# One point from infinity variety

Given an ideal, I want to compute a non-zero point in the variety of that ideal. This can be done with `.variety()`

if the ideal has 0-dimension. How can I get a non-zero point in the variety if the ideal is not 0-dimensional?

Example:

```
R.<x,y> = PolynomialRing(QQ)
I = R.ideal([x^2-y^2])
I.variety()
```

yields an error. How can I get a point like (1,1) which lies in the variety?

Thanks!

Cut by hyperplanes until the dimension is zero.

Thank you! Two problems come into my mind with that approach: 1. If I intersect with hyperplanes I do not necessarily reduce the dimension by 1. Say I start with dimension 3, I might get the entire ring (so no solution at all) just by adding one hyperplane. 2. I am searching for elements in the variety which are (say) rational. By intersecting with a hyperplane I might get rid of possible rational solutions. However, I suppose mathematically this problem should be quite hard, as it is already very difficult to find rational points on some "easy" curves.