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Lazy Fourier Series #32307

Open mantepse opened 3 years ago

mantepse commented 3 years ago

We possibly implement a lazy version of Fourier series.

CC: @slel @tscrim

Component: calculus

Author: Martin Rubey

Issue created by migration from https://trac.sagemath.org/ticket/32307

mantepse commented 3 years ago

Author: Martin Rubey

mantepse commented 3 years ago

Description changed:

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+We possibly implement a lazy version of Fourier series.
mantepse commented 11 months ago

I realized that this is probably nonsense, because I cannot define multiplication in a formal way. Suppose that we have $s = \sum _{n\geq 0} a_n \cos(n x) +b_n \sin(n x)$, then the constant term of $s^2$ is not well defined, since $\cos(nx)^2 = (\cos(2n x) + 1)/2$.

I guess, formal series make sense only if the grading is such that the degree of a product of homogeneous elements is at least the minimum of the degrees of the factors, right?