# define a polynomial ring

Dear all,

```
sage: R.<x> = PolynomialRing(QQ); R
Univariate Polynomial Ring in x over Rational Field
sage: R([1,2,3])
3*x^2 + 2*x + 1
sage: R1.<x> = PolynomialRing(QQ,1); R1
Multivariate Polynomial Ring in x over Rational Field
sage: R1([1,2,3])
---------------------------------------------------------------------------
TypeError: Could not find a mapping of the passed element to this ring.
```

```
Note that a multivariate polynomial ring is returned when an
explicit number is given.
sage: PolynomialRing(QQ,"x",1)
Multivariate Polynomial Ring in x over Rational Field
sage: PolynomialRing(QQ,"x",0)
Multivariate Polynomial Ring in no variables over Rational Field
```

I want to know the reason .. Why

a multivariate polynomial ring is returned when an explicit number is given.

?

Does it offer users of SAGE any simplicity/convenience?

Thanks in advance!