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For a full list, \ see ", StyleBox[ButtonBox["http://reference.wolfram.com/language/ref/Plot3D.html", BaseStyle->"Hyperlink", ButtonData->{ URL["http://reference.wolfram.com/language/ref/Plot3D.html"], None}, ButtonNote->"http://reference.wolfram.com/language/ref/Plot3D.html"], FontWeight->"Bold"], ". For instance, one can use the option ", StyleBox["BoundaryStyle ", FontWeight->"Bold"], "to color the boundary of the region", StyleBox[". 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evaluates expr repetitively, with the local variable i varying from 1 \ (one) to max in steps of 1(one)\n", StyleBox["Do[expr,{i,min,max,di}]", FontColor->GrayLevel[0]], " - evaluates expr with i varying from min to max in steps of di.\n", StyleBox["Do[expr,{i,list}]", FontColor->GrayLevel[0]], " - evaluates expr with i taking on values from a list\n", StyleBox["Do[expr,{n}]", FontColor->GrayLevel[0]], " - evaluates expr n times" }], "Subsubsection", CellChangeTimes->{ 3.619163049033441*^9, {3.619163088293867*^9, 3.619163125859593*^9}, { 3.6191631588379374`*^9, 3.619163192400408*^9}, {3.619163234458829*^9, 3.619163304635859*^9}, {3.694843708421093*^9, 3.694843737043428*^9}}], Cell[CellGroupData[{ Cell["\<\ Examples with Do:\ \>", "Subsection", CellChangeTimes->{{3.619163486903789*^9, 3.619163505766036*^9}}], Cell[CellGroupData[{ Cell["Print the first 10 positive integers:", "Subsubsection", CellChangeTimes->{ 3.619163500780467*^9, {3.6191635442416143`*^9, 3.619163545281859*^9}}], Cell[BoxData[ RowBox[{"Do", "[", RowBox[{ RowBox[{"Print", "[", "i", "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "10"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.6191635196144*^9, 3.61916354957955*^9}}, FontSize->16, Background->RGBColor[0.87, 0.94, 1]] }, Open ]], Cell[CellGroupData[{ Cell["Print only the odd integers between 4 and 10:", "Subsubsection", CellChangeTimes->{{3.619163581354397*^9, 3.6191636140312767`*^9}, { 3.619163936986806*^9, 3.619163968448168*^9}, 3.6948440899231863`*^9}], Cell[BoxData[ RowBox[{"Do", "[", RowBox[{ RowBox[{"Print", "[", "i", "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "5", ",", "10", ",", "2"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.619163617797778*^9, 3.619163639119095*^9}, { 3.619163760706011*^9, 3.619163854200729*^9}, {3.619163971455134*^9, 3.619163971896738*^9}, {3.6191640039568996`*^9, 3.619164004135662*^9}}, FontSize->16, Background->RGBColor[0.87, 0.94, 1]], Cell[BoxData[ RowBox[{"Do", "[", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Mod", "[", RowBox[{"i", ",", "2"}], "]"}], "!=", "0"}], ",", RowBox[{"Print", "[", "i", "]"}]}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "4", ",", "10", ",", "1"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.619163891304554*^9, 3.619163984323051*^9}, { 3.6191640769293337`*^9, 3.619164078116632*^9}}, FontSize->16, Background->RGBColor[0.87, 0.94, 1]], Cell[BoxData[""], "Input", CellChangeTimes->{{3.69484382520461*^9, 3.694843840236408*^9}}] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Loops and control structures (Break, Return)", "Section", CellChangeTimes->{{3.619164637054865*^9, 3.619164647316288*^9}, { 3.619220195204112*^9, 3.619220199784915*^9}, {3.6502264854865437`*^9, 3.650226491837545*^9}}, FontSize->30], Cell[TextData[{ "We can use some control flow functions to terminate the loop:\n", StyleBox["Break[ ]", FontColor->GrayLevel[0]], " - 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evaluates start, then repetitively evaluates body and incr, \n \ until test fails\n" }], "Subsubsection", CellChangeTimes->{{3.619165403431715*^9, 3.6191654378035088`*^9}, { 3.619165468306382*^9, 3.6191654843774242`*^9}, 3.694843810709793*^9}], Cell[BoxData[ RowBox[{ RowBox[{"For", "[", RowBox[{ RowBox[{"i", "=", "1"}], ",", " ", RowBox[{"i", "<", "4"}], ",", RowBox[{"i", "++"}], ",", RowBox[{"Print", "[", "i", "]"}]}], "]"}], " "}]], "Input", CellChangeTimes->{{3.6191655228274517`*^9, 3.619165575903666*^9}}, FontSize->16, Background->RGBColor[0.87, 0.94, 1]] }, Open ]], Cell[CellGroupData[{ Cell["\<\ First i is assigned the value 1. As long as the condition i < 5 remains true, \ i is incremented by 1 (i++ is just a shortening for i = i + 1) and the body \ of the function For is executed (that is, we print the integer i).