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Note that as of Sage 5.7 (see trac #13393) the normalized method does what you'd expect; normalize has been deprecated, and monic is the old functionality.

sage: v = vector([3, 2, 1])
sage: v.normalized()       
(3/14*sqrt(14), 1/7*sqrt(14), 1/14*sqrt(14))
sage: v.monic()            
(1, 2/3, 1/3)

Note that as of Sage 5.7 (see trac #13393) the normalized method does what you'd expect; expect, normalize has been deprecated, and monic is the old functionality.

sage: v = vector([3, 2, 1])
sage: v.normalized()       
(3/14*sqrt(14), 1/7*sqrt(14), 1/14*sqrt(14))
sage: v.monic()            
(1, 2/3, 1/3)

Note that as of Sage 5.7 (see trac #13393) the normalized method does what you'd expect, normalize has been deprecated, and monic is the old functionality.

sage: v = vector([3, 2, 1])
sage: v.normalized()       
v.normalized()
(3/14*sqrt(14), 1/7*sqrt(14), 1/14*sqrt(14))
sage: v.monic()            
v.monic()
(1, 2/3, 1/3)