(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 12.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] NotebookDataLength[ 157715, 4099] NotebookOptionsPosition[ 125440, 3631] NotebookOutlinePosition[ 126566, 3666] CellTagsIndexPosition[ 126523, 3663] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[TextData[{ "F. Fass\[OGrave]. University of Padova. \n", StyleBox["Introduction to the use of Mathematica in Mathematics and Science", FontSlant->"Italic"], ". SoftSkills course for the PhD program in Mathematics\nLecture 1 (October \ 6, 2023)" }], "Text", CellFrame->{{0, 0}, {0.5, 0}}, CellChangeTimes->{{3.6030403380477047`*^9, 3.6030403496377206`*^9}, { 3.6042342921245947`*^9, 3.604234293844597*^9}, {3.6659842250605717`*^9, 3.665984234810585*^9}, {3.665988776604652*^9, 3.6659887774046535`*^9}, { 3.666106805730517*^9, 3.666106807983646*^9}, {3.686715090311494*^9, 3.68671511399888*^9}, {3.6973875672817383`*^9, 3.6973875784126663`*^9}, { 3.697434883527854*^9, 3.697434886700633*^9}, {3.7288472476388865`*^9, 3.728847250442567*^9}, 3.7290563713306975`*^9, {3.7603265886670856`*^9, 3.760326590879668*^9}, {3.792953448635523*^9, 3.7929534512106314`*^9}, { 3.793001443067047*^9, 3.793001457902358*^9}, {3.793125487673247*^9, 3.7931254933125515`*^9}, {3.823794609368146*^9, 3.8237946203338003`*^9}, { 3.905514199116931*^9, 3.90551422872608*^9}, {3.9055144580037365`*^9, 3.9055145289462028`*^9}, 3.905524053605975*^9, {3.9056541789884577`*^9, 3.90565419524717*^9}}, FontSize->12, Background->None,ExpressionUUID->"ce3fc3e2-c067-4126-8767-5f87fe045881"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["1. A first look at ", FontColor->GrayLevel[0]], StyleBox["Mathematica", FontSlant->"Italic", FontColor->GrayLevel[0]], StyleBox[": What can you do? How?", FontColor->GrayLevel[0]] }], "Title", CellChangeTimes->{{3.7603304738687916`*^9, 3.7603304848477964`*^9}, { 3.823865007385685*^9, 3.823865007955243*^9}, {3.90551453503039*^9, 3.9055145398655195`*^9}, {3.905514613214245*^9, 3.905514628990396*^9}, 3.9055696380856085`*^9}, Background->RGBColor[ 1., 0., 0.],ExpressionUUID->"b5a1964b-aa57-4f2f-b36b-b81a5f61a50d"], Cell[TextData[StyleBox["NB : To open a section of this notebook click on the \ button, if present.\nOtherwise, to open all the cells in a section, select \ them and press ALT + CGO (or use the menu Cell\[Rule]Grouping\[Rule]Open All \ Subgroups).\[LineSeparator]To select all the cells of the notebooks, use \ CTRL+A", FontSize->12]], "Text", CellChangeTimes->{{3.7604539424883003`*^9, 3.760453957356061*^9}, { 3.760454013424907*^9, 3.760454114084244*^9}, {3.7930014940117555`*^9, 3.7930015369808016`*^9}, {3.7931254998270607`*^9, 3.793125554454295*^9}, { 3.8237946303908854`*^9, 3.8237946717945075`*^9}, {3.8238650468292117`*^9, 3.8238650553872647`*^9}, {3.9055146494733753`*^9, 3.9055147386446548`*^9}, { 3.9055147882224016`*^9, 3.9055148289642267`*^9}, {3.9055717881544695`*^9, 3.9055717934542513`*^9}}, FontSize->14,ExpressionUUID->"edb7b4c4-6b5b-4a25-b6c4-3ffc763af743"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["1. 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Architecture of ", FontSize->24, FontSlant->"Italic"], StyleBox["Mathematica", FontSize->24, FontSlant->"Italic"], StyleBox[": Kernel and Front End", FontSize->24, FontSlant->"Italic"] }], "Section", CellChangeTimes->{{3.7603305394751625`*^9, 3.760330552624377*^9}, { 3.7603798490998344`*^9, 3.7603798499042997`*^9}, {3.7929893543089256`*^9, 3.7929893583080654`*^9}, {3.7931274848259177`*^9, 3.793127484904027*^9}, { 3.905514870952041*^9, 3.9055148984418287`*^9}, 3.9056550148239064`*^9, 3.905655092004068*^9}, Background->RGBColor[ 0., 1., 1.],ExpressionUUID->"c543aa15-20f7-43b5-9b4c-51360427fb55"], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " consists of two different programs:\n", StyleBox["\[FilledCircle]", FontSize->12], " The ", StyleBox["Kernel, ", FontWeight->"Bold"], "which executs all the