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CellChangeTimes->{{3.4010572932539997`*^9, 3.4010573143929996`*^9}, { 3.4023482045892*^9, 3.4023482076935997`*^9}}], Cell["\<\ However this objection applies to all abbreviated operators (+, *, ^, [[ ]], \ { }, /@, etc.)\ \>", "Text", CellChangeTimes->{{3.401056236013*^9, 3.401056244756*^9}, { 3.4010563801289997`*^9, 3.4010563807139997`*^9}, {3.4010568722650003`*^9, 3.401056909907*^9}, {3.401057801592*^9, 3.401057808594*^9}, { 3.401058061203*^9, 3.40105806292*^9}, {3.402348218676*^9, 3.4023482298924*^9}, {3.4025082832282*^9, 3.4025083003361998`*^9}}], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " is endowed with \"a variety of special characters that greatly increase \ readability and elegance\"" }], "Text", CellChangeTimes->{{3.401058075302*^9, 3.401058094185*^9}}], Cell[TextData[{ "FORTRAN (FORmula TRANslation; early and primitive, but elegant), ", StyleBox["Mathematica", FontSlant->"Italic"], " (an advanced synthesis):\nA conscious effort was made to provide a path of \ least action or smooth transduction from mathematical notation to code" }], "Text", CellChangeTimes->{{3.401060155513*^9, 3.401060198469*^9}, { 3.4010602336540003`*^9, 3.401060263804*^9}, {3.4023482648364*^9, 3.4023482656944*^9}, {3.4023483204504004`*^9, 3.4023483305748*^9}, { 3.4023780303942003`*^9, 3.4023780320322*^9}, {3.4023888141768*^9, 3.4023888506184*^9}, {3.402671597701*^9, 3.4026716195039997`*^9}}], Cell["\<\ Further, a significant feature of V6 is the addition of >100 undefined \ operators to facilitate creating user-defined notations\ \>", "Text", CellChangeTimes->{{3.4023780547146*^9, 3.4023780943854*^9}, { 3.4023890513124*^9, 3.402389058816*^9}}], Cell["\<\ I submit that if you use Prefix, you will use it more often than the most \ common abbreviated operators\ \>", "Text", CellChangeTimes->{{3.4010597624700003`*^9, 3.401059782377*^9}, { 3.4023763893677998`*^9, 3.4023763932678003`*^9}}], Cell[CellGroupData[{ Cell[TextData[StyleBox["Precedence directs the order of abbreviated \ operators' operation", "MR", FontFamily->"Arial", FontWeight->"Bold"]], "Subsection", CellChangeTimes->{{3.4010575931099997`*^9, 3.401057663491*^9}, { 3.4010577079*^9, 3.401057763797*^9}, {3.401057820891*^9, 3.4010578397530003`*^9}, 3.401057889256*^9, {3.4010579211289997`*^9, 3.401057922936*^9}, {3.4011225214040003`*^9, 3.401122556153*^9}}], Cell[TextData[{ StyleBox["Precedence can be symbolized by parenthetical grouping, such as: ", "MR", FontFamily->"Arial"], "a ", StyleBox["+", "MR"], " ", StyleBox["(b", "MR"], " ", StyleBox["^", "MR"], " ", StyleBox["c)", "MR"], " versus ", StyleBox["(a", "MR"], " ", StyleBox["+", "MR"], " ", StyleBox["b)", "MR"], " ", StyleBox["^", "MR"], " ", StyleBox["c", "MR"] }], "Text", CellChangeTimes->{{3.401057939616*^9, 3.401057941487*^9}}], Cell[TextData[{ "The ", StyleBox["Mathematica", FontSlant->"Italic"], " reference on precedence in 5.2 was Table A.2.7, now is in tutorial / \ InputSyntax: Operator Input Forms\n\nIt lists all abbreviated operators in \ tables of decreasing precedence" }], "Text", CellChangeTimes->{{3.40105796469*^9, 3.401057983604*^9}, { 3.4010583787279997`*^9, 3.401058466567*^9}, {3.401058510054*^9, 3.4010585516219997`*^9}, {3.401059077436*^9, 3.4010590965889997`*^9}, 3.4024227151893153`*^9}], Cell["\<\ However, a superior reference can be generated from a little code\ \>", "Text", CellChangeTimes->{{3.4010585976099997`*^9, 3.401058609565*^9}}] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["There exists an undocumented function, Precedence", "Section", CellChangeTimes->{{3.4010586237530003`*^9, 3.4010586424379997`*^9}}], Cell["Voila:", "Text", CellChangeTimes->{{3.402348405876*^9, 3.402348420618*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Precedence", "@", "Prefix"}]], "Input", CellChangeTimes->{{3.401058651391*^9, 3.401058657273*^9}}], Cell[BoxData["640.`"], "Output", CellChangeTimes->{3.401058657962*^9}] }, Open ]], Cell["\<\ It is not listable, but it should be! Either reset Attributes to Listable or \ just Map it:\ \>", "Text", CellChangeTimes->{{3.4010586966280003`*^9, 3.401058701954*^9}, { 3.4023484340808*^9, 3.4023484542047997`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Precedence", "/@", " ", RowBox[{"{", RowBox[{"Prefix", ",", " ", "Factorial"}], "}"}]}]], "Input", CellChangeTimes->{{3.401058707491*^9, 3.401058717424*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{"640.`", ",", "610.`"}], "}"}]], "Output", CellChangeTimes->{3.40105871841*^9}] }, Open ]], Cell["\<\ What happened in the previous slide? Prefix is a little \"stickier\" than Factorial\[Equal]@ sticks to n more than \ ! does\[LongDash]and so we got (IntegerDigits@n)! instead of IntegerDigits[ \ n! ]\ \>", "Text", CellChangeTimes->{{3.401056744592*^9, 3.401056755708*^9}, { 3.4010587260150003`*^9, 3.4010587437469997`*^9}, {3.401058853061*^9, 3.401058867858*^9}, {3.4023484768248*^9, 3.402348579894*^9}, { 3.402671495014*^9, 3.402671496366*^9}}], Cell[CellGroupData[{ Cell["\<\ When faced with a few abbreviated operators, map Precedence onto them in the \ order they present in your expression\ \>", "Subsubsection", CellChangeTimes->{{3.401058877618*^9, 3.40105891116*^9}, { 3.4023486112032003`*^9, 3.40234861398*^9}, {3.402671516293*^9, 3.402671520158*^9}}], Cell[BoxData[ RowBox[{"a", " ", "+", " ", RowBox[{"b", " ", "*", " ", RowBox[{"c", " ", "^", " ", "d"}]}], " ", "-", " ", "e"}]], "Input", CellChangeTimes->{{3.401058959322*^9, 3.401058973781*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Precedence", " ", "/@", " ", 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