Mathematica Mathematica APL * Mathematica Mathematica PDF 2 Mathematica Mathematica Mathematica * 11 If[] For[] A[B] A * 12 B Apply[] Apply[f,{a

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1 In[2]:= Mathematica Mathematica *1 Mathematica Mathematica Mathematica *2 Export["output.txt",Solve[x^2-3x+2==0,x]] 1 sample.m math < sample.m *3 math Mathematica /usr/local/bin/math(linux,mac) C:/Program Files/Wolfram Research/Mathematica/10.0/math.exe (Linux ) /usr/local/bin/math < sample.m *4 Mathematica 10.0 for Linux x86 (64-bit) Copyright Wolfram Research, Inc. In[1]:= Out[1]= output.txt output.txt {x -> 1} {x -> 2} x 2 3x + 2 = *5 1 Mathematica 1. GUI *6 Mathematica GUI Mathematica GUI Mathematica *7 math *8 2. Mathematica Mathematica Mathematica *9 3. *1 *2 sakura jed emacs vi MS WORD Open office *3 CUI *4 Linux Windows *5 5 5 *6 GUI *7 GUI *8 UNIX OS #!/usr/local/bin/math -script *9 Maple maxima Derive Mathematica 1

2 Mathematica Mathematica APL * Mathematica Mathematica PDF 2 Mathematica Mathematica Mathematica * 11 If[] For[] A[B] A * 12 B Apply[] Apply[f,{a,b,c}] f[a,b,c] Map[] Map[f,{a,b,c}] {f[a], f[b], f[c]} Map[] For[] 1 Exit[] Quit[] ListPlot[] % Mathematica %n n math ALT. \ Export[] (* *) 2 2^^ n 2 IntegerString[n, 2] 2 "Roman" * 13??N N[expr] gives the numerical value of expr. Options[] Options[Plot] Plot[] Run[COMMAND] Linux Run[ls] RunThrough[COMMAND, input] COMMAND SendMail["To"->"", "Subject"->" ", "Body"->" ", "Server"->"SMTP ", "From"->""] SeedRandom[123] x Clear[x] f[x_] Clear[f] Remove[] Remove[x] x << "sample.m" << +, -, *, /, ^ *10 Wikipedia Mathematica *11 List[] *12 Head[] *13 * Plus[1,2] 2

3 * 14 * 15 Pi, E, I, Infinity, True, False, Degree Rad, GoldenRatio, EulerGamma, Catalan, Khinchin, Glaisher Re[] Im[] Integer, Rational, Real, Complex 4 Rational Integer 3 Integers, Rationals, Reals Primes Disk[{centerx, centery}] Ball[{centerx,centery,centerz}] for while C for(a;b;c){execute} For[A,B,C,execute] While[condition,execute] condition execute ReplaceAll[original,rule] ReplaceAll[x-x^2,x->N[Pi]] x-x^2 /. x->n[pi] Element[Pi, Reals] Random[] Random[Integer, {1,10}] 2 A B A=B A:=B == * 16 f[x_]:=x^2 f(x) = x 2 x _ If[condition,then,else] condition True then False else If[a>1,Print[a],Print[0]] B A A /; B Which[[condition1,return1,condition2,return2, ] condition1 True return1 condition1 False condition2 True return2 Switch-Case Switch[A,B1,C1,B2,C2, ] A=B1 C1 A=B2 C2 3 N[equation, digits] N[Pi, ] 100 Import["filename","format"] L=Import["sample.csv","CSV"] L sample.csv Export["filename",data,"format"] Export["sample.csv",data,"CSV"] data sample.csv CSV "format" Table EPS, PDF, SVG, PICT, WMF, TIFF, GIF, JPEG, PNG, BMP, PCX, XBM, PBM, PPM, PGM, PNM, DICOM, AVI, DXF, STL, WAV, AU, SND, AIFF * 17 Export ImageSize->72 x(x ) ImageResolution->d(dpi ) 3D POV PovRay C CForm[equation] mdefs.h * 18 Compile[variables, equation] Export["sample.c", Compile[{x}, x+1]] main() C *15 *16 Equal[] *17 C data C *18 find 3

