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Ceiling




Mathematica Notation

Traditional Notation









Integer Functions > Ceiling[z] > Transformations > Products, sums, and powers of the direct function > Sums of the direct function





http://functions.wolfram.com/04.02.16.0018.01









  


  








Input Form





Ceiling[Subscript[z, 1]] + Ceiling[Subscript[z, 2]] == Ceiling[Subscript[z, 1] + Subscript[z, 2]] - Ceiling[Subscript[z, 1] - Ceiling[Subscript[z, 1]] + Subscript[z, 2] - Ceiling[Subscript[z, 2]]]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Ceiling", "[", SubscriptBox["z", RowBox[List[" ", "1"]]], "]"]], "+", RowBox[List["Ceiling", "[", SubscriptBox["z", RowBox[List[" ", "2"]]], "]"]]]], "\[Equal]", RowBox[List[RowBox[List["Ceiling", "[", RowBox[List[SubscriptBox["z", RowBox[List[" ", "1"]]], "+", SubscriptBox["z", RowBox[List[" ", "2"]]]]], "]"]], "-", RowBox[List["Ceiling", "[", RowBox[List[SubscriptBox["z", RowBox[List[" ", "1"]]], "-", RowBox[List["Ceiling", "[", SubscriptBox["z", RowBox[List[" ", "1"]]], "]"]], "+", SubscriptBox["z", RowBox[List[" ", "2"]]], "-", RowBox[List["Ceiling", "[", 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> <mrow> <mo> &#8968; </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> &#8969; </mo> </mrow> <mo> + </mo> <mrow> <mo> &#8968; </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> &#8969; </mo> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mo> &#8968; </mo> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> <mo> &#8969; </mo> </mrow> <mo> - </mo> <mrow> <mo> &#8968; </mo> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> - </mo> <mrow> <mo> &#8968; </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> &#8969; </mo> </mrow> <mo> - </mo> <mrow> <mo> &#8968; </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> &#8969; </mo> </mrow> </mrow> <mo> &#8969; </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <plus /> <apply> <ceiling /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ceiling /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <ceiling /> <apply> <plus /> <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> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ceiling /> <apply> <plus /> <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> <times /> <cn type='integer'> -1 </cn> <apply> <ceiling /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ceiling /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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


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





2001-10-29