Hi,

I've been working on making the printing of polynomials prettier and
more consistent between the univariate setting and the multivariate
one.

There is one ticket (with patch) on trac now at

http://trac.sagemath.org/sage_trac/ticket/6551

which focuses on the case of exact coefficients and fixes things like
unnecessary parentheses.


Another issue comes up in the case of inexact coefficients.  Compare these two:

{{{
sage: R.<x> = RR[]
sage: x^2 - 3.2*x + 1
1.00000000000000*x^2 - 3.20000000000000*x + 1.00000000000000
sage:
sage: R.<x, y> = RR[]
sage: x^2 - 3.2*x*y + y
x^2 - 3.20000000000000*x*y + y
}}}

I'd like the second example to look more like the first and it's
pretty easy to make that happen.  However, this means:

{{{
sage: x
1.00000000000000*x
sage: y
1.00000000000000*y
sage: (x^2 - y).variables()
[1.00000000000000*x, 1.00000000000000*y]
}}}

I'm ok with the first two, but the last thing causes all sorts of
problems in many places that expect the list to be [x, y].

However, I'm not sure why .variables() needs to return the variables
*as elements of the polynomial ring*, as opposed to, say, strings such
as ['x', 'y'].  I would be tempted to make this change, but it's
fairly drastic and needs some discussion here.


Best,
Alex

-- 
Alex Ghitza -- Lecturer in Mathematics -- The University of Melbourne
-- Australia -- http://www.ms.unimelb.edu.au/~aghitza/

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