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Flatten[list] converts a nested list to a simple list containing the innermost objects of list. Flatten[list, n] flattens a nested list n times, each time removing the outermost level. The depth of each level is reduced by n or to a minimum level of 1. FlattenAt[list, n] flattens the sublist which is at the nth position of the list by one level. If n is negative, Mathematica counts backward, starting at the end of the list.

list = {1, {2, 3}, {4, 5, {6}}, {7, {8, {9, 10}}}} Flatten[list] {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} Flatten[list, 1] {1, 2, 3, 4, 5, {6}, 7, {8, {9, 10}}} Flatten[list, 2] {1, 2, 3, 4, 5, 6, 7, 8, {9, 10}} FlattenAt[list, 3] {1, {2, 3}, 4, 5, {6}, {7, {8, {9, 10}}}} Only the third sublist of list is flattened one level. FlattenAt[list, 3] {1, 2, 3, {4, 5, {6}}, {7, {8, {9, 10}}}}

In the Search window, just start typing any part of the following categories to find an item (see Figure 26 10): Artist name Album name Composer Song/video name

Flatten converts a nested list into a simpler list. Partition takes simple lists and converts them into nested lists in a very organized and convenient way.

Partition[list, k] converts list into sublists of length k. If list contains k n + m elements, where m < k, Partition will create n sublists and the remaining m elements will be dropped. Partition[list, k, d] partitions list into sublists of length k, offsetting each sublist from the previous sublist by d elements. In other words, each sublist (other than the first) begins with the d+1st element of the previous sublist.

Fig. 8-16.

You will notice that, as soon as you type the first letter, iTunes will narrow your search results (shown in the Main window) by that letter. What it is doing is finding all matching songs/videos that have the letter (or series of letters) that match any part of the artist, album, composer or song/video name.

Note that Partition[list, k] is equivalent to Partition[list, k, k]. Partition is a very convenient command for generating tables and matrices. Only the simplest forms of the command have been described. The reader, if interested, is urged to investigate other forms in Mathematica s Documentation Center.

list = Range[12] {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} Partition[list, 4] {{1, 2, 3, 4}, {5, 6, 7, 8}, {9, 10, 11, 12}} Partition[list, 5] {{1, 2, 3, 4, 5}, {6, 7, 8, 9, 10}}

Partition[list,5, 1] {{1, 2, 3, 4, 5}, {2, 3, 4, 5, 6}, {3, 4, 5, 6, 7}, {4, 5, 6, 7, 8},{5, 6, 7, 8, 9}, {6, 7, 8, 9, 10}, {7, 8, 9, 10, 11}, {8, 9, 10, 11, 12}} Partition[list, 5, 2] {{1, 2, 3, 4, 5}, {3, 4, 5, 6, 7}, {5, 6, 7, 8, 9}, {7, 8, 9, 10, 11}} Partition[list, 5, 3] {{1, 2, 3, 4, 5}, {4, 5, 6, 7, 8}, {7, 8, 9, 10, 11}}

You can type any combination of words to match the item you are trying to find. For example, assume you know that the song has the word love in the title, and the song is by U2. You could just type in those two words, separated by a space; Love U2 will immediately show all matching items (see Figure 26 11). In this case, only two songs match, so you can quickly double-click the song you want to listen to. Search is also contextual. This means that if you are in your music library, the search function will search for music; whereas if you are in your apps library, the search will search only for apps. In every search, both your own library and the App Store will be searched.

12. Draw a system diagram for the B&B system (see Problem 4.3). See Fig. 8-17.

3.11 The Mathematica function IntegerDigits returns a list containing the digits of an integer. How many digits are there in 100! and what is the 50th digit from the left and from the right