ASKSAGE: Sage Q&A Forum - Individual question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Mon, 14 Jan 2013 21:21:17 -0600Extension degree over function fieldhttps://ask.sagemath.org/question/9706/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!
Sat, 12 Jan 2013 19:26:34 -0600https://ask.sagemath.org/question/9706/extension-degree-over-function-field/Comment by nhut for <p>Hello!</p>
<p>I would like to compute the extension degree over a function field.</p>
<p>So I use the commend "degree()".
But I found it didn't work well.
It produces always just the degree of the polynomial.</p>
<p>For example,</p>
<pre><code>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
</code></pre>
<p>In fact, the extension degree [L:K] = 1.</p>
<p>What's wrong?</p>
<p>I'd appreciate it if you could let me know how to compute the extension
degree over a function field?</p>
<p>Thank you!</p>
https://ask.sagemath.org/question/9706/extension-degree-over-function-field/?comment=18395#post-id-18395By y^2 - x^2 = 0, it means y = x or y = -x, the degree is one then.Mon, 14 Jan 2013 21:21:17 -0600https://ask.sagemath.org/question/9706/extension-degree-over-function-field/?comment=18395#post-id-18395