computations\n", StyleBox["\[FilledCircle] ", FontSize->12], " The ", StyleBox["Front End", FontWeight->"Bold"], ", which is the user interface" }], "Text", ShowGroupOpener->False, CellChangeTimes->{ 3.5433055891408176`*^9, 3.7290563713306975`*^9, 3.823795123737399*^9, { 3.9055189316165705`*^9, 3.9055190232681427`*^9}}, Background->RGBColor[ 1, 1, 0],ExpressionUUID->"c176086c-4fa2-4a5c-8d4a-42b964cde6d2"], Cell["\<\ The Kernel is independent of the operating system \[Rule] portability of \ programs written in Mathematica (except for round-off errors, which are platform-dependent) The Front End is adapted to the various operating systems \[Rule] small \ differences between different versions.\ \>", "Text", CellChangeTimes->{{3.793125869955928*^9, 3.7931258823436575`*^9}, { 3.823795133411272*^9, 3.823795158788689*^9}, {3.9055190255351105`*^9, 3.9055190715405884`*^9}, {3.9055193564745207`*^9, 3.905519476279978*^9}, 3.905519722824198*^9, 3.905524298581114*^9, {3.905570245557755*^9, 3.9055702518997164`*^9}}, Background->RGBColor[ 1, 1, 0],ExpressionUUID->"5cbbf95b-6b92-45b2-a65d-68ffc6da3b46"], Cell[TextData[{ "The user exchanges data with the Front End, which in turn exchanges them \ with the Kernel (which executes them)\n ", StyleBox[" User \[LeftRightArrow] FrontEnd \[LeftRightArrow] Kernel", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]] }], "Text", ShowGroupOpener->False, CellChangeTimes->{ 3.5433056285308867`*^9, 3.7290563713306975`*^9, {3.905519481722971*^9, 3.905519550823864*^9}, {3.905570268851651*^9, 3.905570298135762*^9}}, Background->RGBColor[ 1, 1, 0],ExpressionUUID->"5cfd502d-ba69-4fcb-b11f-8e37cde25f61"], Cell[CellGroupData[{ Cell[" ", "Subsubsection", CellChangeTimes->{3.823795178878607*^9, 3.905570315213107*^9},ExpressionUUID->"f4bec09f-4427-40e6-819f-\ 14cbe5b6079c"], Cell[TextData[{ StyleBox["Fact :", FontWeight->"Bold"], "\n Every command entered in a Notebook is executed elsewhere (in the \ Kernel)\n", StyleBox["Corollaries:", FontWeight->"Bold"], "\n \[FilledSmallCircle] It doesn\[CloseCurlyQuote]t matter at which \ point of the Notebook a command is written and executed\n \ \[FilledSmallCircle] It\[CloseCurlyQuote]s only the order of executions of \ the commands that matters: the Kernel numbers them progressively.\n \ \[FilledSmallCircle] The Kernel \[OpenCurlyDoubleQuote]remembers\ \[CloseCurlyDoubleQuote] an output even if the corresponding cell (in the \ FrontEnd) is cancelled.\n \[FilledSmallCircle] Pay attention to \ assignments such as x = 3 because the Kernel remembers them!" }], "Text", CellChangeTimes->{{3.7931259671212225`*^9, 3.793125970511057*^9}, { 3.823795181006797*^9, 3.8237952501307216`*^9}, {3.9055196476719217`*^9, 3.9055197355135403`*^9}, {3.9055203982529087`*^9, 3.905520507472478*^9}, { 3.905520554768265*^9, 3.9055205594556*^9}, {3.90552059575928*^9, 3.9055207046215425`*^9}, {3.9055243174475613`*^9, 3.9055243414968348`*^9}, { 3.905570324612235*^9, 3.905570365506172*^9}}, Background->RGBColor[ 1, 1, 0],ExpressionUUID->"93ef382c-3b45-4446-a886-da198cea598b"] }, Open ]], Cell[CellGroupData[{ Cell[" ", "Subsubsection", CellChangeTimes->{{3.9055703695548086`*^9, 3.9055703710884495`*^9}},ExpressionUUID->"15202931-f0c2-4642-978f-\ e0ac61b4396a"], Cell["\<\ \[FilledSmallCircle] When you close Mathematica, the Kernel is terminated \ \[LongDash] and all its content is lost. Instead, a Notebook may be saved as a file and (re)executed once \ Mathematica is restarted.\ \>", "Text", CellChangeTimes->{{3.7931259833049316`*^9, 3.7931259901939526`*^9}, { 3.8237952603778086`*^9, 3.823795287635994*^9}, {3.905520715623576*^9, 3.905520816182021*^9}, 3.9055703760185814`*^9}, Background->RGBColor[ 1, 1, 0],ExpressionUUID->"f9e96f64-4ea8-4e99-a4d8-19d0d47cb156"], Cell[TextData[{ "\[FilledSmallCircle] Notebooks in use within a given ", StyleBox["Mathematica", FontSlant->"Italic"], " session use (by default) the same Kernel.