UpTo

A count specification meaning at most n, taking fewer when fewer are available.

✓ checked against that system · ! checked, with disagreements (hover a chip)Wolfram LanguageUpTo✓↗

UpTo(n)at most $n$ — never an error for asking for more than a collection holds. Never evaluated on its own — read by Take, Partition and Ordering.

Typed signatures

Type	Package	Applies
(integer) -> unknown	combinatorics	always

Domain: Collections

Details

• Never reduces by itself: a count specification other heads read, not a value.
• In Take, takes at most n elements with no error when fewer are available.
• In Partition, allows a shorter final chunk instead of dropping the ragged remainder.
• In Ordering, the same clamping a plain integer count already gives — at most n positions, fewer if the collection is shorter.

Examples

Basic #

Asking for up to 5 of 3 elements takes all 3, with no error

live ↗

In$\mathrm{Take}(\bigl\lbrack1, 2, 3\bigr\rbrack, \mathrm{UpTo}(5))$Out$\bigl\lbrack1, 2, 3\bigr\rbrack$

When enough elements are available, exactly n is taken

live ↗

In$\mathrm{Take}(\bigl\lbrack1, 2, 3, 4, 5, 6\bigr\rbrack, \mathrm{UpTo}(2))$Out$\bigl\lbrack1, 2\bigr\rbrack$

Asking for up to six from four elements returns all four, with no error

live ↗

In$\mathrm{Take}(\bigl\lbrack a, b, c, d\bigr\rbrack, \mathrm{UpTo}(6))$Out$\bigl\lbrack a, b, c, d\bigr\rbrack$

When enough elements exist, it behaves like an ordinary count

live ↗

In$\mathrm{Take}(\bigl\lbrack a, b, c, d\bigr\rbrack, \mathrm{UpTo}(2))$Out$\bigl\lbrack a, b\bigr\rbrack$

The final block may be short

live ↗

In$\mathrm{Partition}(1..10, \mathrm{UpTo}(3))$Out$\bigl\lbrack\bigl\lbrack1, 2, 3\bigr\rbrack, \bigl\lbrack4, 5, 6\bigr\rbrack, \bigl\lbrack7, 8, 9\bigr\rbrack, \bigl\lbrack10\bigr\rbrack\bigr\rbrack$

Scope #

In Partition, a shorter final chunk is allowed

live ↗

In$\mathrm{Partition}(\bigl\lbrack1, 2, 3, 4, 5, 6\bigr\rbrack, \mathrm{UpTo}(4))$Out$\bigl\lbrack\bigl\lbrack1, 2, 3, 4\bigr\rbrack, \bigl\lbrack5, 6\bigr\rbrack\bigr\rbrack$

In Ordering, at most 6 positions of a 5-element list

live ↗

In$\mathrm{Ordering}(\bigl\lbrack2, 6, 1, 9, 2\bigr\rbrack, \mathrm{UpTo}(6))$Out$\bigl\lbrack3, 1, 5, 2, 4\bigr\rbrack$

live ↗

In$\mathrm{Commonest}(\bigl\lbrack b, a, c, 2, a, b, 1, 2\bigr\rbrack, \mathrm{UpTo}(6))$Out$\bigl\lbrack b, a, c, 2, 1\bigr\rbrack$

live ↗

In$\mathrm{Partition}(\bigl\lbrack a, b, c, d, k, f, g\bigr\rbrack, \mathrm{UpTo}(3))$Out$\bigl\lbrack\bigl\lbrack a, b, c\bigr\rbrack, \bigl\lbrack d, k, f\bigr\rbrack, \bigl\lbrack g\bigr\rbrack\bigr\rbrack$

About

Examples	9
Checked against	Wolfram Language 9 agree
Crosswalk	Wolfram Language

See also: Partition, Ordering, Span