max

Finds the greatest of all real numbers in a container or in a sequence.

Syntax

• max(a, b)

  • a is a real number

  • b is a real number

• max(X)

  • X is a vector, matrix, list, set, or structure

• max(expr, var, a, b)

  • expr is an expression in one variable var

  • var is the variable in expr

  • a is the lower bound

  • b is the upper bound

Description

The greatest of two numbers

If a and b are real numbers, then max(a, b) is the greatest of them.

Finding the greatest number in a container

• If v is a real vector, then max(v) is the greatest component of v.

• If A is a real matrix, then max(A) is the greatest entry of A.

• If L is a non-empty list of real numbers, then max(L) is the greatest of the elements of L.

• If S is a non-empty set of real numbers, then max(S) is the greatest of the elements of S.

• If S is a structure containing real numbers, then max(S) is the greatest of the numbers in S.

Finding the greatest number in a sequence

max(expr, var, a, b) is the greatest value of expr as var takes all integer values from a to b, inclusively. expr must return a real value for every value of var in [a, b] ∩ ℤ. The number of elements in the sequence, b − a + 1, must be at least 1.

Examples

The greatest of two numbers

f ≔ x ↦ 5⋅max(x, 2)

custom function

Finding the greatest number in a container

max('(10/51, 49/256, 5/27, 6/29, 3/14, 24/121))

0.214285714286	(=3/14)

max(RandomVector(100))

0.991129796952

max(RandomIntMatrix(100, 100, 1000000))

999960

max(size(❨❨1, 2❩, ❨4, 1❩, ❨0, 1❩❩))

3

f ≔ n ↦ if(even(n), n/2, 3⋅n + 1);

n ≔ 27; L ≔ IteratedImages(f, n, 100); '(min(L), max(L))

23
9232

st ≔ n ↦ (c ≔ 0; k ≔ n; while(k ≠ 1, (k ≔ f(k); inc(c))); c);

max(SequenceVector(100) @ st)

118

max(compute(prime(succ(n)) − prime(n), n, 1, 1000000))

154

Finding the greatest number in a sequence

max(sin(k/2) + 5⋅cos(k/3) − sin(k/4), k, −10, 10)

5

f ≔ n ↦ if(even(n), n/2, 3⋅n + 1);

st ≔ n ↦ (c ≔ 0; k ≔ n; while(k ≠ 1, (k ≔ f(k); inc(c))); c);

max(st(n), n, 1, 100)

118

See also

• min