Min

The smallest of its arguments.

✓ checked against that system · ! checked, with disagreements (hover a chip)FungrimMin↗Fungrim entry27766c↗540931↗737f2b↗75231e↗805c7a↗da7fb1↗Wolfram LanguageMin!↗SageMathenumeratio_min($*,)SymPyenumeratio_min($*,)Juliaenumeratio_min($*,)

Min(a, b, …)the smallest of two or more values.

Min(list)the smallest value in a list.

Min()the identity element $+\infty$, for a call with no arguments at all.

Min(finset)the smallest member of a Finset.

Typed signatures

Type	Package	Applies
(value+) -> number	analyticreplaces compute-engine	always
(value+) -> number	compute-engine	always
(any*) -> any	combinatoricsreplaces analytic	always
(any*) -> any	structuresreplaces combinatorics	always

Domain: Arithmetic

Details

• The smallest of its arguments, or of a single list argument.
• Multiple arguments -- lists included -- are flattened into one pool rather than compared pairwise or threaded element-wise. See Max.
• Commutative and associative: order and grouping don't matter.
• $\min(a,b) + \max(a,b) = a + b$ for any two values. See Max.
• Infinities participate directly in the comparison.
• With no arguments at all, returns the identity element $+\infty$.
• Takes a Finset too: its smallest member, and NaN for the empty one, as for an empty list.

Examples

1 more kept as data, checked against the oracles

Basic #

live ↗

In$\min(3, 1, 4, 1, 5)$Out$1$

Also accepts a single list argument

live ↗

In$\min(\bigl\lbrack3, 1, 4\bigr\rbrack)$Out$1$

live ↗

In$\min(-1, -5)$Out$-5$

A single argument is returned unchanged

live ↗

In$\min(3)$Out$3$

live ↗

In$\min(9, 2)$Out$2$

live ↗

In$\min(\bigl\lbrack4, 1, 7, 2\bigr\rbrack)$Out$1$

live ↗

In$\min(5.56, -4.8, 7.3)$Out$-4.8$

Scope #

Nested lists are flattened into the pool

live ↗

In$\min(2, 3, \bigl\lbrack\bigl\lbrack\frac{1}{2}, -1\bigr\rbrack, \bigl\lbrack-\frac{5}{3}, \frac{1}{2}\bigr\rbrack\bigr\rbrack)$Out$-\frac{5}{3}$

Exact numbers are compared numerically

live ↗

In$\min(\sqrt{2}, \frac{3}{2})$Out$\sqrt{2}$

The numeric arguments collapse to their minimum; symbolic ones stay

live ↗

In$\min(3, x, 5)$Out$\min(3, x)$

Compares exact constants numerically: $\min(e, \pi, 5) = e$

live ↗

In$\min(\bigl\lbrack e, π, 5\bigr\rbrack)$Out$e$

The min of two Intervals is the interval of possible minima, $[-3, 3]$

live ↗

In$\min(\mathrm{Interval}(1, 3), \mathrm{Interval}(-3, 5))$Out$\mathrm{Interval}(-3, 3)$

A Finset has a smallest member: the subset $\{1,3,4\}$ of $\{1,\dots,6\}$

live ↗

In$\min(\operatorname{Finset}(\operatorname{Tuple}(6,\bigl\lbrack1, 3, 4\bigr\rbrack)))$Out$1$

Applications #

The day's low from the same hourly readings. See Max

live ↗

In$\min(68, 72, 65, 80, 74)$Out$65$

Properties #

Commutative: order doesn't matter

live ↗

In$\min(3, 7)=\min(7, 3)$Out$\mathrm{True}$

$\min(a,b) + \max(a,b) = a + b$. See Max

live ↗

In$\min(4, 9)+\max(4, 9)=4+9$Out$\mathrm{True}$

Idempotent: $\min(x, x) = x$

live ↗

In$\min(x, x)$Out$x$

Possible issues #

Infinities participate directly in the comparison rather than being filtered out

live ↗

In$\min(-∞, 3)$Out$-∞$

Multiple arguments -- lists included -- are flattened into one pool rather than compared list-by-list. See Max

live ↗

In$\min(\bigl\lbrack3, 1\bigr\rbrack, 0)$Out$0$

With no arguments it returns the identity element $+\infty$ (Max, whose identity is $-\infty$, still returns NaN)

live ↗

In$\min()$Out$∞$

The min of an empty list is NaN

live ↗

In$\min(\bigl\lbrack\bigr\rbrack)$Out$\operatorname{NaN}$

ComplexInfinity is unordered, so Min cannot compare it: the call stays unevaluated, as in Wolfram

live ↗

In$\min(\tilde∞, 1)$Out$\min(1, \tilde∞)$

The empty Finset answers as an empty list does: NaN

live ↗

In$\min(\operatorname{Finset}((3,\bigl\lbrack\bigr\rbrack)))$Out$\operatorname{NaN}$

About

Examples	24
Checked against	Wolfram Language 21 agree3 differSageMath 18 agree1 unevaluated4 errorSymPy 20 agree3 differ1 errormathlib4 10 agree7 errorJulia 16 agree4 errorRust 5 agree1 error
Crosswalk	FungrimFungrim entry ×6Wolfram LanguageSageMathSymPyJuliaRust

Implementation

mappedmathlib4packages/oracle/src/mappings.ts

The smallest of the arguments as exact rationals. Several arguments are the pool; a lone argument is a list of numbers. The empty pool (ours is NaN, or +∞ with no arguments) and a nested list (ours flattens it) fail to elaborate rather than defaulting.

mappedmathlib4packages/oracle/src/mappings.ts

A single list of numbers; a lone number fails to elaborate.

mappedwolframpackages/oracle/src/mappings.ts

Same flattening as Max.

mappedsympypackages/oracle/src/mappings.ts

Same flattening as Max.

mappedsagepackages/oracle/src/mappings.ts

Same flattening as Max.

mappedjuliapackages/oracle/src/mappings.ts

mappedrustpackages/oracle/src/mappings.ts

Two operands.

See also: Max, Clamp