       RE: data structure for sets

• To: mathgroup at smc.vnet.net
• Subject: [mg35593] RE: [mg35566] data structure for sets
• From: "David Park" <djmp at earthlink.net>
• Date: Sun, 21 Jul 2002 01:01:13 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Bob,

Here is one approach.

Attributes[set] = {Orderless};

set[d, e, f, a, b, c]   gives
set[a, b, c, d, e, f]

For some test data...

set1 = set[d, e, f, g];
set2 = set[a, b, c, d, e];

set12 = Union[set1, set2]
set[a, b, c, d, e, f, g]

Here are the SubsetQ and SubsetEqualQ routines. (The real mathematicians
will probably have to check if I've captured all the subtleties of sets.)

SubsetQ::usage =
"SubsetQ[set1, set2] returns True if set1 is a subset of set2.";
SubsetQ[set1_set, set2_set] :=
Intersection[set2, set1] === set1 || set1 === set[];

SubsetEqualQ::usage =
"SubsetEqualQ[set1, set2] returns True if set1 is equal to set2.";
SubsetEqualQ[set1_set, set2_set] :=
SubsetQ[set1, set2] && SubsetQ[set2, set1];

SubsetQ[set[a], set1]
False

SubsetQ[set[a, d, c], set12]
True

SubsetQ[set[], set12]
True

SubsetEqualQ[set[e, d, g, f], set1]
True

SubsetEqualQ[set[d, e, f], set1]
False

David Park

From: Robert B. Nachbar [mailto:nachbar at merck.com]
To: mathgroup at smc.vnet.net

Has anyone implemented a data structure for sets that has the
Attribute Orderless and automatically deletes duplicate elements or
else ignores them when using Equal or SameQ? Functions such as SubsetQ
and SubsetEqualQ would also be helpful.

Thanks,

Bob

```

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