[with patch, positive review] make an apply_map function for vectors

[jason]

Matrices have the function; it would be handy for vectors to also have this utility function.

[was]

You could also do this in the first example:

sage: m = vector(ZZ, 9, range(9)) 
sage: k.<a> = GF(9) 
sage: m.apply_map(k)
(0, 1, 2, 0, 1, 2, 0, 1, 2)

I think it would be nice to have a really simple first example, that requires much less knowledge of "abstract algebra". Maybe the first example could be for engineers or something?

sage: m = vector([1,x,sin(x+1)])
sage: m.apply_map(x^2)
(1, x^2, sin(x + 1)^2)
sage: m.apply_map(sin)
(sin(1), sin(x), sin(sin(x + 1)))

[was]

By the way, definitely positive review pending adding the doctests suggested above.

[jason]

updated patch with the suggestions. Accordingly, marking this positive review.

[mabshoff]

Merged in Sage 3.2.2.alpha1