# Groebner bases

`Symbolics.groebner_basis`

— Functiongroebner_basis(polynomials; ordering=:deglex)

Computes a Groebner basis of the ideal generated by the given `polynomials`

. The basis is reduced, thus guaranteed to be unique.

**Example**

```
julia> using Symbolics
julia> @variables x y;
julia> groebner_basis([x*y^2 + x, x^2*y + y])
```

The coefficients in the resulting basis are in the same domain as for input polynomials. Hence, if the coefficient becomes too large to be represented exactly, `DomainError`

is throwed.

By default, degree lexicographic monomial ordering is used. All possible orderings are:

`lex`

for lexicographic;`deglex`

for degree lexicographic;`degrevlex`

for degree reversed lexicographic.

The basis will be correct with respect to the specified ordering, however, the terms in the output will always be ordered with `deglex`

.