Mathematica Tips

Mathematica Tips @MathematicaTip

New in 10: A volume mesh region in 3D from DelaunayMesh: DelaunayMesh[RandomReal[1, {50, 3}]]

Mathematica Tips @MathematicaTip

Check for serial correlation in data: ListLinePlot@CorrelationFunction[RandomFunction[ARProcess[{.8},1],{1000}],{100}]

Mathematica Tips @MathematicaTip

Split a list into sublists according to a specified function: GatherBy[{1, 2, 3, 4, 5, 6, 7, 8}, PrimeQ]

Mathematica Tips @MathematicaTip

Make a list of all the steps taken in evaluating FindRoot: Reap[FindRoot[Cos[x] == x, {x, 1}, StepMonitor :> Sow[x]]]

Mathematica Tips @MathematicaTip

Use plot functions to create 3D graphics from different data types: Plot3D[Sin[x y], {x,0,3}, {y,0,3}, ColorFunction->"Rainbow", Mesh->None]

Mathematica Tips @MathematicaTip

Thumbnails of all gradients: Grid[Partition[Show[ColorData[#,"Image"],ImageSize->110] & /@ColorData["Gradients"], 4, 4, 1, {}],Spacings->.5]

Mathematica Tips @MathematicaTip

Fourier spectrum of "white noise": ListLinePlot[Abs[Fourier[RandomReal[1, 200]]]^2]

Mathematica Tips @MathematicaTip

Play averaged random noise: ListPlay[MovingAverage[RandomReal[1, {5000}], 200]]

Mathematica Tips @MathematicaTip

Check the quality of a result: Precision[Sin[1000`20] + 1`22]

Mathematica Tips @MathematicaTip

Search for Mersenne primes: Parallelize[Select[Range[9000, 10000], PrimeQ[2^# - 1] &], Method -> "FinestGrained"]

Mathematica Tips @MathematicaTip

Make a 3D graphic from a test image: ListPlot3D[ExampleData[{"TestImage", "Clock"}, "GrayLevels"], PlotStyle -> Yellow, Mesh -> None]

Mathematica Tips @MathematicaTip

Make a dynamically updating clock: Dynamic[Refresh[DateString[], UpdateInterval -> 1]]

Mathematica Tips @MathematicaTip

Show that there are only 5 regular polyhedrons: Show[PolyhedronData[#], ImageSize -> Tiny] & /@ PolyhedronData["Platonic"]

Mathematica Tips @MathematicaTip

Plot Abs at Gaussian integers: ArrayPlot[ Table[Mod[Round[Abs[x + I y]], 2], {x, -36, 36}, {y, -36, 36}]]

Mathematica Tips @MathematicaTip

Compute the GCD of two numbers: {a, b} = {27, 6}; While[b = 0, {a, b} = {b, Mod[a, b]}]; a

Mathematica Tips @MathematicaTip

Selecting the nth prime: DynamicModule[{n=1000},{Slider[Dynamic[n], {1,10^5,1}], Subscript[p,Dynamic[n]]\[LongRightArrow]Dynamic[Prime[n]]}]

Mathematica Tips @MathematicaTip

Find log distribution of daily returns for S&P 500: ListLinePlot[Log[1+BinCounts[FinancialData["SP500", "Return",All,"Value"],0.001]]]

Mathematica Tips @MathematicaTip

Create a list of array plots: Table[ArrayPlot[Table[Mod[Binomial[i, j], n], {i, 30}, {j, 30}]], {n, 2, 5}]

Mathematica Tips @MathematicaTip

Cluster string data using Hamming distance: FindClusters[{"abc", "xyz", "bca", "xyw"}, DistanceFunction -> HammingDistance]

Mathematica Tips @MathematicaTip

Find how deeply nested results from integrals are: Table[Depth[Integrate[1/(x^n - 1), x]], {n, 10}]

Mathematica Tips @MathematicaTip

Plot any function: Panel[DynamicModule[{f = Sin[x]}, Column[{InputField[Dynamic[f]], Dynamic[Plot[f, {x, -5, 5}]]}]]]

Mathematica Tips @MathematicaTip

Generate an array of Cayley graphs: GraphicsGrid[Partition[GraphData /@ SortBy[GraphData["Cayley", ;; 10], GraphData[#, "V"] &], 7]]

Mathematica Tips @MathematicaTip

Construct a surface from random heights: ListPlot3D[Log[RandomReal[1, {50, 50}]]]

Mathematica Tips @MathematicaTip

Find the ways to make change for 156 cents with 10 or fewer standard coins: IntegerPartitions[156, 10, {1, 5, 10, 25}]

Mathematica Tips @MathematicaTip

Divide eigenvectors by their corresponding eigenvalues: Eigensystem[{{1, 3}, {2, 7}}]