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 Quotient

 http://functions.wolfram.com/04.07.27.0008.01

 Input Form

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

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Quotient", "[", RowBox[List["m", ",", "n"]], "]"]], "\[Equal]", RowBox[List["Round", "[", RowBox[List[FractionBox["m", "n"], "-", FractionBox["1", "2"]]], "]"]]]], "/;", RowBox[List[RowBox[List[FractionBox["m", "n"], "\[Element]", "Reals"]], "\[And]", RowBox[List["Not", "[", RowBox[List[FractionBox[RowBox[List["m", "+", "n"]], RowBox[List["2", "n"]]], "\[Element]", "Integers"]], "]"]]]]]]]]

 MathML Form

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

 Rule Form

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

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

 2007-05-02