Skip to content

Max

Status: Stable

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

Description

Max[x1, x2, ...]
    yields the numerically largest of the xi.
Max[{x1, x2, ...}, {y1, ...}, ...]
    yields the largest element of any of the lists.

Examples

All examples below are verified against the current Mathilda build.

In[1]:= Min[9, 2]
Out[1]= 2

In[2]:= Min[{4, 1, 7, 2}]
Out[2]= 1

In[3]:= Max[Infinity, 5]
Out[3]= Infinity

Implementation notes

Algorithm. builtin_max flattens any List arguments into a flat argument sequence, then scans for the maximum among real-numeric atoms (compared with expr_compare) while collecting distinct non-numeric/symbolic terms. Infinity/-Infinity and Overflow[] are handled as absorbing/identity elements. If everything reduces to numbers it returns the single largest value; otherwise it returns Max[...] over the numeric maximum plus the remaining symbolic terms (returning NULL to stay unevaluated when nothing simplified). Empty Max[] is -Infinity.

  • Flat, NumericFunction, OneIdentity, Orderless, Protected.
  • Flattens List arguments.
  • Min[] returns Infinity.
  • Max[] returns -Infinity.
  • Handles Infinity and -Infinity.
  • Simplifies numeric arguments to a single value.

Attributes: Flat, NumericFunction, OneIdentity, Orderless, 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]:= Max[3, 7, 2]
Out[1]= 7

In[1]:= Max[{1, 5}, {9, 2}]
Out[1]= 9

In[1]:= Max[2^100, 3^60, 5^40]
Out[1]= 1267650600228229401496703205376

In[1]:= Max[Abs[Eigenvalues[{{2, 1}, {1, 2}}]]]
Out[1]= 3

In[1]:= Max[x, 3, x]
Out[1]= Max[3, x]

Notes

Max[x1, x2, ...] returns the numerically largest argument, and Max of a collection of lists returns the largest element across all of them. Comparisons are exact: Max[2^100, 3^60, 5^40] resolves a contest between three large bignums (with automatic GMP promotion) and returns 2^100, the actual winner. Because Max is variadic and flattens lists, it composes naturally with other operations — Max[Abs[Eigenvalues[...]]] computes the spectral radius of a matrix in one line. When some arguments are non-numeric symbols, Max keeps the call symbolic but still simplifies what it can: it discards duplicate operands and drops any argument provably smaller than another, so Max[x, 3, x] collapses to Max[3, x].