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IntegerPart




Mathematica Notation

Traditional Notation









Integer Functions > IntegerPart[z] > Representations through equivalent functions > With related functions > With Quotient > For complex arguments





http://functions.wolfram.com/04.04.27.0035.01









  


  








Input Form





IntegerPart[z] == Quotient[z, 1] + 1 + I /; Re[z] < 0 && Im[z] < 0








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["IntegerPart", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List["Quotient", "[", RowBox[List["z", ",", "1"]], "]"]], "+", "1", "+", "\[ImaginaryI]"]]]], "/;", RowBox[List[RowBox[List[RowBox[List["Re", "[", "z", "]"]], "<", "0"]], "\[And]", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "<", "0"]]]]]]]]








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> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mi> quotient </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mn> 1 </mn> <mo> + </mo> <mi> &#8520; </mi> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &lt; </mo> <mn> 0 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &lt; </mo> <mn> 0 </mn> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> int </ci> <ci> z </ci> </apply> <apply> <plus /> <apply> <ci> quotient </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 1 </cn> <imaginaryi /> </apply> </apply> <apply> <and /> <apply> <lt /> <apply> <real /> <ci> z </ci> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <lt /> <apply> <imaginary /> <ci> z </ci> </apply> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["IntegerPart", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["Quotient", "[", RowBox[List["z", ",", "1"]], "]"]], "+", "1", "+", "\[ImaginaryI]"]], "/;", RowBox[List[RowBox[List[RowBox[List["Re", "[", "z", "]"]], "<", "0"]], "&&", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "<", "0"]]]]]]]]]]


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





2007-05-02