html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 IntegerPart

 http://functions.wolfram.com/04.04.27.0021.01

 Input Form

 IntegerPart[x] == Ceiling[x] - 1 + Sign[UnitStep[-x] + CharacteristicFunction[-x, Integers]] /; Element[x, Reals]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["IntegerPart", "[", "x", "]"]], "\[Equal]", RowBox[List[RowBox[List["Ceiling", "[", "x", "]"]], "-", "1", "+", RowBox[List["Sign", "[", RowBox[List[RowBox[List["UnitStep", "[", RowBox[List["-", "x"]], "]"]], "+", RowBox[List["CharacteristicFunction", "[", RowBox[List[RowBox[List["-", "x"]], ",", "Integers"]], "]"]]]], "]"]]]]]], "/;", RowBox[List["x", "\[Element]", "Reals"]]]]]]

 MathML Form

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

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["IntegerPart", "[", "x_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["Ceiling", "[", "x", "]"]], "-", "1", "+", RowBox[List["Sign", "[", RowBox[List[RowBox[List["UnitStep", "[", RowBox[List["-", "x"]], "]"]], "+", RowBox[List["CharacteristicFunction", "[", RowBox[List[RowBox[List["-", "x"]], ",", "Integers"]], "]"]]]], "]"]]]], "/;", RowBox[List["x", "\[Element]", "Reals"]]]]]]]]

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

 2007-05-02

© 1998-2013 Wolfram Research, Inc.