D[Mod[m, n], n] == -Floor[m/n]

Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", "n"], RowBox[List["Mod", "[", RowBox[List["m", ",", "n"]], "]"]]]], "\[Equal]", RowBox[List["-", RowBox[List["Floor", "[", FractionBox["m", "n"], "]"]]]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mfrac> <mrow> <mo> &#8706; </mo> <mrow> <mo> ( </mo> <semantics> <mrow> <mi> m </mi> <mo> &#8290; </mo> <mi> mod </mi> <mo> &#8290; </mo> <mi> n </mi> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <rem /> <ci> $CellContext`m </ci> <ci> $CellContext`n </ci> </apply> </annotation-xml> </semantics> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <mi> n </mi> </mrow> </mfrac> <mo> &#10869; </mo> <mrow> <mo> - </mo> <mrow> <mo> &#8970; </mo> <mfrac> <mi> m </mi> <mi> n </mi> </mfrac> <mo> &#8971; </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <partialdiff /> <bvar> <ci> n </ci> </bvar> <apply> <rem /> <ci> $CellContext`m </ci> <ci> $CellContext`n </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <floor /> <apply> <times /> <ci> m </ci> <apply> <power /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["n_"]]], RowBox[List["Mod", "[", RowBox[List["m_", ",", "n_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List["-", RowBox[List["Floor", "[", FractionBox["m", "n"], "]"]]]]]]]]

2001-10-29