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Floor




Mathematica Notation

Traditional Notation









Integer Functions > Floor[z] > Transformations > Related transformations





http://functions.wolfram.com/04.01.16.0020.01









  


  








Input Form





Subscript[z, 1] Subscript[z, 2] == Subscript[z, 2] Floor[Subscript[z, 1]] + Subscript[z, 1] Floor[Subscript[z, 2]] + (Subscript[z, 1] - Floor[Subscript[z, 1]]) (Subscript[z, 2] - Floor[Subscript[z, 2]]) - Floor[Subscript[z, 1]] Floor[Subscript[z, 2]]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["z", RowBox[List[" ", "1"]]], SubscriptBox["z", RowBox[List[" ", "2"]]]]], "\[Equal]", RowBox[List[RowBox[List[SubscriptBox["z", RowBox[List[" ", "2"]]], RowBox[List["Floor", "[", SubscriptBox["z", RowBox[List[" ", "1"]]], "]"]]]], "+", RowBox[List[SubscriptBox["z", RowBox[List[" ", "1"]]], RowBox[List["Floor", "[", SubscriptBox["z", RowBox[List[" ", "2"]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["z", RowBox[List[" ", "1"]]], "-", RowBox[List["Floor", "[", SubscriptBox["z", RowBox[List[" ", "1"]]], "]"]]]], ")"]], RowBox[List["(", RowBox[List[SubscriptBox["z", RowBox[List[" ", "2"]]], "-", RowBox[List["Floor", "[", SubscriptBox["z", RowBox[List[" ", "2"]]], "]"]]]], ")"]]]], "-", RowBox[List[RowBox[List["Floor", "[", SubscriptBox["z", RowBox[List[" ", "1"]]], "]"]], RowBox[List["Floor", "[", SubscriptBox["z", RowBox[List[" ", "2"]]], "]"]]]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> &#8290; </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> - </mo> <mrow> <mo> &#8970; </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> &#8971; </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> - </mo> <mrow> <mo> &#8970; </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> &#8971; </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <mo> &#8970; </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> &#8971; </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8970; </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> &#8971; </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> &#8970; </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> &#8971; </mo> </mrow> <mo> &#8290; </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mrow> <mo> &#8970; </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> &#8971; </mo> </mrow> <mo> &#8290; </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <times /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <floor /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <floor /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <floor /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <floor /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <floor /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <apply> <floor /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["z_", "1"], " ", SubscriptBox["z_", "2"]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SubscriptBox["zz", "2"], " ", RowBox[List["Floor", "[", SubscriptBox["zz", "1"], "]"]]]], "+", RowBox[List[SubscriptBox["zz", "1"], " ", RowBox[List["Floor", "[", SubscriptBox["zz", "2"], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["zz", "1"], "-", RowBox[List["Floor", "[", SubscriptBox["zz", "1"], "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List[SubscriptBox["zz", "2"], "-", RowBox[List["Floor", "[", SubscriptBox["zz", "2"], "]"]]]], ")"]]]], "-", RowBox[List[RowBox[List["Floor", "[", SubscriptBox["zz", "1"], "]"]], " ", RowBox[List["Floor", "[", SubscriptBox["zz", "2"], "]"]]]]]]]]]]


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





2001-10-29