4 WolframLibrary.h WolframRTL.h SystemFiles/IncludeFiles/C/ Mathematica Export["sample.c", Compile[{x}, N[Pi, ]]] // FullForm x-y*z-x/z // FullFormPlus[x, Times[-1, x, Power[z, -1]], Times[-1, y, z]] Mathematica Mathematica 1 //TableFrom //MatrixForm // Short 1 {{1,2},{3,4}} {,,, } {3,1,4,1,5} {} Table[] Table[k*2, {k,1,6}]{2, 4, 6, 8, 10, 12} Table[k^2, {k,1,6,1/2}] Table[k*a, {k,1,6},{a,1,4}] Range[a,b] a b, Array[f,n] f i n, ConstantArray[c,n] c n, RandomInteger[{1,10},n] 1 10 n 3 Mathematica C Mathematica 1 C 0 L n L[[n]] Print[{3,1,4,1,5}[[3]]] n Part[] Part[{3,1,4,1,5,},3] 1 Solve[] Solve[x^2-4==0,x] {{x -> -2}, {x -> 2}} x /. Solve[x^2-4==0,x] Plot[] Plot[{x^2,x^3},{x,-2,2}] {x,-2,2} (For[] ) {1,2,3,4}*5 5 {1,2,3,4}+{5,4,3,2} 6 3 L Length[L] L Dimensions[L] L x MemberQ[L,x] L Count[L, Integer] 4 ReplacePart[L, {1->3, 4->6}] Append[L,tsuika] * 19, Prepend[L,tsuika], Insert[L,tsuika,n]( n ), Join[L1,L2], Riffle[L1,L2] Union[L1,L2] * 20, Intersection[L1,L2], Complement[L,l1,l2,l3], Subsets[L] Part[] First[L], Last[L], Rest[L], Most[L], Take[L,n] n, Drop[L,n] n, *19 Append[] *20 Join[] 4

5 Select[L,conditions], Cases[L,pettern] Partition[L,n] Cases[] Cases[L, Integer] Except[] Cases[L, Except[ Integer]] Cases[] Cases[L, Integer :> x^2] DeleteCases[list, Integer] Reverse[] Sort[] RotateLeft[], RotateRight[], Flatten[] Permutations[] IntegerDigits[] IntegerDigits[1234] {1,2,3,4} IntegerDigits[1234,3] 3 5. M.M Cross[] Det[] Transpose[] Inverse[] Eigenvalues[] Eigenvectors[] IdentityMatrix[n] n n DiagonalMatrix[l] l CharacteristicPolynomial[M, x] 6 Graph[] Graph[{1 <-> 2, 2 <-> 3, 3 <-> 1}] <-> -> Export[] EdgeWeight-> CompleteGraph[] CompleteGraph[6] 6 15 AdjacencyGraph[] AdjacencyGraph[{{0, 1, 0}, {0, 0, 1}, {1, 0, 0}}] 3 RandomGraph[n,m] n m KaryTree[] KaryTree[n,k] n k g FindSpanningTree[g] g e EdgeDelete[g,e] GraphUnion[] GraphIntersection[] GraphDifference[] g HamiltonianGraphQ[g] EulerianGraphQ[g] EmptyGraphQ[] SymmetricMatrixQ[g] ReflexiveQ[g] 2 UndirectedGraphQ[g] LoopFreeGraphQ[g] AcyclicGraphQ[g] 4 1 Mathematica Solve[x^2-1==0,x] x->5 x /. x /. x->5 NSolve[] NSolve[x^3/Pi-1==0,x] ( ) Sqrt[] e x Exp[x] log e x Ln[x] Log[x] Reduce[x>0 && x^2-2*x-3==0,x,reals] x > 0 x==3 Solve[] && FindRoot[equation,{valiable,init}] FindRoot[x^5-x^4+x^3-x^2+x^1+4==0,{x,2}] {x -> } N[] Print[$MachinePrecision] 5

