Lists are very important and general structures in
Mathematica. They allow you treat collections of all kinds of objects as a single entity. There are many ways to construct them.
Use the shorthand notation {} to make a list:
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Or use
List, which automatically is changed to {}:
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Use
Range with one argument to create a list of integers starting at 1:
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Or use
Range with two arguments to create a list of integers starting higher:
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With three arguments the offset can be different than 1:
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This squares each element of the list:
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Or use
Table to create the first 10 squares:
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Just like
Range,
Table can start higher or jump by any amount:
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Use
NestList to create a list of the results of applying
f to
x for 0 through 3 times:
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Use
Array to create a list of length 4, with elements
f[i]:
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Use
List to create lists of strings:
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A matrix in
Mathematica is a list of lists.
Use
RandomInteger to create a 4×4 matrix of random integers between 0 and 10 (stored as
m):
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Use
MatrixForm to see
m as a 2D matrix:
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You can apply functions to a list.
You can directly apply math functions to a list:
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Math functions keep going deeper:
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Some functions give a number as a result:
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Length gives the length of a list:
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Use
Map to apply a function to the elements of a list (not needed for math functions):
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This uses
Map to apply
Length to each sublist:
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Similarly, this finds the maximum of each sublist:
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