5.7 Sets

Python has a built-in set type. The main feature it offers is very fast lookup of whether an element is in the set or not, along with standard set-theoretic operations.

sage: X = set([1,19,'a']);   Y = set([1,1,1, 2/3])
sage: X
set(['a', 1, 19])
sage: Y
set([1, 2/3])
sage: 'a' in X
True
sage: 'a' in Y
False
sage: X.intersection(Y)
set([1])

Sage also has its own set type that is (in some cases) implemented using the built-in Python set type, but has a little bit of extra Sage-related functionality. Create a Sage set using Set(...). For example,

sage: X = Set([1,19,'a']);   Y = Set([1,1,1, 2/3])
sage: X
{'a', 1, 19}
sage: Y
{1, 2/3}
sage: X.intersection(Y)
{1}
sage: print latex(Y)
\left\{1, \frac{2}{3}\right\}
sage: Set(ZZ)
Set of elements of Integer Ring

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