Description Usage Arguments Details Author(s) References Examples
Gives a magic square that is a product of two magic squares.
1 2 | magic.product(a, b, mat=NULL)
magic.product.fast(a, b)
|
a |
First magic square; if |
b |
as above |
mat |
Matrix, of same size as |
Function magic.product.fast()
does not take a mat
argument, and is equivalent to magic.product()
with mat
taking the default value of NULL
. The improvement in speed is
doubtful unless order(a)
>>order(b)
, in which
case there appears to be a substantial saving.
Robin K. S. Hankin
William H. Benson and Oswald Jacoby. New recreations with magic squares, Dover 1976 (and that paper in JRM)
1 2 3 4 5 6 7 8 9 | magic.product(magic(3),magic(4))
magic.product(3,4)
mat <- matrix(0,3,3)
a <- magic.product(3,4,mat=mat)
mat[1,1] <- 1
b <- magic.product(3,4,mat=mat)
a==b
|
Loading required package: abind
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
[1,] 17 28 24 29 97 108 104 109 81 92 88 93
[2,] 31 22 26 19 111 102 106 99 95 86 90 83
[3,] 30 23 27 18 110 103 107 98 94 87 91 82
[4,] 20 25 21 32 100 105 101 112 84 89 85 96
[5,] 129 140 136 141 65 76 72 77 1 12 8 13
[6,] 143 134 138 131 79 70 74 67 15 6 10 3
[7,] 142 135 139 130 78 71 75 66 14 7 11 2
[8,] 132 137 133 144 68 73 69 80 4 9 5 16
[9,] 49 60 56 61 33 44 40 45 113 124 120 125
[10,] 63 54 58 51 47 38 42 35 127 118 122 115
[11,] 62 55 59 50 46 39 43 34 126 119 123 114
[12,] 52 57 53 64 36 41 37 48 116 121 117 128
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
[1,] 17 28 24 29 97 108 104 109 81 92 88 93
[2,] 31 22 26 19 111 102 106 99 95 86 90 83
[3,] 30 23 27 18 110 103 107 98 94 87 91 82
[4,] 20 25 21 32 100 105 101 112 84 89 85 96
[5,] 129 140 136 141 65 76 72 77 1 12 8 13
[6,] 143 134 138 131 79 70 74 67 15 6 10 3
[7,] 142 135 139 130 78 71 75 66 14 7 11 2
[8,] 132 137 133 144 68 73 69 80 4 9 5 16
[9,] 49 60 56 61 33 44 40 45 113 124 120 125
[10,] 63 54 58 51 47 38 42 35 127 118 122 115
[11,] 62 55 59 50 46 39 43 34 126 119 123 114
[12,] 52 57 53 64 36 41 37 48 116 121 117 128
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
[1,] TRUE FALSE FALSE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
[2,] FALSE TRUE FALSE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
[3,] FALSE FALSE TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
[4,] FALSE FALSE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
[5,] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
[6,] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
[7,] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
[8,] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
[9,] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
[10,] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
[11,] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
[12,] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
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