Mathematica 入門

1

Solve[x^2 - 3 x + 2 == 0, x]

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{{x -> 1}, {x -> 2}}

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Solve[x^2 - 3 x + 2 == 0 && 0 <= x <= 2, x, Integers]

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{{x -> 1}, {x -> 2}}

1

Solve[{x + y == 3, x - y == 1}, {x, y}]

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{{x -> 2, y -> 1}}

1

Reduce[x^2 - 3 x + 2 > 0, x]

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x < 1 || x > 2

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D[x^2, x]

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2 x

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Integrate[x^2, x]

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x^3/3

1

Limit[1/x, x -> 0]

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Infinity

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Sum[1/n^2, {n, 1, Infinity}]

1

π^2/6

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m = {{1, 2}, {3, 4}}

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m . m

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{{7, 10}, {15, 22}}

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Inverse[m]

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{{-2, 1}, {1.5, -0.5}}

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Eigensystem[m]

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{{5, 0}, {{1, 1}, {1, -1}}}

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{1, 2} . {3, 4}

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11

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Cross[{1, 2, 3}, {4, 5, 6}]

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{-3, 6, -3}

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Norm[{1, 2, 3}]

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√14

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ArcCos[{1, 2} . {3, 4}/(Norm[{1, 2}] Norm[{3, 4}])]

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ArcCos[11/(√5 √25)]

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{1, 2} . {3, 4}/Norm[{3, 4}] {3, 4}/Norm[{3, 4}]

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{11/5, 22/5}

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RotationMatrix[π/2].{1, 0}

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{0, 1}

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TranslationTransform[{1, 2}][{3, 4}]

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{4, 6}

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ScalingTransform[{2, 3}][{1, 1}]

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{2, 3}

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ReflectionTransform[{1, 1}][{1, 1}]

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{0, 0}

1

RandomReal[]

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0.123456

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RandomInteger[]

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123456

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RandomReal[{1, 10}]

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5.6789

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RandomInteger[{1, 10}]

1

5

1

RandomVariate[NormalDistribution[0, 1]]

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0.123456

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RandomVariate[NormalDistribution[0, 1], 10]

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{0.123456, 0.234567, ..., 0.987654}

1
2

SeedRandom[12345]
RandomVariate[NormalDistribution[0, 1], 10]

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{0.123456, 0.234567, ..., 0.987654}

1
2
3

Map[Sqrt, {1, 4, 9}]
Sqrt /@ {1, 4, 9}
Map[#^(1/2)&, {1, 4, 9}]

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{1, 2, 3}

1
2

f = Function[x, x^2]
f[3]

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9

1
2
3
4

f = Function[x, x^2]
g = Function[x, x + 1]
h = Function[x, f[g[x]]]
h[3]

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16

1

% + 1

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17

1

(#+3)&[5]

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8

1
2

Select[{1, 2, 3, 4, 5}, EvenQ]
Select[{1, 2, 3, 4, 5}, Mod[#,2]==0&]

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{2, 4}