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http://functions.wolfram.com/04.06.16.0004.01
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Mod[-m, n] == n - Mod[m, n] /; Element[m, Reals] && Element[n, Reals] &&
!Element[m/n, Integers]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Mod", "[", RowBox[List[RowBox[List["-", "m"]], ",", "n"]], "]"]], "\[Equal]", RowBox[List["n", "-", RowBox[List["Mod", "[", RowBox[List["m", ",", "n"]], "]"]]]]]], "/;", RowBox[List[RowBox[List["Element", "[", RowBox[List["m", ",", "Reals"]], "]"]], "\[And]", RowBox[List["Element", "[", RowBox[List["n", ",", "Reals"]], "]"]], "\[And]", RowBox[List["Not", "[", RowBox[List["Element", "[", RowBox[List[FractionBox["m", "n"], ",", "Integers"]], "]"]], "]"]]]]]]]]
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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> <mrow> <mo> - </mo> <mi> m </mi> </mrow> <mo> ⁢ </mo> <mi> mod </mi> <mo> ⁢ </mo> <mi> n </mi> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <rem /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> $CellContext`m </ci> </apply> <ci> $CellContext`n </ci> </apply> </annotation-xml> </semantics> <mo> ⩵ </mo> <mrow> <mi> n </mi> <mo> - </mo> <semantics> <mrow> <mi> m </mi> <mo> ⁢ </mo> <mi> mod </mi> <mo> ⁢ </mo> <mi> n </mi> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <rem /> <ci> $CellContext`m </ci> <ci> $CellContext`n </ci> </apply> </annotation-xml> </semantics> </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> <mo> ∧ </mo> <mrow> <mfrac> <mi> m </mi> <mi> n </mi> </mfrac> <mo> ∉ </mo> <semantics> <mi> ℤ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] </annotation> </semantics> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <rem /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> $CellContext`m </ci> </apply> <ci> $CellContext`n </ci> </apply> <apply> <plus /> <ci> n </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <rem /> <ci> $CellContext`m </ci> <ci> $CellContext`n </ci> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <ci> m </ci> <reals /> </apply> <apply> <in /> <ci> n </ci> <reals /> </apply> <apply> <notin /> <apply> <times /> <ci> m </ci> <apply> <power /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> <integers /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Mod", "[", RowBox[List[RowBox[List["-", "m_"]], ",", "n_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["n", "-", RowBox[List["Mod", "[", RowBox[List["m", ",", "n"]], "]"]]]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Reals"]], "&&", RowBox[List["n", "\[Element]", "Reals"]], "&&", RowBox[List["!", RowBox[List[FractionBox["m", "n"], "\[Element]", "Integers"]]]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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