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Floor




Mathematica Notation

Traditional Notation









Integer Functions > Floor[z] > Transformations > Transformations and argument simplifications > Argument involving basic arithmetic operations





http://functions.wolfram.com/04.01.16.0003.01









  


  








Input Form





Floor[-z] == -Floor[z] + CharacteristicFunction[z, Integers] - 1 /; Element[z, Reals]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Floor", "[", RowBox[List["-", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", RowBox[List["Floor", "[", "z", "]"]]]], "+", RowBox[List["CharacteristicFunction", "[", RowBox[List["z", ",", "Integers"]], "]"]], "-", "1"]]]], "/;", RowBox[List["Element", "[", RowBox[List["z", ",", "Reals"]], "]"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mo> &#8970; </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> &#8971; </mo> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <msub> <mi> &#967; </mi> <mi> &#8484; </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mo> &#8970; </mo> <mi> z </mi> <mo> &#8971; </mo> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> z </mi> <mo> &#8712; </mo> <semantics> <mi> &#8477; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalR]&quot;, Function[Reals]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <floor /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <apply> <ci> Subscript </ci> <ci> &#967; </ci> <ci> &#8484; </ci> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <floor /> <ci> z </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <in /> <ci> z </ci> <reals /> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Floor", "[", RowBox[List["-", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", RowBox[List["Floor", "[", "z", "]"]]]], "+", RowBox[List["CharacteristicFunction", "[", RowBox[List["z", ",", "Integers"]], "]"]], "-", "1"]], "/;", RowBox[List["z", "\[Element]", "Reals"]]]]]]]]


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





2001-10-29