{
  "__type": "IngestedDoc",
  "__tag": 4010,
  "_content": {
    "Notes": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "Both "
            },
            {
              "__type": "ParamRef",
              "__tag": 4071,
              "name": "u"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " and "
            },
            {
              "__type": "ParamRef",
              "__tag": 4071,
              "name": "v"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " must be 0-d or 1-d (ndim = 0 or 1), but "
            },
            {
              "__type": "InlineRole",
              "__tag": 4003,
              "value": "u.ndim",
              "domain": null,
              "role": null,
              "inventory": null
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " need not equal "
            },
            {
              "__type": "InlineRole",
              "__tag": 4003,
              "value": "v.ndim",
              "domain": null,
              "role": null,
              "inventory": null
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ". In other words, all four possible combinations - "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "u.ndim = v.ndim = 0"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ", "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "u.ndim = v.ndim = 1"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ", "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "u.ndim = 1, v.ndim = 0"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ", and "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "u.ndim = 0, v.ndim = 1"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " - work."
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Warns": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Raises": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Yields": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Methods": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Returns": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Parameters",
          "__tag": 4026,
          "children": [
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "q",
              "annotation": "ndarray",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Coefficients, including those equal to zero, of the quotient."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "r",
              "annotation": "ndarray",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Coefficients, including those equal to zero, of the remainder."
                    }
                  ]
                }
              ]
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Summary": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "Returns the quotient and remainder of polynomial division."
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Receives": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Warnings": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Attributes": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Parameters": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Parameters",
          "__tag": 4026,
          "children": [
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "u",
              "annotation": "array_like or poly1d",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Dividend polynomial's coefficients."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "v",
              "annotation": "array_like or poly1d",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Divisor polynomial's coefficients."
                    }
                  ]
                }
              ]
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Extended Summary": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Admonition",
          "__tag": 4056,
          "kind": "note",
          "base_type": "note",
          "children": [
            {
              "__type": "AdmonitionTitle",
              "__tag": 4055,
              "children": [
                {
                  "__type": "Text",
                  "__tag": 4046,
                  "value": "note "
                }
              ]
            },
            {
              "__type": "Paragraph",
              "__tag": 4045,
              "children": [
                {
                  "__type": "Text",
                  "__tag": 4046,
                  "value": "This forms part of the old polynomial API. Since version 1.4, the new polynomial API defined in "
                },
                {
                  "__type": "CrossRef",
                  "__tag": 4002,
                  "value": "numpy.polynomial",
                  "reference": {
                    "__type": "LocalRef",
                    "__tag": 4022,
                    "kind": "module",
                    "path": "numpy.polynomial"
                  },
                  "kind": "module"
                },
                {
                  "__type": "Text",
                  "__tag": 4046,
                  "value": " is preferred. A summary of the differences can be found in the "
                },
                {
                  "__type": "CrossRef",
                  "__tag": 4002,
                  "value": "transition guide",
                  "reference": {
                    "__type": "LocalRef",
                    "__tag": 4022,
                    "kind": "docs",
                    "path": "/reference/routines.polynomials"
                  },
                  "kind": "docs"
                },
                {
                  "__type": "Text",
                  "__tag": 4046,
                  "value": "."
                }
              ]
            }
          ]
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "The input arrays are the coefficients (including any coefficients equal to zero) of the \"numerator\" (dividend) and \"denominator\" (divisor) polynomials, respectively."
