{
  "near_singular_case": {
    "A": [
      [
        "1",
        "1"
      ],
      [
        "1",
        "1001/1000"
      ]
    ],
    "inverse": [
      [
        "1001",
        "-1000"
      ],
      [
        "-1000",
        "1000"
      ]
    ],
    "b": [
      "2",
      "2001/1000"
    ],
    "delta_b": [
      "0",
      "1/1000"
    ],
    "x": [
      "1",
      "1"
    ],
    "perturbed_x": [
      "0",
      "2"
    ],
    "condition_infinity": "4004001/1000",
    "relative_b_change_infinity": "1/2001",
    "relative_x_change_infinity": "1",
    "condition_times_relative_b_bound": "2001/1000"
  },
  "comparison_case": {
    "A": [
      [
        "1",
        "1"
      ],
      [
        "1",
        "2"
      ]
    ],
    "inverse": [
      [
        "2",
        "-1"
      ],
      [
        "-1",
        "1"
      ]
    ],
    "b": [
      "2",
      "3"
    ],
    "delta_b": [
      "0",
      "1/1000"
    ],
    "x": [
      "1",
      "1"
    ],
    "perturbed_x": [
      "999/1000",
      "1001/1000"
    ],
    "condition_infinity": "9",
    "relative_b_change_infinity": "1/3000",
    "relative_x_change_infinity": "1/1000",
    "condition_times_relative_b_bound": "3/1000"
  },
  "singular_rejected": true,
  "arithmetic": "exact Fraction; no floating point rounding measured",
  "norm": "infinity, row-sum induced matrix norm",
  "A_perturbation_tested": false
}