5 Operations on Lists

5Operations on Lists There are thousands of functions in the Wolfram Language that work with lists. You can do arithmetic with lists: {1, 2, 3} + 10   {1, 1, 2}*{1, 2, 3}   Compute the first 10 squares: Range[10]^2   Plot the first 20 squares: ListPlot[Range[20]^2]   Sort sorts a list into order: Sort[{4, 2, 1, 3, 6}]   Length finds how long a list is: Length[{5, 3, 4, 5, 3, 4, 5}]   Total gives the total from adding up a list: Total[{1, 1, 2, 2}]   Find the total of the numbers from 1 to 10: Total[Range[10]]   Count counts the number of times something appears in a list. Count the number of times a appears in the list: Count[{a, b, a, a, c, b, a}, a]   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: First[{7, 6, 5}]   Pick out the last element: Last[{7, 6, 5}]   Pick out element number 2: Part[{7, 6, 5}, 2]   Picking out the first element in a list you’ve sorted is the same as finding the minimum element: First[Sort[{6, 7, 1, 2, 4, 5}]]   Min[{6, 7, 1, 2, 4, 5}]   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: IntegerDigits[1988]   Find the last digit: Last[IntegerDigits[1988]]   Take lets you take a specified number of elements from the beginning of a list. Take the first 3 elements from a list: Take[{101, 203, 401, 602, 332, 412}, 3]   Take the first 10 digits of 2 to the power 100: Take[IntegerDigits[2^100], 10]   Drop drops elements from the beginning of a list. Drop[{101, 203, 401, 602, 332, 412}, 3]   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 Exercises Check your answers in the Wolfram Cloud 5.1Make a list of the first 10 squares, in reverse order. » Expected output: Out[]= Answer & check your solution 5.2Find the total of the first 10 squares. » Expected output: Out[]= Answer & check your solution 5.3Make a plot of the first 10 squares, starting at 1. » Expected output: Out[]= Answer & check your solution 5.4Use Sort, Join and Range to create {1, 1, 2, 2, 3, 3, 4, 4}. » Expected output: Out[]= Answer & check your solution 5.5Use Range and + to make a list of numbers from 10 to 20, inclusive. » Expected output: Out[]= Answer & check your solution 5.6Make a combined list of the first 5 squares and cubes (numbers raised to the power 3), sorted into order. » Expected output: Out[]= Answer & check your solution 5.7Find the number of digits in 2^128. » Expected output: Out[]= Answer & check your solution 5.8Find the first digit of 2^32. » Expected output: Out[]= Answer & check your solution 5.9Find the first 10 digits in 2^100. » Expected output: Out[]= Answer & check your solution 5.10Find the largest digit that appears in 2^20. » Expected output: Out[]= Answer & check your solution 5.11Find how many zeros appear in the digits of 2^1000. » Expected output: Out[]= Answer & check your solution 5.12Use Part, Sort and IntegerDigits to find the second-smallest digit in 2^20. » Expected output: Out[]= Answer & check your solution 5.13Make a line plot of the sequence of digits that appear in 2^128. » Expected output: Out[]= Answer & check your solution 5.14Use Take and Drop to get the sequence 11 through 20 from Range[100]. » Expected output: Out[]= Answer & check your solution +5.1Make a list of the first 10 multiples of 3. » Expected output: Out[]= Answer & check your solution +5.2Make a list of the first 10 squares using only Range and Times. » Expected output: Out[]= Answer & check your solution +5.3Find the last digit of 2^37. » Expected output: Out[]= Answer & check your solution +5.4Find the second-to-last digit of 2^32. » Expected output: Out[]= Answer & check your solution +5.5Find the sum of all the digits of 3^126. » Expected output: Out[]= Answer & check your solution +5.6Make a pie chart of the sequence of digits that appear in 2^32. » Expected output: Out[]= Answer & check your solution +5.7Make a list of pie charts for the sequence of digits in 2^20, 2^40, 2^60. » Expected output: Out[]= Answer & check your solution 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.

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