{
  "$schema": "https://json-schema.org/draft/2020-12/schema",
  "$id": "https://www.calculatorx.com/schemas/math.transform.laplace/1.0.4/input.json",
  "title": "Laplace transform — input",
  "type": "object",
  "properties": {
    "s": {
      "oneOf": [
        {
          "type": "number"
        },
        {
          "type": "string",
          "pattern": "^\\s*[+\\-−–—]?(?:\\d+(?:\\.\\d*)?|\\.\\d+)(?:[eE][+\\-]?\\d+)?\\s*$"
        }
      ],
      "description": "Finite decimal; nonzero underflow rejected before binary64 conversion."
    },
    "t": {
      "oneOf": [
        {
          "type": "number"
        },
        {
          "type": "string",
          "pattern": "^\\s*[+\\-−–—]?(?:\\d+(?:\\.\\d*)?|\\.\\d+)(?:[eE][+\\-]?\\d+)?\\s*$"
        }
      ],
      "description": "Finite decimal; nonzero underflow rejected before binary64 conversion."
    },
    "a": {
      "anyOf": [
        {
          "oneOf": [
            {
              "type": "number"
            },
            {
              "type": "string",
              "pattern": "^\\s*[+\\-−–—]?(?:\\d+(?:\\.\\d*)?|\\.\\d+)(?:[eE][+\\-]?\\d+)?\\s*$"
            }
          ],
          "description": "Finite decimal; nonzero underflow rejected before binary64 conversion."
        },
        {
          "type": "string",
          "pattern": "^\\s*$"
        }
      ],
      "description": "Blank uses default (a=0,omega=1,n=1 for power else0); null is invalid. n integer0–8, validated by engine."
    },
    "omega": {
      "anyOf": [
        {
          "oneOf": [
            {
              "type": "number"
            },
            {
              "type": "string",
              "pattern": "^\\s*[+\\-−–—]?(?:\\d+(?:\\.\\d*)?|\\.\\d+)(?:[eE][+\\-]?\\d+)?\\s*$"
            }
          ],
          "description": "Finite decimal; nonzero underflow rejected before binary64 conversion."
        },
        {
          "type": "string",
          "pattern": "^\\s*$"
        }
      ],
      "description": "Blank uses default (a=0,omega=1,n=1 for power else0); null is invalid. n integer0–8, validated by engine."
    },
    "w": {
      "anyOf": [
        {
          "oneOf": [
            {
              "type": "number"
            },
            {
              "type": "string",
              "pattern": "^\\s*[+\\-−–—]?(?:\\d+(?:\\.\\d*)?|\\.\\d+)(?:[eE][+\\-]?\\d+)?\\s*$"
            }
          ],
          "description": "Finite decimal; nonzero underflow rejected before binary64 conversion."
        },
        {
          "type": "string",
          "pattern": "^\\s*$"
        }
      ],
      "description": "Blank uses default (a=0,omega=1,n=1 for power else0); null is invalid. n integer0–8, validated by engine."
    },
    "n": {
      "anyOf": [
        {
          "oneOf": [
            {
              "type": "number"
            },
            {
              "type": "string",
              "pattern": "^\\s*[+\\-−–—]?(?:\\d+(?:\\.\\d*)?|\\.\\d+)(?:[eE][+\\-]?\\d+)?\\s*$"
            }
          ],
          "description": "Finite decimal; nonzero underflow rejected before binary64 conversion."
        },
        {
          "type": "string",
          "pattern": "^\\s*$"
        }
      ],
      "description": "Blank uses default (a=0,omega=1,n=1 for power else0); null is invalid. n integer0–8, validated by engine."
    },
    "mode": {
      "type": "string",
      "minLength": 1,
      "maxLength": 80,
      "description": "Named table token; case/space/hyphen normalized; aliases must agree. laplace|forward|l|s_domain|analysis; inverse|inverse_laplace|ilaplace|t_domain|synthesis"
    },
    "method": {
      "type": "string",
      "minLength": 1,
      "maxLength": 80,
      "description": "Named table token; case/space/hyphen normalized; aliases must agree. laplace|forward|l|s_domain|analysis; inverse|inverse_laplace|ilaplace|t_domain|synthesis"
    },
    "f": {
      "type": "string",
      "minLength": 1,
      "maxLength": 80,
      "description": "Named table token; case/space/hyphen normalized; aliases must agree. exp|sin|cos|step|ramp|power|exp_sin|exp_cos and published aliases"
    },
    "pair": {
      "type": "string",
      "minLength": 1,
      "maxLength": 80,
      "description": "Named table token; case/space/hyphen normalized; aliases must agree. exp|sin|cos|step|ramp|power|exp_sin|exp_cos and published aliases"
    },
    "integrand": {
      "type": "string",
      "minLength": 1,
      "maxLength": 80,
      "description": "Named table token; case/space/hyphen normalized; aliases must agree. exp|sin|cos|step|ramp|power|exp_sin|exp_cos and published aliases"
    }
  },
  "additionalProperties": false,
  "allOf": [
    {
      "if": {
        "anyOf": [
          {
            "required": [
              "mode"
            ],
            "properties": {
              "mode": {
                "pattern": "^\\s*(?:[Ii][Nn][Vv][Ee][Rr][Ss][Ee](?:[-_\\s]+[Ll][Aa][Pp][Ll][Aa][Cc][Ee])?|[Ii][Ll][Aa][Pp][Ll][Aa][Cc][Ee]|[Tt][-_\\s]+[Dd][Oo][Mm][Aa][Ii][Nn]|[Ss][Yy][Nn][Tt][Hh][Ee][Ss][Ii][Ss])\\s*$"
              }
            }
          },
          {
            "required": [
              "method"
            ],
            "properties": {
              "method": {
                "pattern": "^\\s*(?:[Ii][Nn][Vv][Ee][Rr][Ss][Ee](?:[-_\\s]+[Ll][Aa][Pp][Ll][Aa][Cc][Ee])?|[Ii][Ll][Aa][Pp][Ll][Aa][Cc][Ee]|[Tt][-_\\s]+[Dd][Oo][Mm][Aa][Ii][Nn]|[Ss][Yy][Nn][Tt][Hh][Ee][Ss][Ii][Ss])\\s*$"
              }
            }
          }
        ]
      },
      "then": {
        "required": [
          "t"
        ]
      },
      "else": {
        "required": [
          "s"
        ]
      }
    }
  ],
  "description": "Unilateral causal table. s inside conservative ROC for forward; t≥0 inverse. Omitted mode/f defaults laplace/exp. Active coordinate required. Optional blank parameters use stated defaults; null/underflow/alias conflicts rejected. Secondary engine validation enforces normalized token/domain/n constraints. (calculation_version 1.0.4)"
}