Comment #4 on issue 1900 by smichr: factor((1+2*x+x**2)**100) works too hard
http://code.google.com/p/sympy/issues/detail?id=1900
regarding commnent 1: expanding. I wonder if it's possible to never use real
expansion on a polynomial/multinomial once it's been created. e.g. you
don't have to
expand (1+x)**2 to know what the 3 terms will be, you already know what
they will be.
This, I believe, is what makes polynomial differentiation and integration
so fast.
Can the same insight be used when trying to figure out how to factor the
sum of
Polys?, e.g. Poly(1-x, x) + Poly(x**3+x,x) -> Poly(1-x**3,x) without having
to expand
the individual Polys and collect terms.
Perhaps there would be a Polyx object to represent a polynomial in expanded
form.
This would behave differently in printing and in substitution. e.g.
Polyx((1+x)**2)
would represent 1 + 2*x + x**2 and Polyx((1+x)**2).subs(2*x, a) -> 1 + a +
x**2 (the
substitution would force it out of the Polyx form.) Similarily,
Poly((1+x)**2).expand() -> Polyx((1+x)**2).
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