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Quotient






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/04.07.27.0013.01









  


  










Input Form





Quotient[m, n] == Ceiling[m/n] + UnitStep[CharacteristicFunction[m/n, Integers] - 1] - 1 /; Element[m/n, Reals]










Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Quotient", "[", RowBox[List["m", ",", "n"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["Ceiling", "[", FractionBox["m", "n"], "]"]], "+", RowBox[List["UnitStep", "[", RowBox[List[RowBox[List["CharacteristicFunction", "[", RowBox[List[FractionBox["m", "n"], ",", "Integers"]], "]"]], "-", "1"]], "]"]], "-", "1"]]]], "/;", RowBox[List[FractionBox["m", "n"], "\[Element]", "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> <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> <mrow> <semantics> <mi> &#952; </mi> <annotation-xml encoding='MathML-Content'> <ci> UnitStep </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mrow> <msub> <mi> &#967; </mi> <mi> &#8484; </mi> </msub> <mo> ( </mo> <mtext> </mtext> <mfrac> <mi> m </mi> <mi> n </mi> </mfrac> <mo> ) </mo> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </mrow> <mo> /; </mo> <mrow> <mfrac> <mi> m </mi> <mi> n </mi> </mfrac> <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> <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> <apply> <ci> UnitStep </ci> <apply> <plus /> <apply> <apply> <ci> Subscript </ci> <ci> &#967; </ci> <ci> &#8484; </ci> </apply> <apply> <times /> <ci> m </ci> <apply> <power /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <in /> <apply> <times /> <ci> m </ci> <apply> <power /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> <reals /> </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"], "]"]], "+", RowBox[List["UnitStep", "[", RowBox[List[RowBox[List["CharacteristicFunction", "[", RowBox[List[FractionBox["m", "n"], ",", "Integers"]], "]"]], "-", "1"]], "]"]], "-", "1"]], "/;", RowBox[List[FractionBox["m", "n"], "\[Element]", "Reals"]]]]]]]]










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





2007-05-02