# Documentation

### This is machine translation

Translated by
Mouseover text to see original. Click the button below to return to the English verison of the page.

# `groebner`::`eliminate`

Eliminate variables

MATLAB live scripts support most MuPAD functionality, though there are some differences. For more information, see Convert MuPAD Notebooks to MATLAB Live Scripts.

## Syntax

```groebner::eliminate(`sys`, `vars`)
```

## Description

`groebner::eliminate(sys, vars)` returns a list of polynomial expressions obtained by eliminating the elements of `vars` from `sys`. In other words, the return value does not contain the variables in `vars`, every zero of the original system `sys` must be a zero of the return value, and every tuple of numbers that makes the return value zero can be extended to a solution of `sys`.

## Examples

### Example 1

Suppose that x2 + y = 0 and x + y = 0, what does this imply for y?

`groebner::eliminate({x^2 +y, y+x}, {x})`

We infer that for every pair (x, y) solving the system, y must satisfy y2 + y = 0, that is, y = 0 or y = - 1. Indeed:

`solve({x^2 +y, y+x}, {x, y})`

## Parameters

 `sys` A set or list of polynomial expressions. The coefficients in these polynomial expressions can be arbitrary arithmetical expressions. `vars` A set or list of identifiers

## Return Values

List of polynomial expressions

## Algorithms

`groebner::eliminate` proceeds by computing a lexical-order Gröbner basis. Hence the computation complexity grows fast when increasing the number of variables.