{"id":"integer-mod-inverse","version":"1.0.0","description":"Compute the modular multiplicative inverse of a modulo modulus, when it exists.","supported_operations":["integer mod inverse","modular multiplicative inverse","modular inverse","inverse mod m"],"unsupported_operations":["modular exponentiation","extended gcd output","inverse when gcd is not 1"],"semantics":["a and modulus are canonical integer strings; modulus must be a positive canonical integer.","a may be negative or exceed modulus; it is reduced modulo modulus before inverting.","The inverse exists only when gcd(a mod modulus, modulus) = 1; otherwise the request is rejected as undefined.","modulus 1 is a degenerate ring where every residue is 0; this contract returns value 0 for modulus 1.","The result is the unique value in [0, modulus) such that (a * value) mod modulus = 1 (or 0 when modulus is 1).","Each input may have at most 1000 digits excluding sign."],"limits":{"max_digits":1000},"pricing":{"status":"unpriced","charge_usd":null},"input_schema":{"type":"object","additionalProperties":false,"required":["a","modulus"],"properties":{"a":{"type":"string","minLength":1,"maxLength":1001},"modulus":{"type":"string","minLength":1,"maxLength":1001}}},"output_schema":{"type":"object","additionalProperties":false,"required":["value"],"properties":{"value":{"type":"string"}}},"examples":[{"input":{"a":"3","modulus":"11"},"output":{"value":"4"}}],"execute_url":"/v1/tools/integer-mod-inverse/versions/1.0.0/execute"}