Extension degree over function field

asked 2013-01-12 19:26:34 -0600

anonymous user

Anonymous

updated 2015-01-13 14:37:02 -0600

FrédéricC gravatar image

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!

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Comments

By y^2 - x^2 = 0, it means y = x or y = -x, the degree is one then.

nhut gravatar imagenhut ( 2013-01-14 21:21:17 -0600 )edit