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 Quotient

 http://functions.wolfram.com/04.07.27.0010.01

 Input Form

 Quotient[m, n] == Round[m/n - 1/2] + CharacteristicFunction[(m + n)/(2 n), Integers] /; Element[m/n, Reals]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Quotient", "[", RowBox[List["m", ",", "n"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["Round", "[", RowBox[List[FractionBox["m", "n"], "-", FractionBox["1", "2"]]], "]"]], "+", RowBox[List["CharacteristicFunction", "[", RowBox[List[FractionBox[RowBox[List["m", "+", "n"]], RowBox[List["2", "n"]]], ",", "Integers"]], "]"]]]]]], "/;", RowBox[List[FractionBox["m", "n"], "\[Element]", "Reals"]]]]]]

 MathML Form

 quotient ( m , n ) m n - 1 2 + χ ( m + n 2 n ) /; m n TagBox["\[DoubleStruckCapitalR]", Function[Reals]] quotient ( m , n ) m n - 1 2 + χ ( m + n 2 n ) /; m n TagBox["\[DoubleStruckCapitalR]", Function[Reals]] [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Quotient", "[", RowBox[List["m_", ",", "n_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["Round", "[", RowBox[List[FractionBox["m", "n"], "-", FractionBox["1", "2"]]], "]"]], "+", RowBox[List["CharacteristicFunction", "[", RowBox[List[FractionBox[RowBox[List["m", "+", "n"]], RowBox[List["2", " ", "n"]]], ",", "Integers"]], "]"]]]], "/;", RowBox[List[FractionBox["m", "n"], "\[Element]", "Reals"]]]]]]]]

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

 2007-05-02

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