﻿ min – Algosim documentation
Algosim documentation: min

# min

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

## Syntax

• `min(a, b)`

• `a` is a real number

• `b` is a real number

• `min(X)`

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

• `min(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 smallest of two numbers

If `a` and `b` are real numbers, then `min(a, b)` is the smallest of them.

### Finding the smallest number in a container

• If `v` is a real vector, then `min(v)` is the smallest component of `v`.

• If `A` is a real matrix, then `min(A)` is the smallest entry of `A`.

• If `L` is a non-empty list of real numbers, then `min(L)` is the smallest of the elements of `L`.

• If `S` is a non-empty set of real numbers, then `min(S)` is the smallest of the elements of `S`.

• If `S` is a structure containing real numbers, then `min(S)` is the smallest of the numbers in `S`.

### Finding the smallest number in a sequence

`min(expr, var, a, b)` is the smallest 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 smallest of two numbers

`f ≔ x ↦ 5⋅min(x, 2)`
`custom function`

### Finding the smallest number in a container

`min('(10/51, 49/256, 5/27, 6/29, 3/14, 24/121))`
`0.185185185185	(=5/27)`
`min(RandomVector(100))`
`0.00970940268598`
`min(RandomIntMatrix(100, 100, 1000000))`
`135`
`min(size(❨❨1, 2❩, ❨4, 1❩, ❨0, 1❩❩))`
`2`
`f ≔ n ↦ if(even(n), n/2, 3⋅n + 1);`
`n ≔ 27; L ≔ IteratedImages(f, n, 100); '(min(L), max(L))`
```23
9232
```

### Finding the smallest number in a sequence

`min(sin(k/2) + 5⋅cos(k/3) − sin(k/4), k, −10, 10)`
`−6.70556579756`