# inverse image under ring homomorphism

Hi there!

Just starting to learn Sage and can't get why both `inverse_image`

calls
below give an error saying the given element does not have a preimage,
while `y^2`

clearly has `xbar`

as preimage.

Referring to the generators of `R1`

and `R2`

explicitly doesn't help either.

```
sage: R.<x, y> = QQ[]
sage: R1 = R.quotient(R.ideal(y^2 - x^3))
sage: R2 = R.quotient(R.ideal(x))
sage: h = R1.hom([y^2, y^3], R2)
sage: h
Ring morphism:
From: Quotient of Multivariate Polynomial Ring in x, y over Rational Field by the ideal (-x^3 + y^2)
To: Quotient of Multivariate Polynomial Ring in x, y over Rational Field by the ideal (x)
Defn: xbar |--> y^2
ybar |--> y^3
sage: h.inverse_image(y)
Traceback (most recent call last)
...
ValueError: element y does not have preimage
sage: h.inverse_image(y^2)
Traceback (most recent call last)
...
ValueError: element y^2 does not have preimage
```

Thanks!