6 * 21 Expand[] FunctionExpand[] ExpandAll[] TrigExpand[] TrigExpandAll[] Factor[] Factor[x*x+9,GaussianIntegers->True] TrigFactor[] FactorTerms[] FactorSquareFree[] Reduce[] Simplify[] FullSimplify[] TrigReduce[] MinimalPloynomial[numbers,variable] Rationalize[] CoefficientList[] MonomialList[] Variables[] PolynomialQuotient[y,z,x] x y z PolynomialRemainder[] Maximize[y,x] x y Together[] Apart[] Collect[equation, term] ContinuedFraction[equation,n] n 2 Rationalize[number] RootApproximant[number] number 1 RootApproximant[number,n] n n ContinuedFraction[number,n] FindSequenceFunction[numbers] numbers 3 FindFit Mathematica Fit[] Mathematica data = {{0, 1}, {1, 0}, {3, 2}, {5, 4}} Fit[data, {1, x, x^2}, x] 3 1, x, x 2 x FindFit[] FindFit[data, {equation, conditions},parameters, variables] data {{x1, y1}, {x2, y2}, {x3, y3}} 3 {{x1, y1, z1}, {x2, y2, z2}, {x3, y3, z3}} variables {x,y,z} {{p1, p1init},{p2, p2init}} conditions, Print[FindFit[data,{y=(1+Exp[b*Log[x]]) /(2+Exp[-a*Log[x]]+Exp[b*Log[x]])},a,b,x]] 4 Sum[x,{i,imin,imax}] Product[x,{i,imin,imax}] 5 1 Plot[] * 22 Plot[Sin[3*x]*Cos[5*x], {x, -Pi, Pi}] Plot[] PlotStype-> PlotStyle->Hue[2/3] Hue[h,s,b] (hue) (saturation) (brightness) RGB RGBColor[0,0,1] PlotStyle->Dashing[0.05] PlotLabel->"string" *21 Linux *22 Linux X Windows Xming 6

7 AxisLabel->{"x","sin x"} Frame->True False GridLines->Autometic DefaultFont->{"Helvetica",18} AspectRatio->0.2 ContourPlot[equation,{xrange},{yrange}] Contours->n PlotPoints-> ContourPlot[Cos[x] + Cos[y], {x, 0, 4 Pi}, {y, 0, 4 Pi}] DensityPlot[equation,{xrange},{yrange}] PlotPoints-> {100,50} Mesh->False PlotRange-> 0,4 AspectRation->Automatic ListPlot[list, PlotJoined->True] ParametricPlot[equations,ranges] DiscretePlot[list,ranges] 3 GraphicsGrid[plots] GraphicsRow[plots] Column[plots] Show[plots] Show[Plot[x^2, {x, 0, 3.5}], ListPlot[{1, 4, 9}]] 2 Plot3D[] POV Export[] PovRay POV 3 ParametricPlot3D[equations, ranges], PlotPoints->{40,80} BoxRarios->{1,1,0.3} 3 ListPlot3D[list, PlotJoined->True] SphericalPlot3D[] RevolutionPlot3D[] 3D ContourPlot3D[] 3 3D ListSurfacePlot3D[] 3D ListContourPlot3D[] CuboidSphere Cylinder Point Polygon ExampleData/@Take[ExampleData["Geometry3D"],16] PNG Export["exampledata.png",Column[ExampleData/@ Take[ExampleData["Geometry3D"],2]],"PNG"] GeometricTransformation[] ShearingTransform[] 4 3D Specularity[] Specularity[{White,10}] Glow[] Scale[] Translate[] Rotate[] 5 3D 3D Axes->None AxesEdge-> {1,-1} 3 BoundaryStyle-> Directive[Black, Thickness[0.0123]] Boxed-> True False BoxRatios-> {1,2,1} BoxStyle-> ColorFunction-> Function[{x, y, z}, Glow[RGBColor[z, z, z]]] PlotLabel-> Imagesize-> {500,500}

