### Extension degree over function field

Hello!

I would like to compute the extension degree over a function field.

So I use the commend "degree()".
But I found it didn't work well.
It produces always just the degree of the polynomial.

For example,

sage: K.<x> = FunctionField(QQ)
sage: R.<y> = K[]
sage: L.<y> = K.extension(y^2 - (x^2)); L
Function field in y defined by y^2 - x^2
sage: L.degree()
2

In fact, the extension degree [L:K] = 1.

What's wrong?

I'd appreciate it if you could let me know how to compute the extension
degree over a function field?

Thank you!