\n \[Implies] it does not \ matter in which of them you enter a command (they all \ \[OpenCurlyDoubleQuote]talk\[CloseCurlyDoubleQuote] to the same Kernel)" }], "Text", PageWidth:>Infinity, ShowGroupOpener->False, CellChangeTimes->{{3.543305655004133*^9, 3.543305718215444*^9}, { 3.5989528642521696`*^9, 3.5989528672121735`*^9}, {3.697435407127179*^9, 3.69743542447222*^9}, 3.7290563713306975`*^9, {3.9055208208985868`*^9, 3.905520896338438*^9}, {3.905570384722144*^9, 3.9055704314820337`*^9}}, TextAlignment->Left, Background->RGBColor[ 1, 1, 0],ExpressionUUID->"4a50f9f3-fc16-47b6-9746-86659f230427"], Cell[CellGroupData[{ Cell[" ", "Subsubsection", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.5433057353598742`*^9, 3.5433057389166803`*^9}, 3.7290563713306975`*^9},ExpressionUUID->"81a5a7f5-d198-4d21-a7ba-\ cc7cb6939121"], Cell[TextData[{ "Example: execute the command\n ", StyleBox[" x=8.1", FontFamily->"Courier New"], "\nthen cancel the Input and Output cells and execute the command\n x" }], "Text", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{ 3.6219263461470437`*^9, 3.7290563713306975`*^9, {3.792989793352533*^9, 3.792989796320587*^9}, {3.90552091831452*^9, 3.9055209777003393`*^9}}, Background->RGBColor[ 0., 1., 0.],ExpressionUUID->"0c16665b-84fe-46b7-9b21-bd715c431d60"] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["4. Symbolic computations 1: Operations on polynomials", "Chapter", CellChangeTimes->{{3.7603305394751625`*^9, 3.760330552624377*^9}, 3.7603305908582544`*^9, {3.760330621878708*^9, 3.7603306472378387`*^9}, { 3.7603798587701907`*^9, 3.7603798746499395`*^9}, {3.905521259124189*^9, 3.9055212592753143`*^9}, {3.905521337611317*^9, 3.905521362836508*^9}, { 3.905522454249137*^9, 3.9055224549844584`*^9}, {3.905524389268314*^9, 3.9055243984433517`*^9}, {3.9055677660821476`*^9, 3.9055677692045207`*^9}}, FontSize->24, Background->RGBColor[ 0., 1., 1.],ExpressionUUID->"19e84f6a-1117-41a0-a3d0-54abd69bfe1c"], Cell[TextData[{ "To give a look at what, and how, ", StyleBox["Mathematica ", FontSlant->"Italic"], "does, let us begin with ", "symbolic computations" }], "Text", CellFrame->False, ShowGroupOpener->False, CellChangeTimes->{ 3.7290563713306975`*^9, {3.9055213800868587`*^9, 3.905521441930726*^9}, 3.905524411327388*^9},ExpressionUUID->"ba621b5e-016c-44be-a6a8-\ e5411eb8ec25"], Cell[CellGroupData[{ Cell[TextData[StyleBox["4.1 Symbolic operations on polynomials", FontSize->24, FontColor->GrayLevel[0]]], "Section", CellChangeTimes->{{3.7603308525788794`*^9, 3.7603308717124143`*^9}, { 3.7604544229795322`*^9, 3.7604544318817544`*^9}, {3.9055214612523317`*^9, 3.9055214775897026`*^9}}, Background->RGBColor[ 0., 1., 1.],ExpressionUUID->"7a80eb35-9cfb-4802-86f2-1ac12f2dc5bb"], Cell[CellGroupData[{ Cell["Expansions and factorization", "Subsection", CellChangeTimes->{{3.9055234601425323`*^9, 3.9055235023866158`*^9}},ExpressionUUID->"7da6b9d3-8bdb-4ae0-99cc-\ e5dab38d592a"], Cell[TextData[{ "Expansion of a polynomial into monomials, factorization of a polynomial\n \ ", StyleBox["Expand[ polynomial]", FontWeight->"Bold"], "\n ", StyleBox["Factor[ polynomial ]\n \n", FontWeight->"Bold"], "NB: Here, \[OpenCurlyDoubleQuote]polynomial\[CloseCurlyDoubleQuote] is the \ expression of the polynomial", StyleBox[" ", FontWeight->"Bold"] }], "Text", CellChangeTimes->{{3.7931260538741693`*^9, 3.7931260538741693`*^9}, 3.7931260926620984`*^9, {3.905521483166831*^9, 3.905521518090457*^9}, { 3.905570478072192*^9, 3.905570528813552*^9}}, Background->RGBColor[ 1, 1, 0],ExpressionUUID->"02167c78-b208-455a-85bd-1b8646953b95"], Cell[BoxData[ RowBox[{"Expand", "[", " ", StyleBox[ RowBox[{ RowBox[{"(", RowBox[{"a", "+", "b", "+", "c"}], ")"}], "^", "3"}], FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontColor->RGBColor[0, 0, 1]], "]"}]], "Input",ExpressionUUID->"a9d6f46b-\ a4c4-4c1d-816a-4d4e00c0e827"], Cell[BoxData[ RowBox[{"Factor", "[", "%", "]"}]], "Input",ExpressionUUID->"ac4170f6-2975-42bf-87b2-be6f3eff262b"], Cell[CellGroupData[{ Cell["", "Subsubsection",ExpressionUUID->"4129757f-b643-4e33-9ca8-db349dcb884f"], Cell[TextData[{ StyleBox["Notes", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], ": \n 1. The arguments of functions are always delimited by square \ brackets ", StyleBox[" [ ]", FontFamily->"Terminal", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " (NOT round brackets ", StyleBox[" ( ) ", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox[")", FontColor->GrayLevel[0]], "\n Examples: ", StyleBox["Sin[x], Log[3x+1], .....