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Mod




Mathematica Notation

Traditional Notation









Integer Functions > Mod[m,n] > Specific values > Values at fixed points





http://functions.wolfram.com/04.06.03.0026.01









  


  








Input Form





Mod[-3 + Pi I, -2 - 3 I E] == -3 + (1 + I) (-2 - 3 I E) + I Pi








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Mod", "[", RowBox[List[RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]]]], ",", RowBox[List[RowBox[List["-", "2"]], "-", RowBox[List["3", " ", "\[ImaginaryI]", " ", "\[ExponentialE]"]]]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "-", RowBox[List["3", " ", "\[ImaginaryI]", " ", "\[ExponentialE]"]]]], ")"]]]], "+", RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <semantics> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> + </mo> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> mod </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> - </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> &#8519; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <rem /> <apply> <plus /> <cn type='integer'> -3 </cn> <apply> <times /> <pi /> <imaginaryi /> </apply> </apply> <apply> <plus /> <cn type='integer'> -2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <imaginaryi /> <exponentiale /> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> <mo> &#10869; </mo> <mrow> <mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mi> &#8520; </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> - </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> &#8519; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <rem /> <apply> <plus /> <cn type='integer'> -3 </cn> <apply> <times /> <pi /> <imaginaryi /> </apply> </apply> <apply> <plus /> <cn type='integer'> -2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='integer'> 3 </cn> <imaginaryi /> <exponentiale /> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> -3 </cn> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <imaginaryi /> </apply> <apply> <plus /> <cn type='integer'> -2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <imaginaryi /> <exponentiale /> </apply> </apply> </apply> </apply> <apply> <times /> <imaginaryi /> <pi /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Mod", "[", RowBox[List[RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]]]], ",", RowBox[List[RowBox[List["-", "2"]], "-", RowBox[List["3", " ", "\[ImaginaryI]", " ", "\[ExponentialE]"]]]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "-", RowBox[List["3", " ", "\[ImaginaryI]", " ", "\[ExponentialE]"]]]], ")"]]]], "+", RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]]]]]]]]


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





2001-10-29