Abstract: In this review talk we expose remarkably tight relations between the four topics mentioned in the title. Starting from the paper by H.Abel published in 1826 and subsequent results of Chebyshev and Zolotarev we finish at the recent results by Burskii, Zhedanov, Malyshev (et al.) devoted to algorithmic decidability of some identities for the values of the Weierstrass P-function, unexpected elementary geometric applications and many, many more hidden equivalences in seemingly unrelated areas of analysis, modern computer algebra and geometry.
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