Modular arithmetic workspace

Open Modular arithmetic workspace 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": "modular-arithmetic-workspace",
  "category": "calculators",
  "built": true,
  "requirements": "Choose linear congruence a*x ≡ b mod modulus, modular inverse, or a system of up to 32 residue/modulus pairs. Moduli must be integers at least two. The extended Euclidean algorithm supplies Bezout coefficients and division steps. A linear congruence exists exactly when gcd(a,modulus) divides b. Compatible non-coprime systems are combined using generalized CRT; incompatible systems report no solution. A residue and positive period parameterize every integer solution without enumerating a huge residue set. 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": [
      {
        "key": "operation",
        "label": "Operation",
        "value": "Linear congruence",
        "type": "select",
        "values": [
          "Linear congruence",
          "Modular inverse",
          "Congruence system"
        ]
      }
    ],
    "presentation": "metrics",
    "inputMaxLength": 100000,
    "inputErrorCode": "EXACT_MATH_INPUT",
    "note": "Choose linear congruence a*x ≡ b mod modulus, modular inverse, or a system of up to 32 residue/modulus pairs. Moduli must be integers at least two. The extended Euclidean algorithm supplies Bezout coefficients and division steps. A linear congruence exists exactly when gcd(a,modulus) divides b. Compatible non-coprime systems are combined using generalized CRT; incompatible systems report no solution. A residue and positive period parameterize every integer solution without enumerating a huge residue set. 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  \"a\": 6,\n  \"b\": 8,\n  \"modulus\": 14\n}",
      "help": "Choose linear congruence a*x ≡ b mod modulus, modular inverse, or a system of up to 32 residue/modulus pairs. Moduli must be integers at least two. The extended Euclidean algorithm supplies Bezout coefficients and division steps. A linear congruence exists exactly when gcd(a,modulus) divides b. Compatible non-coprime systems are combined using generalized CRT; incompatible systems report no solution. A residue and positive period parameterize every integer solution without enumerating a huge residue set. 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": [
        "Choose linear congruence a*x ≡ b mod modulus, modular inverse, or a system of up to 32 residue/modulus pairs. Moduli must be integers at least two. The extended Euclidean algorithm supplies Bezout coefficients and division steps. A linear congruence exists exactly when gcd(a,modulus) divides b. Compatible non-coprime systems are combined using generalized CRT; incompatible systems report no solution. A residue and positive period parameterize every integer solution without enumerating a huge residue set. 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"
  }
}

Page guide