|   | 1 |  initial version  | 
As seen in the documentation for Euclidean domains the Euclidean function is implemented as a method on elements named euclidean_degree:
sage: R.<x> = QQ[]
sage: x.euclidean_degree()
1
 Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.
 
                
                Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.