\n ", FontFamily->"Terminal", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], "\n 2. The names of all native commands in ", StyleBox["Mathematica", FontSlant->"Italic"], " are capitalized\n ", "\n 3. ", StyleBox[" ( )", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " group terms together (as in math) \n \n 4. ", StyleBox["f[x]", FontFamily->"Terminal", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " is the same as ", StyleBox["f@x", FontWeight->"Bold", FontColor->RGBColor[1., 0., 0.]], " and ", StyleBox["x//f", FontFamily->"Terminal", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " " }], "Text", ShowGroupOpener->False, CellChangeTimes->{{3.5432974724040194`*^9, 3.543297492356454*^9}, { 3.590480789942774*^9, 3.590480790332775*^9}, {3.6867155460127115`*^9, 3.6867155596611567`*^9}, {3.686717361083518*^9, 3.6867173636181345`*^9}, { 3.697435488792112*^9, 3.6974355122159557`*^9}, 3.7290563713306975`*^9, { 3.7603277881845765`*^9, 3.7603278119264164`*^9}, {3.823795389825655*^9, 3.8237954261142464`*^9}, 3.905521525794051*^9, {3.9055216496365213`*^9, 3.9055217214296503`*^9}, {3.905521760167492*^9, 3.90552188787348*^9}, { 3.9055219620286074`*^9, 3.9055220187602034`*^9}, {3.9055705493946123`*^9, 3.9055705669457483`*^9}}, Background->RGBColor[ 1, 1, 0],ExpressionUUID->"e343e3db-3299-4ddd-afbc-ec0d613faf41"], Cell[BoxData[""], "Input", CellChangeTimes->{{3.793126150649802*^9, 3.7931261541026144`*^9}},ExpressionUUID->"677482c8-364a-408a-8b43-\ 8f4ca7a002da"], Cell["\<\ Example: compute cos(\[Pi]) (\[Pi] is \[OpenCurlyDoubleQuote]Pi\[CloseCurlyDoubleQuote])\ \>", "Text", CellChangeTimes->{ 3.6219263461470437`*^9, 3.7290563713306975`*^9, {3.792989793352533*^9, 3.792989796320587*^9}, {3.90552091831452*^9, 3.9055209777003393`*^9}, 3.9055220796750746`*^9, {3.9055221170858192`*^9, 3.9055221363277287`*^9}, { 3.9055705774945364`*^9, 3.905570585378411*^9}}, Background->RGBColor[ 0., 1., 0.],ExpressionUUID->"0a4370f2-1112-48bb-98af-565aa6d3bccc"], Cell[BoxData[ RowBox[{"ArcSin", "@", RowBox[{"Cos", "[", "Pi", "]"}]}]], "Input", CellChangeTimes->{{3.8237954399441414`*^9, 3.823795445129141*^9}, { 3.823844391152134*^9, 3.823844393135672*^9}, {3.9055220323157625`*^9, 3.905522038548396*^9}, {3.9055790691760035`*^9, 3.9055790752380447`*^9}},ExpressionUUID->"24cd0b78-49e3-4f33-a700-\ 1f9e8700fd39"], Cell[BoxData[ RowBox[{"Cos", "@", "Pi"}]], "Input", CellChangeTimes->{{3.823795448596713*^9, 3.8237954490866957`*^9}, { 3.8238444071211147`*^9, 3.823844407279689*^9}, {3.9055220264330893`*^9, 3.905522027791785*^9}},ExpressionUUID->"4bc1c1aa-acf6-4bd2-ad47-\ ddb40a86a579"], Cell[BoxData[ RowBox[{"Pi", "//", "Cos"}]], "Input", CellChangeTimes->{{3.823795452554914*^9, 3.8237954539079833`*^9}, { 3.9055789804321303`*^9, 3.905579001121815*^9}},ExpressionUUID->"1f44108d-4715-4c7a-b128-\ 64c68872fa63"], Cell[BoxData[" "], "Input", CellChangeTimes->{ 3.7931261793305826`*^9},ExpressionUUID->"ac84e3f4-9fa2-4894-a675-\ b9b0f984ec4a"], Cell[TextData[{ "Now compute arcsin(cos(\[Pi])) \n(arcsin is \[OpenCurlyDoubleQuote]ArcSin\ \[CloseCurlyDoubleQuote]) \nYou can: \n\n- ", StyleBox["rewrite", FontSlant->"Italic"], " everything\n\n- ", StyleBox["go back ", FontSlant->"Italic"], "to one of the previous cells and insert\n ArcSin[ .... ]\n \ ArcSin@ ... \n ... // ArcSin\n\n- ", StyleBox["copyand paste ", FontSlant->"Italic"], "one of the ", "cells and do the same thing" }], "Text", CellChangeTimes->{{3.7603278955280557`*^9, 