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Quotient




Mathematica Notation

Traditional Notation









Integer Functions > Quotient[m,n] > Representations through equivalent functions > With related functions > With Ceiling > For complex arguments





http://functions.wolfram.com/04.07.27.0017.01









  


  








Input Form





Quotient[m, n] == Ceiling[m/n] - 1 - I /; !Element[Re[m/n], Integers] && !Element[Im[m/n], Integers]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Quotient", "[", RowBox[List["m", ",", "n"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["Ceiling", "[", FractionBox["m", "n"], "]"]], "-", "1", "-", "\[ImaginaryI]"]]]], "/;", RowBox[List[RowBox[List["Not", "[", RowBox[List[RowBox[List["Re", "[", FractionBox["m", "n"], "]"]], "\[Element]", "Integers"]], "]"]], "\[And]", RowBox[List["Not", "[", RowBox[List[RowBox[List["Im", "[", FractionBox["m", "n"], "]"]], "\[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> quotient </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> m </mi> <mo> , </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mo> &#8968; </mo> <mfrac> <mi> m </mi> <mi> n </mi> </mfrac> <mo> &#8969; </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> <mfrac> <mi> m </mi> <mi> n </mi> </mfrac> <mo> ) </mo> </mrow> <mo> &#8713; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[Integers]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mi> m </mi> <mi> n </mi> </mfrac> <mo> ) </mo> </mrow> <mo> &#8713; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[Integers]] </annotation> </semantics> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> quotient </ci> <ci> m </ci> <ci> n </ci> </apply> <apply> <plus /> <apply> <ceiling /> <apply> <times /> <ci> m </ci> <apply> <power /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> </apply> </apply> <apply> <and /> <apply> <notin /> <apply> <real /> <apply> <times /> <ci> m </ci> <apply> <power /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <integers /> </apply> <apply> <notin /> <apply> <imaginary /> <apply> <times /> <ci> m </ci> <apply> <power /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <integers /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Quotient", "[", RowBox[List["m_", ",", "n_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["Ceiling", "[", FractionBox["m", "n"], "]"]], "-", "1", "-", "\[ImaginaryI]"]], "/;", RowBox[List[RowBox[List["!", RowBox[List[RowBox[List["Re", "[", FractionBox["m", "n"], "]"]], "\[Element]", "Integers"]]]], "&&", RowBox[List["!", RowBox[List[RowBox[List["Im", "[", FractionBox["m", "n"], "]"]], "\[Element]", "Integers"]]]]]]]]]]]]


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





2007-05-02