# Relations in a polynomial ring

Suppose Sage hands me a multivariable polynomial ring specified by some number of generators, and some relations that I don't know. How can I get a list of relations among the generators? In particular, here is the code I'm using:

```
rays = [(0,0,1),(1,0,-2),(0,1,-2),(-1,0,-2),(0,-1,-2)]
cones = [(1,2,3,4)]
Delta = Fan(cones,rays)
T = ToricVariety(Delta)
R = T.affine_patch(0).coordinate_ring()
```

I've tried defining a morphism from R to itself which just sends the generators to themselves, then computing a groebner basis for the ideal of the kernel.

```
generators = R.gens()
phi = R.hom(generators)
```

Sage doesn't seem to let me do this, since kernel isn't implemented for morphisms defined this way. At this point I'm not sure what else to try. I feel like there must be a simpler way to extract relations among generators in a ring, but after spending a couple of days scouring the documentation I can't seem to notice anything relevant. Help is much appreciated!