Min¶

Status: Stable

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

Description¶

Min[x1, x2, ...]

yields the numerically smallest of the xi.

Min[{x1, x2, ...}, {y1, ...}, ...]

yields the smallest element of any of the lists.

Examples (5)¶

Every input below was run against the current Mathilda build and its output recorded.

Basic examples (1)¶

In[1]:= MinMax[<|"a" -> 3, "b" -> 1, "c" -> 9|>]
Out[1]= {1, 9}

Applications (4)¶

In[2]:= Min[3, 7, 2]
Out[2]= 2

In[3]:= Min[1/3, 2/7, 5/11]
Out[3]= 2/7

In[4]:= Min[x, 0, Infinity]
Out[4]= Min[0, x]

In[5]:= Min[{}]
Out[5]= Infinity

Performance¶

Against other systems, from the benchmark suite (same input, results cross-checked for agreement):

case	Mathilda	Wolfram	Python
Clip to [0.25, 0.75] over 4x10^6	575 s	1.95 s	0.953 s
MapThread[Max] over 4x10^6	14.8 s	692 s	0.772 s
MapThread[Min] over 4x10^6	14.7 s	687 s	0.769 s
integer Mod over 4x10^6	3.88 s	0.504 s	3.28 s
a b + a over 4x10^6	0.754 s	1.07 s	1.41 s
a + b over 4x10^6	0.383 s	0.516 s	0.74 s

Implementation notes¶

Algorithm. builtin_min mirrors Max: it flattens List arguments, scans real-numeric atoms for the minimum (via expr_compare), collects distinct symbolic terms, and treats Infinity/-Infinity/Overflow[] as identity/absorbing elements. All-numeric input returns the single smallest value; mixed input returns Min[...] over the numeric minimum and the remaining symbolic terms, or NULL if nothing simplified. Empty Min[] is Infinity.

Attributes: Flat, NumericFunction, OneIdentity, Orderless, Protected.

References¶

See also: Max, MinMax

Source: src/list.c
Specification: docs/spec/builtins/data-structures.md
Tests: tests/test_association.c
Tests: tests/test_autocompile.c
Tests: tests/test_bignum_rational_numeric.c
Tests: tests/test_compile.c

Notes & additional examples¶

Notes¶

Min[x1, x2, ...] returns the numerically smallest argument, and Min of several lists returns the smallest element across all of them. Comparisons are exact, so rationals are ordered without converting to floating point — Min[1/3, 2/7, 5/11] correctly picks 2/7. With symbolic arguments Min stays unevaluated but still prunes operands it can decide: Min[x, 0, Infinity] drops Infinity (which can never be a minimum) and returns Min[0, x]. The empty case Min[{}] returns Infinity, the identity element of minimisation — the value that leaves any subsequent Min unchanged.