### Linear Independence in Quotients of Polynomial Rings

Consider the following:

```
K = GF(2) # can be an arbitrary field
R.<a,b> = PolynomialRing(K)
I = R.ideal(a^2-1,a*b)
Q = R.quo(I)
```

Now $1,a,b$ are linearly dependent in `Q`

because $b=0$ (in `Q`

).

Is there an elegant way to check this with Sage, especially when the ideals get more complicated? That is: Is there a method to check whether ~~$(1,a_1,\dots,a_n)$ ~~$1,a_1,\dots,a_n$ are linearly (in)dependent in a given quotient $K[a_1,\dots,a_n]/I$?