Mathematica Tips 2

Mathematica Tips @MathematicaTip

Plot a vector field over a surface: data = Table[{y, -x, z}, {z, -3, 3}, {y, -2, 2}, {x, -2, 2}]; ListSliceVectorPlot3D[data,"CenterPlanes"]

Mathematica Tips @MathematicaTip

Random ball collections: Graphics3D[ Table[{Hue[RandomReal[]], Ball[RandomReal[1, {3}], RandomReal[0.1]]}, {200}]]

Mathematica Tips @MathematicaTip

The permanent of a square matrix of all ones is the factorial of the dimension: Table[Permanent[ConstantArray[1, {n, n}]], {n, 10}]

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Generate a set of pseudorandom matrices with GaussianSymplecticMatrixDistribution: RandomVariate[GaussianSymplecticMatrixDistribution[2]]

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Bandpass filtering of vector: data=Table[Sin[i^2+i]+RandomReal[{-.2,.3}], {i,0,Pi,0.01}];ListLinePlot/@{data,BandpassFilter[data,{.01,.02}]}

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Show the current locale time zone setting: $TimeZoneEntity

Mathematica Tips @MathematicaTip

Display the grammatical structure of a sentence: TextStructure["The cat sat on the mat."]

Mathematica Tips @MathematicaTip

Get total mass of 10 hydrogen atoms: EntityValue[EntityCopies[Entity["Element", "Hydrogen"], 10], EntityProperty["Element", "AtomicMass"]]

Mathematica Tips @MathematicaTip

Partition into blocks that are up to 3 elements long; the last block is shorter: Partition[Range[10], UpTo[3]]

Mathematica Tips @MathematicaTip

Open a connection to a server at a specified socket address: bit.ly/1m8HyER

Mathematica Tips @MathematicaTip

Sample from matrix distribution: sigR = {{3, 1}, {1, 4}}; sigC = {{1, -1/2}, {-1/2, 2}}; RandomVariate[MatrixTDistribution[sigR, sigC, 3]]

Mathematica Tips @MathematicaTip

Generate a Cornu spiral: DSolve[{x'[s] == Cos[t[s]], y'[s] == Sin[t[s]], t'[s] == s, x[0] == 0, y[0] == 0, t[0] == 0}, {x, y, t}, s]

Mathematica Tips @MathematicaTip

Surface area of the Earth: GeoArea["World"]

Mathematica Tips @MathematicaTip

With IncludeInflections->True, inflected forms will be included in results: MemberQ[WordList[IncludeInflections -> True], "zooming"]

Mathematica Tips @MathematicaTip

Find a sample of 5 "Volcano" entities: RandomEntity["Volcano", 5]

Mathematica Tips @MathematicaTip

Search for articles by title: WikipediaSearch["Artificial intelligence", "MaxItems" -> 2]

Mathematica Tips @MathematicaTip

Shortest path (geodesic) between two locations: GeoGraphics[GeoPath[{{-35, -55}, {70, 100}}], GeoRange -> "World", Frame -> True]

Mathematica Tips @MathematicaTip

Give the total atomic mass of all chemical elements: EntityValue[EntityGroup[ElementData[]], "AtomicMass"]

Mathematica Tips @MathematicaTip

Print the result of an intermediate computation: expr1; Echo[x = 1 + 1]; expr2

Mathematica Tips @MathematicaTip

Look up the IP addresses associated with a host: HostLookup["localhost"]

Mathematica Tips @MathematicaTip

Single pseudorandom matrix w/ nonzero mean: RandomVariate[MatrixTDistribution[{{1,2,3}, {4,5,6}}, {{1,1/3}, {1/3,1}}, IdentityMatrix[3], 2]]

Mathematica Tips @MathematicaTip

Get a "pure function" solution for y: DSolve[{y'[x] + y[x] == a Sin[x], y[0] == 0}, y, x]

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Compare offset btw Eastern Time & London Time on different dates: TimeZoneOffset["America/New_York","Europe/London",DateObject[{2015,3,7}]]

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Get a sorted list of 2000 random words: AlphabeticSort[RandomSample[WordList[Language -> "Russian"], 2000], "Russian"]

Mathematica Tips @MathematicaTip

Compute detailed properties of the standard ocean model with StandardOceanData: bit.ly/1iS0RQw