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 Quotient

 http://functions.wolfram.com/04.07.16.0010.01

 Input Form

 Quotient[m, (-I) n] == I Quotient[m, n] + CharacteristicFunction[Im[m/n], Integers] - 1

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Quotient", "[", RowBox[List["m", ",", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "n"]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", RowBox[List["Quotient", "[", RowBox[List["m", ",", "n"]], "]"]]]], "+", RowBox[List["CharacteristicFunction", "[", RowBox[List[RowBox[List["Im", "[", FractionBox["m", "n"], "]"]], ",", "Integers"]], "]"]], "-", "1"]]]]]]

 MathML Form

 quotient ( m , - n ) χ ( Im ( m n ) ) + quotient ( m , n ) - 1 quotient m -1 n Subscript χ m n -1 quotient m n -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Quotient", "[", RowBox[List["m_", ",", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "n_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", RowBox[List["Quotient", "[", RowBox[List["m", ",", "n"]], "]"]]]], "+", RowBox[List["CharacteristicFunction", "[", RowBox[List[RowBox[List["Im", "[", FractionBox["m", "n"], "]"]], ",", "Integers"]], "]"]], "-", "1"]]]]]]

 Date Added to functions.wolfram.com (modification date)

 2001-10-29