3.760328040538474*^9}, { 3.823795475281083*^9, 3.823795492751483*^9}, {3.9055220917649727`*^9, 3.905522245910968*^9}, {3.905570598417407*^9, 3.905570640028268*^9}, { 3.905579028414646*^9, 3.905579031090187*^9}}, Background->RGBColor[ 1, 1, 0],ExpressionUUID->"e1d346c1-dcab-4ab6-bf72-7da3c0e6f756"], Cell[BoxData[ RowBox[{"ArcSin", "[", RowBox[{"Cos", "[", "Pi", "]"}], "]"}]], "Input", CellChangeTimes->{{3.9055790418073797`*^9, 3.9055790579601007`*^9}},ExpressionUUID->"3b703c57-c89a-4ef2-964c-\ 1fe8628fb1b6"], Cell[BoxData[ RowBox[{"ArcSin", "[", RowBox[{"Cos", "@", "Pi"}], "]"}]], "Input", CellChangeTimes->{{3.905570664311809*^9, 3.905570667456295*^9}, 3.9055790968812437`*^9},ExpressionUUID->"12d24e1d-44bd-4c7c-bb21-\ fe8d204aca28"] }, Open ]], Cell[CellGroupData[{ Cell["", "Subsubsection",ExpressionUUID->"53a1af50-b3ad-4cda-862f-c0e848b80df2"], Cell["\<\ The previous expansions and factorizations were easy. Let\[CloseCurlyQuote]s try something more challenging:\ \>", "Text", CellChangeTimes->{{3.7931262978212614`*^9, 3.793126301164235*^9}, { 3.8237955159462643`*^9, 3.8237955219770117`*^9}, {3.905522522082883*^9, 3.905522579947422*^9}, 3.90557067539462*^9}, Background->RGBColor[ 0., 1., 0.],ExpressionUUID->"b64dce92-c59b-4999-8e6e-a4805bbeaa20"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"a", "+", "b", "+", "c"}], ")"}], StyleBox["^", FontColor->RGBColor[1, 0, 0]], StyleBox["20", FontColor->RGBColor[1, 0, 0]]}], "//", "Expand"}]], "Input", CellChangeTimes->{{3.90557069463838*^9, 3.905570694716486*^9}, { 3.9055791361678295`*^9, 3.9055791729815245`*^9}},ExpressionUUID->"7d0de161-24fc-4bcd-9586-\ 9a78b8e8b8e9"], Cell[BoxData[ RowBox[{"%", "//", "Factor"}]], "Input",ExpressionUUID->"e98e500e-8636-408a-aaff-d5346492dbe4"] }, Open ]], Cell[CellGroupData[{ Cell["", "Subsubsection",ExpressionUUID->"6e38d530-f7d1-44cc-a1ae-629397b70b1e"], Cell["Something even more challenging?", "Text", 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output is very large, a shortened text is shown (this prevents long \ transfer times from the Kernel to the FrontEnd) \ \>", "Text", CellChangeTimes->{{3.9055226270251827`*^9, 3.905522665733447*^9}, { 3.905522723343988*^9, 3.905522747347511*^9}}, Background->RGBColor[ 1, 1, 0],ExpressionUUID->"e14e0501-93ae-4e63-a690-fd8061f3cd4f"], Cell[BoxData[ RowBox[{"Factor", "@", "%"}]], "Input",ExpressionUUID->"9ad4d311-4fad-4c0f-9593-9e1dda46678a"] }, Open ]], Cell[CellGroupData[{ Cell[" ", "Subsubsection",ExpressionUUID->"1e21503c-c395-46a5-bedb-0c4567b625c4"], Cell[TextData[{ StyleBox["Note: ", FontWeight->"Bold"], "A", "n output may be very (even extremely) large\n \[Bullet] In such a case, ", StyleBox["if possible", FontSlant->"Italic"], ", ", StyleBox["Mathematica", FontSlant->"Italic"], " shows a shortened version. \n \[Bullet] However, it might happen that \ the program becomes unresponsive (and even crashes).\n \[Bullet] If in \ doubt test all codes with small numbers\n\n To reduce the size of the \ FrontEnd, it may also be useful \n \[Bullet] suppress the output with \ \[OpenCurlyDoubleQuote]:\[CloseCurlyDoubleQuote] \n \[Bullet] cancel the \ output cell (results remains memorized)" }], "Text", CellChangeTimes->{{3.7931263720604825`*^9, 3.7931263748571424`*^9}, { 3.823795578633686*^9, 3.8237956015768614`*^9}, {3.90552282030928*^9, 3.9055229270167027`*^9}, {3.9055230050557632`*^9, 3.9055230937359605`*^9}, {3.905523385704773*^9, 3.9055234426074677`*^9}, 3.9055235134514446`*^9, {3.9055707910199995`*^9, 3.9055708491107044`*^9}}, Background->RGBColor[ 1, 1, 0],ExpressionUUID->"447d0690-83de-4e35-85e6-8d553673c641"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["\[OpenCurlyDoubleQuote]Symplifying\[CloseCurlyDoubleQuote] polynomials \ and expressions", "Subsection", CellChangeTimes->{{3.9055234601425323`*^9, 3.9055235023866158`*^9}, { 3.905523534718034*^9, 3.9055235629957232`*^9}},ExpressionUUID->"aa992332-dcbb-4b50-b0f5-\ 5a1974f80ab8"], Cell[TextData[{ "- ", 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We had assigned a value to the symbol x !