\ \>", "Subsubsection", CellChangeTimes->{{3.650226961780487*^9, 3.6502269747282343`*^9}}], Cell[BoxData[""], "Input", CellChangeTimes->{{3.69484386490125*^9, 3.694843866285252*^9}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Loops (While)", "Section", CellChangeTimes->{{3.619164637054865*^9, 3.619164647316288*^9}, { 3.650226637436263*^9, 3.650226643417068*^9}}], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["While[condition, body]", FontColor->GrayLevel[0]], " - evaluates body repetitively, so long as condition is True" }], "Subsubsection", CellChangeTimes->{{3.619164685078524*^9, 3.6191647142254333`*^9}, 3.61916488132228*^9, 3.619165434357695*^9}], Cell[BoxData[ RowBox[{ RowBox[{"n", "=", "17"}], ";", " ", RowBox[{"While", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"n", "=", RowBox[{"Floor", "[", RowBox[{"n", "/", "2"}], "]"}]}], ")"}], "\[NotEqual]", "0"}], ",", " ", RowBox[{"Print", "[", "n", "]"}]}], "]"}]}]], "Input", CellChangeTimes->{{3.619164969090837*^9, 3.61916502297512*^9}, { 3.619165179729019*^9, 3.6191651849432583`*^9}, {3.6191652181232023`*^9, 3.619165219757729*^9}, {3.619165261365477*^9, 3.619165264630196*^9}}, FontSize->16, Background->RGBColor[0.87, 0.94, 1]] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Even if the last value printed by the While function is 1, the current value \ of n is not 1, as one may assume, but 0. This value was not printed when we \ ran the While command, because when n is 0, the condition n != 0 is false, so \ the body of the function While (which would have been Print[0]) is not \ executed.\ \>", "Subsubsection", CellChangeTimes->{{3.6502268290417013`*^9, 3.650226849526196*^9}}], Cell[CellGroupData[{ Cell[BoxData["n"], "Input", CellChangeTimes->{{3.619203322146377*^9, 3.619203326091908*^9}}, FontSize->18], Cell[BoxData["0"], "Output", CellChangeTimes->{3.6192033268891068`*^9}, FontSize->16] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["\<\ In the Wolfram Language, both While and For always evaluate the loop test \ before evaluating the body of the loop. As soon as the loop test fails to be \ True, While and For terminate. The body of the loop is thus only evaluated in \ situations where the loop test is True.\ \>", "Subsubsection", CellChangeTimes->{{3.619165655160328*^9, 3.619165667625835*^9}}, TextJustification->1., FontColor->GrayLevel[0]], Cell[BoxData[ RowBox[{"While", "[", RowBox[{"False", ",", " ", RowBox[{"Print", "[", "\"\\"", "]"}]}], "]"}]], "Input", CellChangeTimes->{{3.619165771569379*^9, 3.619165795974082*^9}}, FontSize->16, Background->RGBColor[0.87, 0.94, 1]] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "The command ", StyleBox["While[False, Print[\"False\"]]", FontColor->GrayLevel[0]], " does not print anything, because the test condition is always False, so \ the body of the function is never executed." }], "Subsubsection", CellChangeTimes->{{3.6502270648933487`*^9, 3.6502270718764763`*^9}}], Cell[BoxData[""], "Input", CellChangeTimes->{{3.694844000683878*^9, 3.69484400177145*^9}}] }, Open ]], Cell[TextData[{ StyleBox["The functions While and For in the Wolfram Language are similar to \ the control structures While and For in languages such as C++. 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