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EXAMPLE 14
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CharacterRange["a","e"] {a,b,c,d,e} CharacterRange[" " ," ~ "] { , !, \, #, $, %, &, , (,), *, +, ,, , ., /, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, :, ;, <, =, >, , @, A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, [, \\, ], ^, _, `, a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, {, |, }, ~}
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Even though the output of Characters and CharacterRange appears to be individual characters, in actuality they are strings of length 1. By Mathematica s convention, quotation marks are not printed.
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digits = CharacterRange["0"," 9"] {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} These are not numbers but strings of characters of length 1. FullForm[digits] List["0", "1", "2", "3", "4", "5", "6", "7", "8", "9"]
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3.5 Construct a list of the positive multiples of 7 that do not exceed 100.
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Range[7, 100, 7] {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98}
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SOLUTION 2
Table[7 k,{k, 1, 14}] {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98}
3.6 Construct a list of the first ten prime numbers.
SOLUTION 1
Table[Prime[k], {k, 1, 10}] {2, 3, 5, 7, 11, 13, 17, 19, 23, 29}
SOLUTION 2
Array[Prime, 10] {2, 3, 5, 7, 11, 13, 17, 19, 23, 29}
SOLUTION 3
Prime[Range[10]] {2, 3, 5, 7, 11, 13, 17, 19, 23, 29}
3.7 Construct a list of the reciprocals of the first ten even integers.
SOLUTION 1
Table[1/k, {k, 2, 20, 2}]
1, 1, 1, 1, 1 , 1 , 1 , 1 , 1 , 1 2 4 6 8 10 12 14 16 18 20 0
SOLUTION 2
1 Range[2,20,2] 1, 1, 1, 1, 1 , 1 , 1 , 1 , 1 , 1 2 4 6 8 10 12 14 16 18 20 0
3.8 Construct a list of five objects, each of which is a list consisting of six integers. The first list is to contain the first six multiples of 2, the second, multiples of 3, the third, multiples of 4, and so forth.
SOLUTION 1
Table[i * j, {i, 2, 6}, {j, 1, 6}] {{2, 4, 6, 8, 10, 12},{3, 6, 9, 12, 15, 18}, {4, 8, 12, 16, 20, 24}, {5, 10, 15, 20, 25, 30}, {6, 12, 18, 24, 30, 36}}
SOLUTION 2
Times[x, y]= x * y
Array[Times, {5, 6}, {2, 1}] {{2, 4, 6, 8, 10, 12},{3, 6, 9, 12, 15, 18}, {4, 8, 12, 16, 20, 24}, {5, 10, 15, 20, 25, 30}, {6, 12, 18, 24, 30, 36}}
Lists
3.9 Let p(x) = x2 8x + 10. Construct a list of values of p(x) for x = 1, 2, 3, . . . , 10.
SOLUTION 1
p[x_] = x2 8 x + 10; Array[p, 10] {3, 2, 5, 6, 5, 2, 3, 10, 19, 30}
SOLUTION 2
p[x_] = x2 8 x + 10; p[Range[10]] {3, 2, 5, 6, 5, 2, 3, 10, 19, 30}
3.10 Approximate the sum of the square roots of the first 100 positive integers.
SOLUTION
Total[Sqrt[Range[100]]] //N 671.463
3.3 List Manipulation
Length[list] returns the length of list, i.e., the number of elements in list. First[list] returns the element of list in the first position. Last[list] returns the element of list in the last position.
EXAMPLE 16
list = {a, b, c, d, e, f, g}; Length[list] 7 First[list] a Last[list] g
The function Part returns individual elements of a list.
Part[list, k] or list[[k]] returns the kth element of list. Part[list, k] or list[[ k]] returns the kth element from the end of list.
Note: Part[list, 1] and Part[list, 1] are equivalent to First[list] and Last[list] , respectively.
EXAMPLE 17
list = {a, b, c, d, e, f, g}; Part[list, 1] a Part[list, 3] c or or list[[1]] list[[3]] list[[ 3]]
Part[list, 3] or e
Part[list, 1] or list[[ 1]] g
Lists may be nested. The elements of a list may themselves be lists.
Lists
EXAMPLE 18
list = {{a, b, c, d}, {e, f, g, h}, {i, j, k, l}}; First[list] {a, b, c, d} Last[list] {i, j, k, l} list[[2]] {e, f, g, h}
Since list[[2]] is itself a list, its third entry, for example, can be obtained as list[[2]][[3]] (the third entry of the second list). For convenience, this can be represented as list[[2, 3]] or Part[list, 2, 3]. Part[Part[list, 2], 3]can also be used, but is somewhat clumsy.
Part[list, m, n] or list[[m, n]] returns the nth entry of the mth element of list, provided list has depth at least 2.
This command extends to lists of depth greater than 2 in a natural way provided the Part specification does not exceed the depth of the list.
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