Documentation

# le

Define less than or equal to condition

## Syntax

``A <= B``
``le(A,B)``

## Description

example

````A <= B` defines the condition less than or equal to.```
````le(A,B)` is equivalent to `A <= B`.```

## Examples

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Set the assumption that `x` is less than or equal to 3 by using `assume`.

```syms x cond = x <= 3; assume(cond)```

Solve an equation for `x`. The solver only returns solutions that are valid under the assumption on `x`.

```eqn = (x-1)*(x-2)*(x-3)*(x-4) == 0; solve(eqn,x)```
```ans = 1 2 3```

Set the condition `abs(sin(x)) <= 1/2`.

```syms x cond = abs(sin(x)) <= 1/2;```

Find multiples of π/24 that satisfy the condition by using a `for` loop from `0` to π.

```for i = 0:sym(pi/12):sym(pi) if subs(cond, x, i) disp(i) end end```
```0 pi/12 pi/6 (5*pi)/6 (11*pi)/12 pi```

## Input Arguments

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Input, specified as a number, vector, matrix, or array, or a symbolic number, variable, array, function, or expression.

Input, specified as a number, vector, matrix, or array, or a symbolic number, variable, array, function, or expression.

## Tips

• Calling `<=` or `le` for non-symbolic `A` and `B` invokes the MATLAB® `le` function. This function returns a logical array with elements set to logical ```1 (true)``` where `A` is less than or equal to `B`; otherwise, it returns logical ```0 (false)```.

• If both `A` and `B` are arrays, then these arrays must have the same dimensions. `A <= B` returns an array of relations `A(i,j,...) <= B(i,j,...)`.

• If one input is scalar and the other an array, then the scalar input is expanded into an array of the same dimensions as the other array.

• The field of complex numbers is not an ordered field. MATLAB projects complex numbers in relations to the real axis. For example, `x <= i` becomes `x <= 0`, and ```x <= 3 + 2*i``` becomes `x <= 3`.