> > > I think the ring series can only be used for n terms, i.e. if you have > some expression, like sin(x)*cos(x), then you first expand sin(x) and > cos(x) into n-terms, and then you multiply them out, and cut the > result appropriately (at n-terms in this case). > > But you can use any "n". How do you store infinite number of terms in > your approach? > > FormalPowerSeries class, will compute the explicit formula for finding the coefficients. This formula can be plugged in sequences, which will generate coefficients lazily. Computed coefficients will be stored in a sparse representation (python dictionary), for retrieval at a later stage. The main benefit of this is that now users will be able to play around with infinite representation of Formal Power Series (addition, subtraction, etc) without explicitly computing the coefficients. Only computing when required. Much of this is inspired from lazy evaluation in Haskell. Sympy only supports truncated representation of series for now. My approach will allow infinite representation as well. Should series by default be truncated? (this allows good use of ring_series) or should their be separate representations for infinite and truncated representation?
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