Max

The largest of its arguments.

✓ checked against that system · ! checked, with disagreements (hover a chip)FungrimMax↗Fungrim entry632d1c↗bfe28b↗Wolfram LanguageMax!↗SageMathenumeratio_max($*,)SymPyenumeratio_max($*,)Juliaenumeratio_max($*,)

Max(a, b, …)the largest of two or more values.

Max(list)the largest value in a list.

Max(finset)the largest member of a Finset.

Typed signatures

Type	Package	Applies
(value*) -> number	analyticreplaces compute-engine	always
(value*) -> number	compute-engine	always
(any*) -> any	combinatoricsreplaces structures	on Finset
(any*) -> any	structuresreplaces analytic	always

Domain: Arithmetic

Details

• The largest 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 Min.
• Commutative and associative: order and grouping don't matter.
• NaN poisons the result: it beats every other comparison, even $+\infty$.
• With no arguments, compute-engine returns NaN rather than $-\infty$, the true identity element.
• Takes a Finset too: its largest 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$\max(3, 1, 4, 1, 5)$Out$5$

Also accepts a single list argument

live ↗

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

live ↗

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

A single argument is returned unchanged

live ↗

In$\max(3)$Out$3$

live ↗

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

live ↗

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

live ↗

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

Scope #

Nested lists are flattened into the pool

live ↗

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

Exact numbers are compared numerically

live ↗

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

live ↗

In$\max(1, ∞)$Out$∞$

The numeric arguments collapse to their maximum; symbolic ones stay

live ↗

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

Compares exact constants numerically: $\max(e, \pi, 2) = \pi$

live ↗

In$\max(\bigl\lbrack e, π, 2\bigr\rbrack)$Out$π$

The max of two Intervals is the interval of possible maxima, $[1, 5]$

live ↗

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

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

live ↗

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

Applications #

The day's high from a handful of hourly readings. See Min

live ↗

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

Properties #

Commutative: order doesn't matter

live ↗

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

Multiple list arguments are flattened into one pool rather than compared pairwise

live ↗

In$\max(\bigl\lbrack3, 1, 4\bigr\rbrack, \bigl\lbrack9, 2\bigr\rbrack)=9$Out$\mathrm{True}$

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

live ↗

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

Possible issues #

With no arguments, compute-engine returns NaN rather than $-\infty$, the true identity element

live ↗

In$\max()$Out$\operatorname{NaN}$

NaN poisons the result, overriding every other argument

live ↗

In$\max(\operatorname{NaN}, 3)$Out$\operatorname{NaN}$

The max of an empty list is NaN too

live ↗

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

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

live ↗

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

The empty Finset answers as an empty list does: NaN

live ↗

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

About

Examples	24
Checked against	Wolfram Language 19 agree5 differSageMath 18 agree1 differ1 unevaluated3 errorSymPy 17 agree4 differ3 errormathlib4 9 agree6 errorJulia 15 agree1 unevaluated4 errorRust 4 agree2 error
Crosswalk	FungrimFungrim entry ×2Wolfram LanguageSageMathSymPyJuliaRust

Implementation

mappedmathlib4packages/oracle/src/mappings.ts

The largest 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) 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

Wolfram (and our Max) flattens nested lists into one pool; bare SymPy Max()/Sage max() on a list (or a list of lists) either raise or compare lexicographically instead, so both go through a flattening helper (run.ts's SYMPY_PREAMBLE / SAGE_PREAMBLE).

mappedsympypackages/oracle/src/mappings.ts

Wolfram (and our Max) flattens nested lists into one pool; bare SymPy Max()/Sage max() on a list (or a list of lists) either raise or compare lexicographically instead, so both go through a flattening helper (run.ts's SYMPY_PREAMBLE / SAGE_PREAMBLE).

mappedsagepackages/oracle/src/mappings.ts

Wolfram (and our Max) flattens nested lists into one pool; bare SymPy Max()/Sage max() on a list (or a list of lists) either raise or compare lexicographically instead, so both go through a flattening helper (run.ts's SYMPY_PREAMBLE / SAGE_PREAMBLE).

mappedjuliapackages/oracle/src/mappings.ts

mappedrustpackages/oracle/src/mappings.ts

Two operands.

See also: Min, Clamp