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http://functions.wolfram.com/04.06.27.0021.01
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Mod[m, n] == m - n (IntegerPart[m/n] - 1 +
Sign[UnitStep[m/n] + CharacteristicFunction[m/n, Integers]]) /;
Element[m/n, Reals]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Mod", "[", RowBox[List["m", ",", "n"]], "]"]], "\[Equal]", RowBox[List["m", "-", RowBox[List["n", RowBox[List["(", RowBox[List[RowBox[List["IntegerPart", "[", FractionBox["m", "n"], "]"]], "-", "1", "+", RowBox[List["Sign", "[", RowBox[List[RowBox[List["UnitStep", "[", FractionBox["m", "n"], "]"]], "+", RowBox[List["CharacteristicFunction", "[", RowBox[List[FractionBox["m", "n"], ",", "Integers"]], "]"]]]], "]"]]]], ")"]]]]]]]], "/;", RowBox[List[FractionBox["m", "n"], "\[Element]", "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> <semantics> <mrow> <mi> m </mi> <mo> ⁢ </mo> <mi> mod </mi> <mo> ⁢ </mo> <mi> n </mi> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <rem /> <ci> FE`Conversion`Private`m </ci> <ci> $CellContext`n </ci> </apply> </annotation-xml> </semantics> <mo> ⩵ </mo> <mrow> <mi> m </mi> <mo> - </mo> <mrow> <mi> n </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> int </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mi> m </mi> <mi> n </mi> </mfrac> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> sgn </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <msub> <mi> χ </mi> <mi> ℤ </mi> </msub> <mo> ( </mo> <mtext> </mtext> <mfrac> <mi> m </mi> <mi> n </mi> </mfrac> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <semantics> <mi> θ </mi> <annotation-xml encoding='MathML-Content'> <ci> UnitStep </ci> </annotation-xml> </semantics> <mo> ( </mo> <mfrac> <mi> m </mi> <mi> n </mi> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mfrac> <mi> m </mi> <mi> n </mi> </mfrac> <mo> ∈ </mo> <semantics> <mi> ℝ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalR]", Function[Reals]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <rem /> <ci> FE`Conversion`Private`m </ci> <ci> $CellContext`n </ci> </apply> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> n </ci> <apply> <plus /> <apply> <ci> int </ci> <apply> <times /> <ci> m </ci> <apply> <power /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> Sign </ci> <apply> <plus /> <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> <apply> <ci> UnitStep </ci> <apply> <times /> <ci> m </ci> <apply> <power /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </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>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Mod", "[", RowBox[List["m_", ",", "n_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["m", "-", RowBox[List["n", " ", RowBox[List["(", RowBox[List[RowBox[List["IntegerPart", "[", FractionBox["m", "n"], "]"]], "-", "1", "+", RowBox[List["Sign", "[", RowBox[List[RowBox[List["UnitStep", "[", FractionBox["m", "n"], "]"]], "+", RowBox[List["CharacteristicFunction", "[", RowBox[List[FractionBox["m", "n"], ",", "Integers"]], "]"]]]], "]"]]]], ")"]]]]]], "/;", RowBox[List[FractionBox["m", "n"], "\[Element]", "Reals"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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