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 Quotient

 http://functions.wolfram.com/04.07.27.0021.01

 Input Form

 Quotient[m, n] == IntegerPart[m/n] - 1 + Sign[UnitStep[m/n] + CharacteristicFunction[m/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["IntegerPart", "[", FractionBox["m", "n"], "]"]], "-", "1", "+", RowBox[List["Sign", "[", RowBox[List[RowBox[List["UnitStep", "[", FractionBox["m", "n"], "]"]], "+", RowBox[List["CharacteristicFunction", "[", RowBox[List[FractionBox["m", "n"], ",", "Integers"]], "]"]]]], "]"]]]]]], "/;", RowBox[List[FractionBox["m", "n"], "\[Element]", "Reals"]]]]]]

 MathML Form

 quotient ( m , n ) int ( m n ) - 1 + sgn ( χ ( m n ) + θ UnitStep ( m n ) ) /; m n TagBox["\[DoubleStruckCapitalR]", Function[Reals]] Condition quotient m n int m n -1 -1 Sign Subscript χ m n -1 UnitStep m n -1 m n -1 [/itex]

 Rule Form

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

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

 2007-05-02