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GCD




Mathematica Notation

Traditional Notation









Integer Functions > GCD[n1,n2,...,nm] > Specific values > Specialized values





http://functions.wolfram.com/04.08.03.0006.01









  


  








Input Form





GCD[Subscript[p, 1], Subscript[p, 2]] == 1 /; Subscript[p, 1] != Subscript[p, 2] && Element[Subscript[p, 1], Primes] && Element[Subscript[p, 2], Primes]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["GCD", "[", RowBox[List[SubscriptBox["p", "1"], ",", SubscriptBox["p", "2"]]], "]"]], "\[Equal]", "1"]], "/;", RowBox[List[RowBox[List[SubscriptBox["p", "1"], "\[NotEqual]", SubscriptBox["p", "2"]]], "\[And]", RowBox[List[SubscriptBox["p", "1"], "\[Element]", "Primes"]], "\[And]", RowBox[List[SubscriptBox["p", "2"], "\[Element]", "Primes"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mi> gcd </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <msub> <mi> p </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> p </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mn> 1 </mn> </mrow> <mo> /; </mo> <mrow> <mrow> <msub> <mi> p </mi> <mn> 1 </mn> </msub> <mo> &#8800; </mo> <msub> <mi> p </mi> <mn> 2 </mn> </msub> </mrow> <mo> &#8743; </mo> <mrow> <msub> <mi> p </mi> <mn> 1 </mn> </msub> <mo> &#8712; </mo> <semantics> <mi> &#8473; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalP]&quot;, Function[Primes]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <msub> <mi> p </mi> <mn> 2 </mn> </msub> <mo> &#8712; </mo> <semantics> <mi> &#8473; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalP]&quot;, Function[Primes]] </annotation> </semantics> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <gcd /> <apply> <ci> Subscript </ci> <ci> p </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> p </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <and /> <apply> <neq /> <apply> <ci> Subscript </ci> <ci> p </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> p </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <in /> <apply> <ci> Subscript </ci> <ci> p </ci> <cn type='integer'> 1 </cn> </apply> <primes /> </apply> <apply> <in /> <apply> <ci> Subscript </ci> <ci> p </ci> <cn type='integer'> 2 </cn> </apply> <primes /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["GCD", "[", RowBox[List[SubscriptBox["p_", "1"], ",", SubscriptBox["p_", "2"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["1", "/;", RowBox[List[RowBox[List[SubscriptBox["p", "1"], "\[NotEqual]", SubscriptBox["p", "2"]]], "&&", RowBox[List[SubscriptBox["p", "1"], "\[Element]", "Primes"]], "&&", RowBox[List[SubscriptBox["p", "2"], "\[Element]", "Primes"]]]]]]]]]]


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





2001-10-29