8 InterpolationOrder-> : FaceGrids-> FaceGridsStyle-> Lighting-> Automatic Neutral None {"Point", Red, {0,0,2}} {"Ambient", Green} {"Directional", Blue, {0,0,1},{-1,1,1}} Mesh-> None Opacity-> RegionFunction-> Function[{T,F},Sin[T F]<0.3] ViewAngle-> ViewCenter-> 0.5,0.5,0.5 ViewPoint-> Top Front ViewRange-> ViewVector-> ViewVertical-> 3 6 Limit[] Limit[(x-2)/(x-1),x->0] Series[] Series[Sin[x],{x,0,10}] Normal[] FindGenerationgFunction[{1,3,5,7,9},x] FindSequenceFunction[{1,3,5,7,9},x] InverseSeries[equation] D[] D[Sin[x],x] Sin [x] D[Sin[x],{x,2}] Integrate[equation,x] Integrate[1/x,{x,1,Infinity}] NIntegrate[] Assumptions-> DSolve[m y [t]+k y[t]==0, y[t],t] LaplaceTransform[equation,t,s] InverseLaplaceTransform[equation,s,t] FourierTransform[equation,t,s] InverseFourierTransform[equation,s,t] s t Z ZTransform[equation,n,z] InverseZTransform[equation,z,n] 7 1 n FactorInteger[n] Mod[k,n] k/n Quotient[k,n] k/n Divisible[k,n] k n Divisors[n] n CoprimeQ[n1, n2, n3] n 1, n 2, n 3 n GCD[n1, n2, n3] LCM[n1, n2, n3] PrimitiveRoot[n] n PrimitiveRootList[n] 2 n Prime[n] Prime[ ] n PrimePi[] PrimePi[ ] PrimQ[number] PrimePowerQ[number] n PrimeNu[n] PrimeOmega[n] 8

9 3 µ(n) MoebiusMu[n] λ(n) LiouvilleLambda[n] (n/m) JacobiSymbol[n,m] KroneckerDelta[n1,n2,n3] λ(n) CarmichaelLambda[n] ϕ(n) EulerPhi[n] Needs["NumericalDifferentialEquationAnalysis "] Needs["VariationalMethods "] Needs["FiniteFields "] Needs["Quaternions "] Needs["PolyhedronOperations "] Needs["Polytopes "] Needs["ComputerArithmetic "] Needs["PrimalityProving "] Needs["Audio "] 4 a n RSolve[{equation,init},a[n],n] RSolve[{a[n+1]==2*a[n]+1, a[0]==1},a[n],n] a[n]->-1+2^(1+n) RecurrenceTable[] RecurrenceTable[{a[n+1]==3*a[n],a[1]==2},a,{n, 1, 10}] Fibonacci[n] n * 23 LucasL[n] n 8 1 Mathematica * 24 Needs[ ] Wolfram Mathematica Needs["ANOVA "] Needs["HierarchicalClustering "] Needs["HypothesisTesting "] Needs["MultivariateStatistics "] Needs["StatisticalPlots "] Needs["ErrorBarPlots "] Needs["EquationTrekker "] Needs["FourierSeries "] Needs["FunctionApproximations "] Needs["NumericalCalculus "] Needs["Music "] Needs["BlackBodyRadiation "] Needs["ResonanceAbsorptionLines "] Needs["StandardAtmosphere "] Needs["Benchmarking "] Needs["Developer "] Needs["Experimental "] Needs["Notation "] XML Needs["XML "] Benchmark[] PrimeQCertificate[ ] {2, , } PowerMod[] 1 Apply[PowerMod,%] PowerMod[2,p-1,p] p 2 p 1 p (2 p 1 1 mod p) 1 2./SystemFiles/FrontEnd/SystemResources/FunctionalFrequency/*trie * 25 AstronomicalData CalendarData ChemicalData CityData ColorData CountryData ElementData FinancialData GalaxyData GraphData ImportFormats KnotData StarData ThermodynamicData WeatherData WordData C 2 H 6 O ChemicalData["C2H6O"] {Entity[Chemical, Ethanol], *23 Prime[] *24 Print[$Packages] *25 9