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Other Parameters": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    }
  },
  "_ordered_sections": [
    "Summary",
    "Extended Summary",
    "Parameters",
    "Attributes",
    "Methods",
    "Returns",
    "Yields",
    "Receives",
    "Other Parameters",
    "Raises",
    "Warns",
    "Warnings",
    "Notes"
  ],
  "item_file": "/dev/numpy/build-install/usr/lib/python3.14/site-packages/numpy/lib/_polynomial_impl.py",
  "item_line": 989,
  "item_type": "_ArrayFunctionDispatcher",
  "aliases": [
    "numpy.polydiv"
  ],
  "example_section_data": {
    "__type": "Section",
    "__tag": 4015,
    "children": [
      {
        "__type": "Text",
        "__tag": 4046,
        "value": ".. math:: \\frac{3x^2 + 5x + 2}{2x + 1} = 1.5x + 1.75, remainder 0.25\n\n"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "import numpy as np\n",
        "execution_status": "success"
      },
      {
        "__type": "Text",
        "__tag": 4046,
        "value": "\n"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "x = np.array([3.0, 5.0, 2.0])\ny = np.array([2.0, 1.0])\nnp.polydiv(x, y)\n",
        "execution_status": "success"
      }
    ],
    "title": [],
    "level": 0,
    "target": null
  },
  "see_also": [
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "poly",
        "reference": {
          "__type": "LocalRef",
          "__tag": 4022,
          "kind": "module",
          "path": "numpy:polydiv"
        },
        "kind": "module"
      },
      "descriptions": [],
      "type": null
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "polyadd",
        "reference": {
          "__type": "RefInfo",
          "__tag": 4000,
          "module": "current-module",
          "version": "current-version",
          "kind": "to-resolve",
          "path": "polyadd"
        },
        "kind": "module"
      },
      "descriptions": [],
      "type": null
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "polyder",
        "reference": {
          "__type": "RefInfo",
          "__tag": 4000,
          "module": "current-module",
          "version": "current-version",
          "kind": "to-resolve",
          "path": "polyder"
        },
        "kind": "module"
      },
      "descriptions": [],
      "type": null
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "polydiv",
        "reference": {
          "__type": "LocalRef",
          "__tag": 4022,
          "kind": "module",
          "path": "numpy:polydiv"
        },
        "kind": "module"
      },
      "descriptions": [],
      "type": null
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "polyfit",
        "reference": {
          "__type": "RefInfo",
          "__tag": 4000,
          "module": "current-module",
          "version": "current-version",
          "kind": "to-resolve",
          "path": "polyfit"
        },
        "kind": "module"
      },
      "descriptions": [],
      "type": null
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "polyint",
        "reference": {
          "__type": "RefInfo",
          "__tag": 4000,
          "module": "current-module",
          "version": "current-version",
          "kind": "to-resolve",
          "path": "polyint"
        },
        "kind": "module"
      },
      "descriptions": [],
      "type": null
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "polymul",
        "reference": {
          "__type": "RefInfo",
          "__tag": 4000,
          "module": "current-module",
          "version": "current-version",
          "kind": "to-resolve",
          "path": "polymul"
        },
        "kind": "module"
      },
      "descriptions": [],
      "type": null
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "polysub",
        "reference": {
          "__type": "RefInfo",
          "__tag": 4000,
          "module": "current-module",
          "version": "current-version",
          "kind": "to-resolve",
          "path": "polysub"
        },
        "kind": "module"
      },
      "descriptions": [],
      "type": null
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "polyval",
        "reference": {
          "__type": "RefInfo",
          "__tag": 4000,
          "module": "current-module",
          "version": "current-version",
          "kind": "to-resolve",
          "path": "polyval"
        },
        "kind": "module"
      },
      "descriptions": [],
      "type": null
    }
  ],
  "signature": {
    "__type": "SignatureNode",
    "__tag": 4029,
    "kind": "function",
    "parameters": [
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "u",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": {
          "__type": "Empty",
          "__tag": 4031
        }
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "v",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": {
          "__type": "Empty",
          "__tag": 4031
        }
      }
    ],
    "return_annotation": {
      "__type": "Empty",
      "__tag": 4031
    },
    "target_name": "polydiv"
  },
  "references": null,
  "qa": "numpy:polydiv",
  "arbitrary": [],
  "local_refs": [
    "q",
    "r",
    "u",
    "v"
  ]
}