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 Mod

 http://functions.wolfram.com/04.06.27.0013.01

 Input Form

 Mod[m, n] == m - n Ceiling[m/n] - n UnitStep[CharacteristicFunction[m/n, Integers] - 1] + n /; Element[m/n, Reals]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Mod", "[", RowBox[List["m", ",", "n"]], "]"]], "\[Equal]", RowBox[List["m", "-", RowBox[List["n", " ", RowBox[List["Ceiling", "[", FractionBox["m", "n"], "]"]]]], "-", RowBox[List["n", " ", RowBox[List["UnitStep", "[", RowBox[List[RowBox[List["CharacteristicFunction", "[", RowBox[List[FractionBox["m", "n"], ",", "Integers"]], "]"]], "-", "1"]], "]"]]]], "+", "n"]]]], "/;", RowBox[List[FractionBox["m", "n"], "\[Element]", "Reals"]]]]]]

 MathML Form

 m mod n FE`Conversion`Private`m \$CellContext`n m + n - n m n - n θ UnitStep ( χ ( m n ) - 1 ) /; m n TagBox["\[DoubleStruckCapitalR]", Function[Reals]] Condition FE`Conversion`Private`m \$CellContext`n m n -1 n m n -1 -1 n UnitStep Subscript χ m n -1 -1 m n -1 [/itex]

 Rule Form

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

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

 2007-05-02