with a 1,024-digit and 200,000-step arithmetic bound. Enumeration is limited to 10,000 complete results and 1,000,000 search steps; exceeding a bound returns an error, not a partial answer. Geometry uses floating-point approximations. JSON and typed JSON Pointer CSV retain the complete input, results, constraints and worked steps. Reports are limited to 4,000,000 JSON and 8,000,000 CSV characters. Each calculation uses a disposable worker with a 10-second timeout.",
    "experience": {
      "automatic": false,
      "single": false,
      "inputMaxLength": 100000,
      "inputMode": "text",
      "label": "JSON input",
      "placeholder": "{\n  \"family\": \"linear\",\n  \"a\": 6,\n  \"b\": 9,\n  \"c\": 3\n}",
      "help": "Supported families are linear a*x + b*y = c and product x*y = n, with integer inputs. Linear equations return the gcd divisibility condition, an exact particular pair and integer direction, including zero-coefficient and all-pairs cases. Product equations enumerate every signed ordered factor pair for |n| ≤ 1000000000000; n=0 has two infinite families. Other named families return unresolved, never a false no-solution claim. This is not a general polynomial equation parser. All processing stays on your device. Paste JSON with dot decimals; quote exact fractions and large integers. Input is limited to 100,000 characters and 100 digits per scalar. Exact results use reduced fractions, with a 1,024-digit and 200,000-step arithmetic bound. Enumeration is limited to 10,000 complete results and 1,000,000 search steps; exceeding a bound returns an error, not a partial answer. Geometry uses floating-point approximations. JSON and typed JSON Pointer CSV retain the complete input, results, constraints and worked steps. Reports are limited to 4,000,000 JSON and 8,000,000 CSV characters. Each calculation uses a disposable worker with a 10-second timeout. Up to 100,000 characters. Review the settings before running.",
      "helpParts": [
        "Supported families are linear a*x + b*y = c and product x*y = n, with integer inputs. Linear equations return the gcd divisibility condition, an exact particular pair and integer direction, including zero-coefficient and all-pairs cases. Product equations enumerate every signed ordered factor pair for |n| ≤ 1000000000000; n=0 has two infinite families. Other named families return unresolved, never a false no-solution claim. This is not a general polynomial equation parser. All processing stays on your device. Paste JSON with dot decimals; quote exact fractions and large integers. Input is limited to 100,000 characters and 100 digits per scalar. Exact results use reduced fractions, with a 1,024-digit and 200,000-step arithmetic bound. Enumeration is limited to 10,000 complete results and 1,000,000 search steps; exceeding a bound returns an error, not a partial answer. Geometry uses floating-point approximations. JSON and typed JSON Pointer CSV retain the complete input, results, constraints and worked steps. Reports are limited to 4,000,000 JSON and 8,000,000 CSV characters. Each calculation uses a disposable worker with a 10-second timeout.",
        "Up to 100,000 characters.",
        "Review the settings before running."
      ],
      "action": null
    },
    "mode": "explicit",
    "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"
  }
}

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