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Re: Select in Math.

• To: mathgroup at smc.vnet.net
• Subject: [mg16518] Re: Select in Math.
• From: BobHanlon at aol.com
• Date: Tue, 16 Mar 1999 03:59:59 -0500
• Sender: owner-wri-mathgroup at wolfram.com

In a message dated 3/8/99 6:43:38 PM, kewjoi at hixnet.co.za writes:

>My question is how can I extract (select) list of lists in increasing
>order?
>For example:
>In[2]:=list={{{1,2,3,4},{1,2,4,3}},{{2,3,1},{5}},{6,7}}
>Out[2]={{{1,2,3,4},{1,2,4,3}},{{2,3,1},{5}},{6,7}}
>
>I 'd like to obtain only the parts in increased order, therefore the
>result should be :
>Out[3]={{1,2,3,4},{5},{6,7}}
>I did try (Cases, Select, and Extract) but definitely not in proper way.
>

Eugene,

This may be what you want.

list={{{1,2,3,4},{1,2,4,3}},{{2,3,1},{5}},{6,7}};

The nesting of the lists does not appear to be pertinent to your problem, 
so simplify the structure by eliminating the nesting.  Also, Sort sublists 
and eliminate duplicates:

list = Union[Sort /@ {list //. 
					{x__List} -> Sequence[x]}]

{{5}, {6, 7}, {1, 2, 3}, {1, 2, 3, 4}}

Eliminate subsets

elements = Union[Flatten[list]];

list = Select[list, Not[Union[Flatten[
					Complement[list, {#}]]] == elements]&]

{{5}, {6, 7}, {1, 2, 3, 4}}

Sort by first element

Sort[list, First[#1] < First[#2]&]

{{1, 2, 3, 4}, {5}, {6, 7}}


Bob Hanlon

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