Comment #6 on issue 1562 by mattpap: Have trigsimp apply factor and  
Poly.cancel() to sin's and cos's
http://code.google.com/p/sympy/issues/detail?id=1562

OK, I misunderstood you. Here you touch a much more general problem of how  
should the
(an) internal representation of expressions look like (mainly what should  
be stored
in `args` and how they should be accessed, which is currently messed up. As  
long as
you play with core classes everything should be fine. Some classes,  
however, make
things complicated by storing non-Basic elements in `args`. Poly, Integral,  
Sum are
good examples of violation of some rules (I say some rules because I can't  
recall if
there was any design specification how to play with `args`, e.g. there is  
function
`iter_basic_args` for convenience but it isn't implemented everywhere,  
where it
should be. So for now new Poly don't mess with `args` at all, but this will  
solve the
problem only temporarily (really it hides it).

> I think we should make RootOf to be more of a user class

Perfectly agree. Current version of RootOf is a very naive implementation,  
just for
completeness, rather for real usage. Much more care must be put to make  
this class
useful for day-to-day work. I don't like to play with rootfinding code, so  
it's the
only thing not touched at all in new implementation of polys.

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