\ \>", "Text", ShowGroupOpener->False, CellChangeTimes->{ 3.729056371346322*^9, {3.760328588017545*^9, 3.7603285934410863`*^9}, { 3.7603288129866776`*^9, 3.7603288568137164`*^9}, 3.7931268942998557`*^9, { 3.905524604673766*^9, 3.9055246324332404`*^9}, 3.905570950925641*^9, { 3.9055709896189127`*^9, 3.9055709953403234`*^9}}, Background->RGBColor[ 1, 1, 0],ExpressionUUID->"781e39c0-cf47-405e-87a3-485dd0bc3057"], Cell[BoxData["x"], "Input", CellChangeTimes->{ 3.793126996273836*^9},ExpressionUUID->"75d29fbe-4024-42c6-9982-\ 0a5b17febb3d"], Cell[CellGroupData[{ Cell[TextData[StyleBox["", FontFamily->"Terminal", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]]], "Subsubsection", ShowGroupOpener->False, CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{ 3.729056371346322*^9, {3.7603287839185247`*^9, 3.7603288217510147`*^9}, { 3.905524733641712*^9, 3.9055247500696354`*^9}, {3.9055710223209147`*^9, 3.9055710243883853`*^9}, {3.9055799052436166`*^9, 3.90557990654643*^9}, 3.9056552461973414`*^9},ExpressionUUID->"e2dca5e5-01a7-4f10-ad70-\ 6aa84bf3c7cb"], Cell[TextData[{ "We need to cancel it:\n ", StyleBox["Clear[ symbols ]", FontFamily->"Terminal", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]] }], "Text", ShowGroupOpener->False, CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{ 3.729056371346322*^9, {3.7603287839185247`*^9, 3.7603288217510147`*^9}, { 3.905524733641712*^9, 3.9055247500696354`*^9}, {3.9055710223209147`*^9, 3.9055710243883853`*^9}, {3.9055799052436166`*^9, 3.90557990654643*^9}}, Background->RGBColor[ 1, 1, 0],ExpressionUUID->"36f47bc1-b1e9-41d0-a2b1-df02bfe8437a"], Cell[BoxData[ RowBox[{ StyleBox["Clear", FontColor->RGBColor[1, 0, 0]], "[", "x", "]"}]], "Input", ShowGroupOpener->False, CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{ 3.729056371346322*^9},ExpressionUUID->"c6e8df27-60b2-483a-bc45-\ 46405c160576"], Cell[BoxData["x"], "Input", ShowGroupOpener->False, CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{ 3.729056371346322*^9},ExpressionUUID->"e2f2bb8a-186e-4297-958c-\ e7d1a7087b57"], Cell[BoxData[ RowBox[{"Solve", "[", RowBox[{ StyleBox[ RowBox[{ RowBox[{ SuperscriptBox["x", "3"], "-", RowBox[{"2", "x"}], "+", "1"}], "==", "0"}], FontColor->RGBColor[0, 0, 1]], ",", "x"}], "]"}]], "Input", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{ 3.5989572379345613`*^9, 3.6659951147644677`*^9, {3.665995289274712*^9, 3.665995289914713*^9}, 3.6974450418533487`*^9, {3.69744519238494*^9, 3.6974451936293955`*^9}, {3.697445225882925*^9, 3.697445228446433*^9}, 3.729056371346322*^9, {3.760341088415078*^9, 3.760341089186864*^9}},ExpressionUUID->"e7f09a8a-c0a0-4eda-aea4-\ e8227f0729d4"] }, Open ]], Cell[BoxData[ RowBox[{"x", "/.", "%"}]], "Input", CellChangeTimes->{{3.9055800897635813`*^9, 3.9055800922979565`*^9}},ExpressionUUID->"dd33098b-dbd5-4698-8956-\ e389260331af"], Cell[BoxData[ RowBox[{"x", "/.", RowBox[{"Solve", "[", RowBox[{ StyleBox[ RowBox[{ RowBox[{ SuperscriptBox["x", "3"], "-", RowBox[{"2", "x"}], "+", "1"}], "==", "0"}], FontColor->RGBColor[0, 0, 1]], ",", "x"}], "]"}]}]], "Input", CellChangeTimes->{{3.9055801099415617`*^9, 3.905580110328026*^9}},ExpressionUUID->"e1403c0f-ca08-4950-a4d1-\ 81c880a506f7"], Cell[CellGroupData[{ Cell[" ", "Subsubsection", CellChangeTimes->{3.7931271503968596`*^9, 3.905571041609064*^9},ExpressionUUID->"dba6ec31-c412-4fae-8372-\ d6b9260f860e"], Cell[TextData[{ StyleBox["???\n\nSolve returns a ", FontSize->14], StyleBox["list of \"substituting rules\"", FontSize->14, FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox[" : the list of values which, substituted to the variable, satisfy \ the equation.