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