﻿ max – Algosim documentation
Algosim documentation: max

# 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`