# How to find linear dependences between rational functions

- Assume I have a list of multivariable rational functions
- Assume I know (or Iat least I have good reasons to hope) that there is a linear relation, let say with integer coefficients, between all these rational functions. How can I find it?

For example, let

- C1=1/x
- C2=1/(x+y)
- C3=y/(x*(x+y))

then, it is easy to check that C1-C2-C3=0. However, how to find this relation automatically?

It does not seem that pari lindep can do it (which indeed is quite clear when reading pari doc):

```
x,y=var('x,y')
C1=1/x
C2=1/(x+y)
C3=y/(x*(x+y))
pari.lindep([C1,C2,C3])
```

returns

```
PariError: incorrect type in lindep_Xadic (t_RFRAC)
```

**NB.** Any Sagemath solution is welcome, even without using pari!