\n(We will see laer how to work with lists and substitution \ rules)", FontSize->14] }], "Text", ShowGroupOpener->False, CellChangeTimes->{ 3.729056371346322*^9, {3.9055247597142925`*^9, 3.905524862488954*^9}, { 3.9055672493819876`*^9, 3.9055672513549185`*^9}}, Background->RGBColor[ 1, 1, 0],ExpressionUUID->"374c77aa-0b0e-4486-b986-5c1f84fb8d75"] }, Open ]], Cell[CellGroupData[{ Cell[" ", "Subsubsection", CellChangeTimes->{3.7931271208080845`*^9, 3.905571038666977*^9},ExpressionUUID->"72be0a20-b0c8-432e-8f95-\ dea9e0787572"], Cell[TextData[{ StyleBox["The list of roots is obtained with\n ", FontSize->14], " ", StyleBox["x /. 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S\[IGrave], perch\[EAcute] hanno un diverso numero di argomenti. \ \>", "Text", CellChangeTimes->{{3.793127624472603*^9, 3.7931276266329093`*^9}, 3.7931279940583453`*^9, {3.823797797417466*^9, 3.823797800775617*^9}}, Background->RGBColor[ 1, 1, 0],ExpressionUUID->"c43fd04b-d64a-48f6-bd57-e1ca153b34fd"], Cell[TextData[{ "Per chiedere a ", StyleBox["Mathematica", FontSlant->"Italic"], " cosa \[EGrave] un simbolo \[OpenCurlyDoubleQuote]symb\ \[CloseCurlyDoubleQuote]\n ", StyleBox["? symb", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " " }], "Text", CellChangeTimes->{{3.793127624472603*^9, 3.7931276266329093`*^9}, 3.7931281905822954`*^9, {3.823797804509209*^9, 3.8237978052487516`*^9}}, Background->RGBColor[ 1, 1, 0],ExpressionUUID->"db7a7210-75c1-4d1c-b804-4c2c634cd6cd"], Cell[BoxData[ RowBox[{"?", "pl"}]], "Input", CellChangeTimes->{{3.793128637166646*^9, 3.793128637992304*^9}},ExpressionUUID->"c346b88e-c14c-474f-adab-\ ff349395498f"], Cell[BoxData["pl"], "Input", CellChangeTimes->{{3.823930267365569*^9, 3.823930267547117*^9}},ExpressionUUID->"c72492ba-72ba-4397-8e29-\ ba32d11b1722"], Cell[BoxData["\[IndentingNewLine]"], "Input", CellChangeTimes->{ 3.7931286489464035`*^9},ExpressionUUID->"becd4133-bcad-4561-95ba-\ 5dca38df6f4f"], Cell[TextData[{ "Quando si esegue una funzione, ", StyleBox["Mathematica", FontSlant->"Italic"], "\n\[FilledSmallCircle] sostituisce l'argomento alla \"x\" che appare \ nell'espressione al secondo membro della definizione ", StyleBox["f[x_]:=.... ", FontFamily->"Terminal", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], "\n\[FilledSmallCircle] ed eventualmente fa dei conti e delle semplificazioni" }], "Text", ShowGroupOpener->False, CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{3.729056371346322*^9}, Background->RGBColor[ 1, 1, 0],ExpressionUUID->"bcbc0944-46ec-49f1-98bd-2ccf5f51327a"], Cell[TextData[{ StyleBox["Esempio:", FontWeight->"Bold"], " se si definisce\n ", StyleBox["f[u_] := ", FontFamily->"Courier New", FontWeight->"Bold"], Cell[BoxData[ SqrtBox[ SuperscriptBox["u", "2"]]], ShowGroupOpener->False, CellChangeTimes->{{3.5401791189040194`*^9, 3.5401791199960213`*^9}, { 3.5433074394620676`*^9, 3.543307439727268*^9}, {3.5904886338707423`*^9, 3.590488638925151*^9}},ExpressionUUID-> "997bac15-a6fe-4f99-828c-0dd87cd9e299"], " ( Sqrt[u^2] )", StyleBox["\n", FontFamily->"Courier New", FontWeight->"Bold"], StyleBox["quale sar\[AGrave] il risultato di ", FontFamily->"Times New Roman", FontSize->16], StyleBox[" ", FontFamily->"Times New Roman", FontWeight->"Bold"], StyleBox["f[2] ", FontFamily->"Courier New", FontWeight->"Bold"], StyleBox["? 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Possiamo forzarlo? \ \>", "Text", CellChangeTimes->{{3.793127624472603*^9, 3.7931276266329093`*^9}, 3.793128767562643*^9}, Background->RGBColor[ 1, 1, 0],ExpressionUUID->"d91899f0-bc9f-4aca-aa99-811909dc653c"], Cell[BoxData[ RowBox[{"FullSimplify", "@", "%"}]], "Input", CellChangeTimes->{{3.823930599362142*^9, 3.8239306072097926`*^9}},ExpressionUUID->"56fd149f-5ac3-4d45-aabf-\ 7d91268e2e19"], Cell["\<\ No. \[CapitalEGrave] ragionevole? \ \>", "Text", CellChangeTimes->{{3.793127624472603*^9, 3.7931276266329093`*^9}, 3.7931287944917364`*^9, {3.8237978370635767`*^9, 3.8237978378507357`*^9}}, Background->RGBColor[ 1, 1, 0],ExpressionUUID->"858f3f07-d07a-4983-9a28-c74ade612a6d"], Cell[TextData[{ Cell[BoxData[ FormBox[ SqrtBox[ SuperscriptBox["u", "2"]], TraditionalForm]],ExpressionUUID-> "ed637656-cbd5-423c-931e-ab4a6fc25b13"], " = u solo se ", StyleBox["u ", FontSlant->"Italic"], " \[EGrave] un reale positivo.