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Stephen Wolfram
An Elementary Introduction to the Wolfram Language
Second Edition (2017)
5Operations on Lists
There are thousands of functions in the Wolfram Language that work with lists.
You can do arithmetic with lists:
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Compute the first 10 squares:
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Plot the first 20 squares:
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Sort sorts a list into order:
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Length finds how long a list is:
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Total gives the total from adding up a list:
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Find the total of the numbers from 1 to 10:
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Count counts the number of times something appears in a list.
Count the number of times a appears in the list:
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It’s often useful to be able to get individual elements of a list. First gives the first element; Last gives the last element. Part gives the element at a particular position.
Pick out the first element of a list:
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Pick out the last element:
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Pick out element number 2:
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Picking out the first element in a list you’ve sorted is the same as finding the minimum element:
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If you have a number, like 5671, you can make a list of its digits using IntegerDigits[5671].
Break a number into a list of digits:
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Find the last digit:
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Take lets you take a specified number of elements from the beginning of a list.
Take the first 3 elements from a list:
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Take the first 10 digits of 2 to the power 100:
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Drop drops elements from the beginning of a list.
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Vocabulary
{2,3,4}+{5,6,2} arithmetic on lists
Sort[{5,7,1}] sort a list into order
Length[{3,3}] length of a list (number of elements)
Total[{1,1,2}] total of all elements in a list
Count[{3,2,3},3] count occurrences of an element
First[{2,3}] first element in a list
Last[{6,7,8}] last element in a list
Part[{3,1,4},2] particular part of a list, also written as {3, 1, 4}[[2]]
Take[{6,4,3,1},2] take elements from the beginning of a list
Drop[{6,4,3,1},2] drop elements from the beginning of a list
IntegerDigits[1234] list of digits in a number
5.1Make a list of the first 10 squares, in reverse order. »
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5.2Find the total of the first 10 squares. »
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5.3Make a plot of the first 10 squares, starting at 1. »
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5.4Use Sort, Join and Range to create {1, 1, 2, 2, 3, 3, 4, 4}. »
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5.5Use Range and + to make a list of numbers from 10 to 20, inclusive. »
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5.7Find the number of digits in 2^128. »
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5.8Find the first digit of 2^32. »
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5.9Find the first 10 digits in 2^100. »
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5.10Find the largest digit that appears in 2^20. »
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5.11Find how many zeros appear in the digits of 2^1000. »
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5.12Use Part, Sort and IntegerDigits to find the second-smallest digit in 2^20. »
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5.13Make a line plot of the sequence of digits that appear in 2^128. »
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5.14Use Take and Drop to get the sequence 11 through 20 from Range[100]. »
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+5.1Make a list of the first 10 multiples of 3. »
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+5.2Make a list of the first 10 squares using only Range and Times. »
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+5.3Find the last digit of 2^37. »
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+5.4Find the second-to-last digit of 2^32. »
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+5.5Find the sum of all the digits of 3^126. »
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+5.6Make a pie chart of the sequence of digits that appear in 2^32. »
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+5.7Make a list of pie charts for the sequence of digits in 2^20, 2^40, 2^60. »
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Q&A
Can one add lists of different lengths?
No. {1, 2}+{1, 2, 3} won’t work. {1, 2, 0}+{1, 2, 3} would be fine, if that’s what you mean.
Can there be a list with nothing in it?
Yes. {} is a list of length 0, with no elements. It’s usually called the null list or the empty list.
Tech Notes
  • IntegerDigits[5671] gives digits in base 10. IntegerDigits[5671, 2] gives digits in base 2. You can use any base you want. FromDigits[{5, 6, 7, 1}] reconstructs a number from its list of digits.
  • Rest[list] gives all the elements of list after the first one. Most[list] gives all elements other than the last one.
More to Explore
Guide to List Manipulation in the Wolfram Language »
 
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