A fast algorithm for solving linearly recurrent sequences
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We present an algorithm which computes the D^th term of a sequence satisfying a linear recurrence relation of order d over a field K in O( M(d̅)log(D) + M(d)log(d)) operations in K, where d̅≤ d is the degree of the squarefree part of the annihilating polynomial of the recurrence and M is the cost of polynomial multiplication in K. This is a refinement of the previously optimal result of O( M(d)log(D) ) operations, due to Fiduccia.
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