{
  "A": [
    [
      "4",
      "1"
    ],
    [
      "1",
      "3"
    ]
  ],
  "b": [
    "1",
    "2"
  ],
  "two_step_run": {
    "x": [
      "1/11",
      "7/11"
    ],
    "residual": [
      "0",
      "0"
    ],
    "residual_squared_norm": "0",
    "converged_exact_zero_residual": true,
    "iteration_cap": 2,
    "steps": 2,
    "trace": [
      {
        "step": 1,
        "x_before": [
          "0",
          "0"
        ],
        "r_before": [
          "1",
          "2"
        ],
        "p": [
          "1",
          "2"
        ],
        "alpha": "1/4",
        "x_after": [
          "1/4",
          "1/2"
        ],
        "r_after": [
          "-1/2",
          "1/4"
        ],
        "beta": "1/16"
      },
      {
        "step": 2,
        "x_before": [
          "1/4",
          "1/2"
        ],
        "r_before": [
          "-1/2",
          "1/4"
        ],
        "p": [
          "-7/16",
          "3/8"
        ],
        "alpha": "4/11",
        "x_after": [
          "1/11",
          "7/11"
        ],
        "r_after": [
          "0",
          "0"
        ],
        "beta": "0"
      }
    ]
  },
  "one_step_cap_run": {
    "x": [
      "1/4",
      "1/2"
    ],
    "residual": [
      "-1/2",
      "1/4"
    ],
    "residual_squared_norm": "5/16",
    "converged_exact_zero_residual": false,
    "iteration_cap": 1,
    "steps": 1,
    "trace": [
      {
        "step": 1,
        "x_before": [
          "0",
          "0"
        ],
        "r_before": [
          "1",
          "2"
        ],
        "p": [
          "1",
          "2"
        ],
        "alpha": "1/4",
        "x_after": [
          "1/4",
          "1/2"
        ],
        "r_after": [
          "-1/2",
          "1/4"
        ],
        "beta": "1/16"
      }
    ]
  },
  "direct_solution": [
    "1/11",
    "7/11"
  ],
  "successive_residual_dot": "0",
  "first_two_directions_A_inner_product": "0",
  "already_solved_run": {
    "x": [
      "1/11",
      "7/11"
    ],
    "residual": [
      "0",
      "0"
    ],
    "residual_squared_norm": "0",
    "converged_exact_zero_residual": true,
    "iteration_cap": 2,
    "steps": 0,
    "trace": []
  },
  "indefinite_rejected_by_full_2by2_SPD_check": true,
  "arithmetic": "exact Fraction, not SciPy tolerance behavior",
  "SciPy_preconditioning_or_large_problem_executed": false
}