Argument: Transformations (formula 12.02.16.0094)

Arg

$Mathematica Notation$

Complex Components

Transformations

Some functions of arguments

http://functions.wolfram.com/12.02.16.0094.01

Input Form

Arg[x^a y^b z^c] == 2 Pi Floor[(Pi - Im[a Log[x]] - Im[b Log[y]] - Im[c Log[z]])/(2 Pi)] + Im[a Log[x]] + Im[b Log[y]] + Im[c Log[z]]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["Arg", "[", RowBox[List[SuperscriptBox["x", "a"], " ", SuperscriptBox["y", "b"], SuperscriptBox["z", "c"]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["2", " ", "\[Pi]", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "-", RowBox[List["Im", "[", RowBox[List["a", " ", RowBox[List["Log", "[", "x", "]"]]]], "]"]], "-", RowBox[List["Im", "[", RowBox[List["b", " ", RowBox[List["Log", "[", "y", "]"]]]], "]"]], "-", RowBox[List["Im", "[", RowBox[List["c", " ", RowBox[List["Log", "[", "z", "]"]]]], "]"]]]], RowBox[List["2", "\[Pi]"]]], "]"]]]], "+", RowBox[List["Im", "[", RowBox[List["a", " ", RowBox[List["Log", "[", "x", "]"]]]], "]"]], "+", RowBox[List["Im", "[", RowBox[List["b", " ", RowBox[List["Log", "[", "y", "]"]]]], "]"]], "+", RowBox[List["Im", "[", RowBox[List["c", " ", RowBox[List["Log", "[", "z", "]"]]]], "]"]]]]]]]]

MathML Form

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> arg </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <msup> <mi> x </mi> <mi> a </mi> </msup> <mo> ⁢ </mo> <msup> <mi> y </mi> <mi> b </mi> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mi> c </mi> </msup> </mrow> <mo> ) </mo> </mrow> <mo>  </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> <mo> ⁢ </mo> <mrow> <mo> ⌊ </mo> <mfrac> <mrow> <mi> π </mi> <mo> - </mo> <mrow> <mi> Im </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> Im </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> b </mi> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> y </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> Im </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> </mfrac> <mo> ⌋ </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> Im </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> Im </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> b </mi> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> y </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> Im </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <arg /> <apply> <times /> <apply> <power /> <ci> x </ci> <ci> a </ci> </apply> <apply> <power /> <ci> y </ci> <ci> b </ci> </apply> <apply> <power /> <ci> z </ci> <ci> c </ci> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> <apply> <floor /> <apply> <times /> <apply> <plus /> <pi /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <imaginary /> <apply> <times /> <ci> a </ci> <apply> <ln /> <ci> x </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <imaginary /> <apply> <times /> <ci> b </ci> <apply> <ln /> <ci> y </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <imaginary /> <apply> <times /> <ci> c </ci> <apply> <ln /> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <imaginary /> <apply> <times /> <ci> a </ci> <apply> <ln /> <ci> x </ci> </apply> </apply> </apply> <apply> <imaginary /> <apply> <times /> <ci> b </ci> <apply> <ln /> <ci> y </ci> </apply> </apply> </apply> <apply> <imaginary /> <apply> <times /> <ci> c </ci> <apply> <ln /> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Arg", "[", RowBox[List[SuperscriptBox["x_", "a_"], " ", SuperscriptBox["y_", "b_"], " ", SuperscriptBox["z_", "c_"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["2", " ", "\[Pi]", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "-", RowBox[List["Im", "[", RowBox[List["a", " ", RowBox[List["Log", "[", "x", "]"]]]], "]"]], "-", RowBox[List["Im", "[", RowBox[List["b", " ", RowBox[List["Log", "[", "y", "]"]]]], "]"]], "-", RowBox[List["Im", "[", RowBox[List["c", " ", RowBox[List["Log", "[", "z", "]"]]]], "]"]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]], "+", RowBox[List["Im", "[", RowBox[List["a", " ", RowBox[List["Log", "[", "x", "]"]]]], "]"]], "+", RowBox[List["Im", "[", RowBox[List["b", " ", RowBox[List["Log", "[", "y", "]"]]]], "]"]], "+", RowBox[List["Im", "[", RowBox[List["c", " ", RowBox[List["Log", "[", "z", "]"]]]], "]"]]]]]]]]

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

2007-05-02