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Select

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description

Select[list, crit]
    selects elements e of list for which crit[e] yields True, preserving
    the head of list.
Select[list, crit, n]
    stops after the first n matching elements.
Select[crit]
    is the operator form: Select[crit][list] == Select[list, crit].

Examples

All examples below are verified against the current Mathilda build.

In[1]:= Select[{1, 2, 4, 7, 6, 2}, EvenQ]
Out[1]= {2, 4, 6, 2}

In[2]:= Select[{1, 2, 4, 7, 6, 2}, # > 2 &, 1]
Out[2]= {4}

Implementation notes

builtin_select filters the arguments of a compound expression by a predicate. It iterates the args of list (any head, not only List), and for each element builds crit[elem] and runs evaluate(); the element is kept only when the result is exactly the symbol True. The optional third argument caps the number of kept elements (n_max), stopping the scan early once reached. The surviving elements are reassembled under the original head via expr_new_function. Returns NULL (unevaluated) when the first argument is an atom or when the count argument is non-integer. Each predicate test allocates a copied call and frees it plus its evaluated result, so memory is bounded per element.

Attributes: Protected.

Implementation status

Stable — documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

References

Notes & additional examples

Worked examples

In[1]:= Select[{1, 2, 3, 4, 5, 6}, EvenQ]
Out[1]= {2, 4, 6}

In[1]:= Select[Range[10], # > 5 &]
Out[1]= {6, 7, 8, 9, 10}

In[1]:= Select[{1, 2, 3, 4, 5}, PrimeQ, 2]
Out[1]= {2, 3}

Combining predicates with logical operators filters by richer conditions — the twin primes below 100, where both p and p + 2 are prime:

In[1]:= Select[Range[100], PrimeQ[#] && PrimeQ[# + 2] &]
Out[1]= {3, 5, 11, 17, 29, 41, 59, 71}

The criterion can itself perform a computation. Selecting the exponents p for which 2^p - 1 is prime yields the Mersenne-prime exponents:

In[1]:= Select[Range[2, 50], PrimeQ[2^# - 1] &]
Out[1]= {2, 3, 5, 7, 13, 17, 19, 31}

The integers below 20 that are coprime to 20 (a GCD-based filter):

In[1]:= Select[Range[1, 20], GCD[#, 20] == 1 &]
Out[1]= {1, 3, 7, 9, 11, 13, 17, 19}

Notes

Select[list, crit] keeps the elements for which crit[elem] returns True; any other result (including False or an unevaluated predicate) drops the element. The criterion is usually a predicate symbol such as EvenQ or PrimeQ, or a pure function like # > 5 &. The optional third argument caps the number of elements returned, which lets Select stop early once enough matches are found.