Dear all,
As some of you might know I am trying to optimize the way in which cluster
algebras are implemented in sage. 

In my current implementation one of the biggest bottleneck happens when 
I take powers of polynomials in n variables (n is usually much smaller than
10) with integer coefficients and quite high degrees (few hundreds). 
The way I am computing things now is, probably, the dumbest possible:

sage: f in PolynomialRing(ZZ,'u0,u1,u2')
True
sage: f.degree()
159
sage: len(f.monomials())
18105
sage: %time foo = f**2
CPU times: user 4min 30s, sys: 5 ms, total: 4min 30s
Wall time: 4min 30

Is there some clever way to save some time here or it is just hopeless?
Thanks
S.




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