Abstract
We present a degree bound for computation trees with equality testing due to Strassen [504]. More specifically, we prove a general lower bound on the multiplicative complexity of collections for subsets of k n, where k is algebraically closed, resp. an arbitrary infinite field. Two applications to the problem of computing the Euclidean representation of two polynomials are discussed. First, we give Strassen’s optimality proof of the Knuth-Schönhage algorithm which has been presented in Sect. 3.1. Then we discuss Schuster’s lower bound [467] for the problem of computing just the degree pattern of the Euclidean representation. The latter relies on an analysis of the Euclidean representation by means of the subresultant theorem.
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© 1997 Springer-Verlag Berlin Heidelberg
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Bürgisser, P., Clausen, M., Shokrollahi, M.A. (1997). Branching and Degree. In: Algebraic Complexity Theory. Grundlehren der mathematischen Wissenschaften, vol 315. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03338-8_10
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DOI: https://doi.org/10.1007/978-3-662-03338-8_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08228-3
Online ISBN: 978-3-662-03338-8
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