10 Entity[Chemical, DimethylEther]} Kashiwa Asahikawa FinancialData["JPY/USD"] cron ChemicalData["C2H6O"][[1]] Entity PolyhedronData["Properties"] GraphData[] KnotData[] EntityValue[] MoleculePlot LatticeData[] Export[PolyhedronData["Cube","NetImage"]] Export["C2H6O.png",EntityValue[ChemicalData["C2H6O"][[1]],"MoleculePlot"]] PolyhedronData["Cube","SkeletonImage"] CityData CityData["Tokyo","Population"] GraphData["CubicalGraph", "AdjacencyMatrix"] people AcyclicGraphQ AdjacencyGraph Apart Append Apply , 9 Array Ball Benchmark CarmichaelLambda Cases , 5 CForm CharacteristicPolynomial ChemicalData CityData Clear CoefficientList Collect Column Compile Complement CompleteGraph ConstantArray ContinuedFraction ContourPlot ContourPlot3D CoprimeQ Cos Count Cross D Dashing DeleteCases DensityPlot Det DiagonalMatrix Dimensions Directive DiscretePlot Disk Divisible Divisors Drop DSolve EdgeDelete Eigenvalues Eigenvectors Element EmptyGraphQ Entity EntityValue Equal EulerianGraphQ EulerPhi ExampleData ExampleData/@Take Except Exit Exp Expand ExpandAll Export , 2, 3, 5, 7, 9, 10 Factor FactorInteger FactorSquareFree FactorTerms Fibonacci FinancialData FindFit FindGenerationgFunction FindRoot FindSequenceFunction , 8 FindSpanningTree First Fit Flatten For , 3, 4 FourierTransform FullSimplify Function , 8 FunctionExpand GCD GeometricTransformation Glow Graph GraphData GraphDifference GraphicsGrid GraphicsRow GraphIntersection GraphUnion HamiltonianGraphQ Head Hue IdentityMatrix If , 3 Im Import Insert IntegerDigits IntegerString Integrate Intersection Inverse InverseFourierTransform InverseLaplaceTransform InverseSeries InverseZTransform JacobiSymbol Join KaryTree KnotData KroneckerDelta LaplaceTransform Last LatticeData LCM Length Limit LiouvilleLambda List ListContourPlot3D ListPlot , 7 ListPlot3D ListSurfacePlot3D Log LoopFreeGraphQ LucasL Map Maximize MemberQ MinimalPloynomial Mod

11 MoebiusMu MonomialList Most N , 5 Needs NIntegrate Normal NSolve Options ParametricPlot ParametricPlot3D Part Partition Permutations Plot , 4, 6, 7 Plot3D Plus , 4 PolyhedronData PolynomialQuotient PolynomialRemainder Power PowerMod Prepend Prime , 9 PrimeNu PrimeOmega PrimePi PrimePowerQ PrimeQCertificate PrimitiveRoot PrimitiveRootList PrimQ Print , 4, 5, 6, 9 Product Quit Quotient Random RandomGraph RandomInteger Range Rationalize Re RecurrenceTable Reduce , 6 ReflexiveQ Remove ReplaceAll ReplacePart Rest Reverse RevolutionPlot3D RGBColor , 7 Riffle RootApproximant Rotate RotateLeft RotateRight RSolve Run RunThrough Scale SeedRandom Select SendMail Series ShearingTransform Show Simplify Sin Solve , 4, 5 Sort Specularity SphericalPlot3D Sqrt Subsets Sum Switch SymmetricMatrixQ Table Take , 7 Thickness Times Together Translate Transpose TrigExpand TrigExpandAll TrigFactor TrigReduce UndirectedGraphQ Union Variables Which While Mathematica PDF PDF ` PDF c Copyright Printed in Japan 11

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