# Creation of Lazy Series Rings

Both univariate and multivariate lazy series rings can be created.

## `LazyPowerSeriesRing(C, n): Rng, RngIntElt -> RngPowLaz`

The lazy power series ring with coefficient ring $C$ and $n$ variables. Any ring is valid input for $C$ and $n$ can be any positive integer.

## `ChangeRing(L, C): RngPowLaz, Rng -> RngPowLaz, Map`

Given a lazy series ring $L$ defined over a ring $R$ and some ring $C$, return the lazy series ring with coefficient ring $C$ but the same number of variables as $L$. A map from $L$ to the new lazy series ring is also returned which takes a series $s$ in $L$ to a series whose coefficients are those of $s$ coerced into $C$.

## `Example: Ring Create (ex-085add)`

Here we illustrate the creation and printing of lazy power series rings.

```magma
> L := LazyPowerSeriesRing(Rationals(), 5);
> L;
Lazy power series ring in 5 variables over Rational Field
> ChangeRing(L, MaximalOrder(CyclotomicField(7)));
Lazy power series ring in 5 variables over Maximal Equation Order with defining
polynomial x^6 + x^5 + x^4 + x^3 + x^2 + x + 1 over Z

```