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IntegerPart




Mathematica Notation

Traditional Notation









Integer Functions > IntegerPart[z] > Representations through equivalent functions > With related functions > With Round > For real arguments





http://functions.wolfram.com/04.04.27.0017.01









  


  








Input Form





IntegerPart[x] == Round[x - 1/2] + 1 /; (Element[x, Reals] && x < 0) || Element[(x + 1)/2, Integers]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["IntegerPart", "[", "x", "]"]], "\[Equal]", RowBox[List[RowBox[List["Round", "[", RowBox[List["x", "-", FractionBox["1", "2"]]], "]"]], "+", "1"]]]], "/;", RowBox[List[RowBox[List[RowBox[List["x", "\[Element]", "Reals"]], "\[And]", RowBox[List["x", "<", "0"]]]], "\[Or]", RowBox[List[FractionBox[RowBox[List["x", "+", "1"]], "2"], "\[Element]", "Integers"]]]]]]]]








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> <mi> int </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mtext> </mtext> <mrow> <mrow> <mo> &#8970; </mo> <mrow> <mi> x </mi> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> &#8969; </mo> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <mi> x </mi> <mo> &#8712; </mo> <semantics> <mi> &#8477; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalR]&quot;, Function[Reals]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <mi> x </mi> <mo> &lt; </mo> <mn> 0 </mn> </mrow> </mrow> <mo> &#8744; </mo> <mrow> <mfrac> <mrow> <mi> x </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> &#8712; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[Integers]] </annotation> </semantics> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <mrow> <mi> int </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mtext> </mtext> <mrow> <mrow> <mo> &#8970; </mo> <mrow> <mi> x </mi> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> &#8969; </mo> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <mi> x </mi> <mo> &#8712; </mo> <semantics> <mi> &#8477; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalR]&quot;, Function[Reals]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <mi> x </mi> <mo> &lt; </mo> <mn> 0 </mn> </mrow> </mrow> <mo> &#8744; </mo> <mrow> <mfrac> <mrow> <mi> x </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> &#8712; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[Integers]] </annotation> </semantics> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["IntegerPart", "[", "x_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["Round", "[", RowBox[List["x", "-", FractionBox["1", "2"]]], "]"]], "+", "1"]], "/;", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["x", "\[Element]", "Reals"]], "&&", RowBox[List["x", "<", "0"]]]], ")"]], "||", RowBox[List[FractionBox[RowBox[List["x", "+", "1"]], "2"], "\[Element]", "Integers"]]]]]]]]]]


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





2007-05-02