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Quotient




Mathematica Notation

Traditional Notation









Integer Functions > Quotient[m,n] > General characteristics > Sets of discontinuity





http://functions.wolfram.com/04.07.04.0004.01









  


  








Input Form





DiscontinuitySets[Quotient[m, n], n] == {SequenceList[{m/Interval[{k - I Infinity, k + I Infinity}], -1}, Element[k, Integers]], SequenceList[ {m/Interval[{I k - Infinity, I k + Infinity}], -I}, Element[k, Integers]]}








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["DiscontinuitySets", "[", RowBox[List[RowBox[List["Quotient", "[", RowBox[List["m", ",", "n"]], "]"]], ",", "n"]], "]"]], "\[Equal]", RowBox[List["{", RowBox[List[RowBox[List["SequenceList", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["m", "/", RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["k", "-", RowBox[List["\[ImaginaryI]", " ", "\[Infinity]"]]]], ",", RowBox[List["k", "+", RowBox[List["\[ImaginaryI]", " ", "\[Infinity]"]]]]]], "}"]], "]"]]]], ",", RowBox[List["-", "1"]]]], "}"]], ",", RowBox[List["k", "\[Element]", "Integers"]]]], "]"]], ",", RowBox[List["SequenceList", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["m", "/", RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "k"]], "-", "\[Infinity]"]], ",", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "k"]], "+", "\[Infinity]"]]]], "}"]], "]"]]]], ",", RowBox[List["-", "\[ImaginaryI]"]]]], "}"]], ",", RowBox[List["k", "\[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> <msub> <mi> &#119967;&#119982; </mi> <mi> n </mi> </msub> <mo> ( </mo> <mrow> <mi> quotient </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> m </mi> <mo> , </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mo> { </mo> <mrow> <mrow> <mo> { </mo> <mrow> <mrow> <mo> { </mo> <mrow> <mfrac> <mi> m </mi> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> k </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> &#8734; </mi> </mrow> </mrow> <mo> , </mo> <mrow> <mi> k </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> &#8734; </mi> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mfrac> <mo> , </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </mrow> <mo> } </mo> </mrow> <mo> /; </mo> <mrow> <mi> k </mi> <mo> &#8712; </mo> <mi> &#8484; </mi> </mrow> </mrow> <mo> } </mo> </mrow> <mo> , </mo> <mrow> <mo> { </mo> <mrow> <mrow> <mo> { </mo> <mrow> <mfrac> <mi> m </mi> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mi> &#8734; </mi> </mrow> <mo> , </mo> <mrow> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> + </mo> <mi> &#8734; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mfrac> <mo> , </mo> <mrow> <mo> - </mo> <mi> &#8520; </mi> </mrow> </mrow> <mo> } </mo> </mrow> <mo> /; </mo> <mrow> <mi> k </mi> <mo> &#8712; </mo> <mi> &#8484; </mi> </mrow> </mrow> <mo> } </mo> </mrow> </mrow> <mo> } </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <msub> <mi> &#119967;&#119982; </mi> <mi> n </mi> </msub> <mo> ( </mo> <mrow> <mi> quotient </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> m </mi> <mo> , </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mo> { </mo> <mrow> <mrow> <mo> { </mo> <mrow> <mrow> <mo> { </mo> <mrow> <mfrac> <mi> m </mi> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> k </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> &#8734; </mi> </mrow> </mrow> <mo> , </mo> <mrow> <mi> k </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> &#8734; </mi> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mfrac> <mo> , </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </mrow> <mo> } </mo> </mrow> <mo> /; </mo> <mrow> <mi> k </mi> <mo> &#8712; </mo> <mi> &#8484; </mi> </mrow> </mrow> <mo> } </mo> </mrow> <mo> , </mo> <mrow> <mo> { </mo> <mrow> <mrow> <mo> { </mo> <mrow> <mfrac> <mi> m </mi> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mi> &#8734; </mi> </mrow> <mo> , </mo> <mrow> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> + </mo> <mi> &#8734; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mfrac> <mo> , </mo> <mrow> <mo> - </mo> <mi> &#8520; </mi> </mrow> </mrow> <mo> } </mo> </mrow> <mo> /; </mo> <mrow> <mi> k </mi> <mo> &#8712; </mo> <mi> &#8484; </mi> </mrow> </mrow> <mo> } </mo> </mrow> </mrow> <mo> } </mo> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["DiscontinuitySets", "[", RowBox[List[RowBox[List["Quotient", "[", RowBox[List["m_", ",", "n_"]], "]"]], ",", "n_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["{", RowBox[List[RowBox[List["SequenceList", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["m", RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["k", "-", RowBox[List["\[ImaginaryI]", " ", "\[Infinity]"]]]], ",", RowBox[List["k", "+", RowBox[List["\[ImaginaryI]", " ", "\[Infinity]"]]]]]], "}"]], "]"]]], ",", RowBox[List["-", "1"]]]], "}"]], ",", RowBox[List["k", "\[Element]", "Integers"]]]], "]"]], ",", RowBox[List["SequenceList", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["m", RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "k"]], "-", "\[Infinity]"]], ",", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "k"]], "+", "\[Infinity]"]]]], "}"]], "]"]]], ",", RowBox[List["-", "\[ImaginaryI]"]]]], "}"]], ",", RowBox[List["k", "\[Element]", "Integers"]]]], "]"]]]], "}"]]]]]]


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





2001-10-29