\nSe non ha questa informazione sull\ \[CloseCurlyQuote]argomento, ", StyleBox["Mathematica", FontSlant->"Italic"], " non fa la semplificazione." }], "Text", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.6975193365951185`*^9, 3.697519418168228*^9}, { 3.728845056299037*^9, 3.728845077085026*^9}, 3.728845492902314*^9, 3.729056371346322*^9, {3.7603779986623545`*^9, 3.760378001052109*^9}, { 3.7603780514848385`*^9, 3.7603780581230817`*^9}, 3.7603785622804356`*^9, { 3.823930615513896*^9, 3.823930616665665*^9}}, Background->RGBColor[ 1, 1, 0],ExpressionUUID->"22974b9d-9da5-4457-8405-111662c4ca90"], Cell[BoxData[" "], "Input", CellChangeTimes->{ 3.760454981586671*^9},ExpressionUUID->"55714328-340c-4b71-91fc-\ 62e4407a8fec"] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Assunzioni", FontSize->24]], "Section", CellChangeTimes->{{3.7931280204658203`*^9, 3.793128024004758*^9}, { 3.7931288592437024`*^9, 3.793128859649885*^9}}, FontColor->GrayLevel[0], Background->RGBColor[ 0., 1., 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Help", "Section", CellChangeTimes->{{3.7603305394751625`*^9, 3.760330552624377*^9}, 3.7603305908582544`*^9, {3.760330621878708*^9, 3.7603306472378387`*^9}, { 3.760330680982297*^9, 3.76033068354846*^9}, {3.7603798770441265`*^9, 3.7603798807094717`*^9}, {3.7603842108160725`*^9, 3.760384216686191*^9}, { 3.760453391881394*^9, 3.7604533948679066`*^9}}, FontSize->24, Background->RGBColor[ 0., 1., 1.],ExpressionUUID->"7351877d-8066-474f-a964-a55013a3fa54"], Cell[TextData[{ "Ci sono due help:\n\[FilledSmallCircle] breve descrizione di un comando \ (Dall\[CloseCurlyQuote]INPUT : ", StyleBox["?comando)", FontWeight->"Bold"], "\n\[FilledSmallCircle] manuale (con descrizione di tutte le funzioni, \ tutorials, e altro)\n \[FilledSmallCircle]\[FilledSmallCircle] o dal MENU \ ", StyleBox["\[OpenCurlyDoubleQuote]Help\[CloseCurlyDoubleQuote] \n ", FontWeight->"Bold"], "\[FilledSmallCircle]\[FilledSmallCircle] o con ", StyleBox["F1 ", FontWeight->"Bold"], " (anche sulla parola)\n \[FilledSmallCircle]\[FilledSmallCircle] o da \ \[OpenCurlyDoubleQuote]i\[CloseCurlyDoubleQuote] sul menu interattivo" }], "Text", CellChangeTimes->{{3.7603792450011234`*^9, 3.760379252699852*^9}, 3.7931291777801065`*^9, 3.7931292292680445`*^9}, Background->RGBColor[ 1, 1, 0],ExpressionUUID->"73180240-d92f-49ea-82c3-4667707a8edf"], Cell["Esempio : chiediamo aiuto per il comando \[OpenCurlyDoubleQuote]Expand\ \[CloseCurlyDoubleQuote]", "Text", CellChangeTimes->{{3.793128071767908*^9, 3.7931281008217955`*^9}, 3.793128146623452*^9, {3.793128675812248*^9, 3.7931286826861773`*^9}, { 3.7931288775836887`*^9, 3.7931288840503845`*^9}, 3.7931290305235744`*^9, 3.793129150630938*^9, 3.793129248047571*^9}, Background->RGBColor[ 0., 1., 0.],ExpressionUUID->"c1333033-c85e-4c8d-b01f-eec5d3b11dbf"], Cell[BoxData[ RowBox[{"?", "Expand"}]], "Input", CellChangeTimes->{{3.823931464729306*^9, 3.823931470673274*^9}},ExpressionUUID->"e82f496f-09b0-4b94-badf-\ 2bdbb9c9432b"], Cell[BoxData["Expand"], "Input", CellChangeTimes->{{3.8239314732260275`*^9, 3.8239314838753023`*^9}},ExpressionUUID->"6f364278-5e41-4736-9427-\ 209845345db3"], Cell["\<\ (dal men\[UGrave] interattivo, anche prima di aver scritto tutto il comando)\ \>", "Text", CellChangeTimes->{{3.760379448803259*^9, 3.760379466518168*^9}, { 3.792992476254651*^9, 3.792992517973962*^9}, {3.823798191984699*^9, 3.823798208515704*^9}}, Background->RGBColor[ 0., 1., 0.],ExpressionUUID->"004fa858-7510-4009-94fd-91e296f5c249"], Cell[BoxData[""], "Input", CellChangeTimes->{{3.7929924453757467`*^9, 3.7929925212859745`*^9}, 3.7931292629659605`*^9},ExpressionUUID->"1fe730c1-aadc-4d0a-bb8a-\ 750a338295e0"] }, Closed]], Cell[CellGroupData[{ Cell[TextData[StyleBox["9. 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