# Defining a power series with variable coefficients

It is not difficult to define a multivariate power series; for example, the following works:

```
R.<a,x,y> = PowerSeriesRing(ZZ,3)
f = a*x + y + x*y + O(a,x,y)^3
```

But what I would really like is to treat the series `f`

as a series in `x`

and `y`

, with `a`

acting as a variable coefficient, so that, for example, I could instead write `f = a*x + y + x*y + O(x,y)^3`

. I tried the following:

```
M = PolynomialRing(ZZ,'a')
R.<x,y> = PowerSeriesRing(M,2)
f = a*x + y + x*y + O(x,y)^3
f
```

This generates the error "name `a`

is not defined." What can I do to get `a`

into the coefficient ring?