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http://functions.wolfram.com/04.07.16.0002.01
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Quotient[m, -n] == -Quotient[m, n] - 1 + CharacteristicFunction[m/n,
Integers] /; Element[m, Reals] && Element[n, Reals]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Quotient", "[", RowBox[List["m", ",", RowBox[List["-", "n"]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", RowBox[List["Quotient", "[", RowBox[List["m", ",", "n"]], "]"]]]], "-", "1", "+", RowBox[List["CharacteristicFunction", "[", RowBox[List[FractionBox["m", "n"], ",", "Integers"]], "]"]]]]]], "/;", RowBox[List[RowBox[List["Element", "[", RowBox[List["m", ",", "Reals"]], "]"]], "\[And]", RowBox[List["Element", "[", RowBox[List["n", ",", "Reals"]], "]"]]]]]]]]
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<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> ⁡ </mo> <mo> ( </mo> <mrow> <mi> m </mi> <mo> , </mo> <mrow> <mo> - </mo> <mi> n </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <mo> - </mo> <mrow> <mi> quotient </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> m </mi> <mo> , </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <msub> <mi> χ </mi> <mi> ℤ </mi> </msub> <mo> ( </mo> <mfrac> <mi> m </mi> <mi> n </mi> </mfrac> <mo> ) </mo> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> m </mi> <mo> ∈ </mo> <semantics> <mi> ℝ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalR]", Function[Reals]] </annotation> </semantics> </mrow> <mo> ∧ </mo> <mrow> <mi> n </mi> <mo> ∈ </mo> <semantics> <mi> ℝ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalR]", Function[Reals]] </annotation> </semantics> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> quotient </ci> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> quotient </ci> <ci> m </ci> <ci> n </ci> </apply> </apply> <apply> <apply> <ci> Subscript </ci> <ci> χ </ci> <ci> ℤ </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> <apply> <and /> <apply> <in /> <ci> m </ci> <reals /> </apply> <apply> <in /> <ci> n </ci> <reals /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Quotient", "[", RowBox[List["m_", ",", RowBox[List["-", "n_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", RowBox[List["Quotient", "[", RowBox[List["m", ",", "n"]], "]"]]]], "-", "1", "+", RowBox[List["CharacteristicFunction", "[", RowBox[List[FractionBox["m", "n"], ",", "Integers"]], "]"]]]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Reals"]], "&&", RowBox[List["n", "\[Element]", "Reals"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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