McKee, James Computing division polynomials. (English) Zbl 0864.12007 Math. Comput. 63, No. 208, 767-771 (1994). Summary: Recurrence relations for the coefficients of the \(n\)-th division polynomial for elliptic curves are presented. These provide an algorithm for computing the general division polynomial without using polynomial multiplications; also a bound is given for the coefficients, and their general shape is revealed, with a means for computing the coefficients as explicit functions of \(n\). Cited in 6 Documents MSC: 12Y05 Computational aspects of field theory and polynomials (MSC2010) 14Q05 Computational aspects of algebraic curves 11G05 Elliptic curves over global fields 11Y16 Number-theoretic algorithms; complexity Keywords:recurrence relations; coefficients of the \(n\)-th division polynomial for elliptic curves × Cite Format Result Cite Review PDF Full Text: DOI Online Encyclopedia of Integer Sequences: Number of sequences of n coin flips that win on the last flip, if the sequence of flips ends with (1,1,0) or (1,0,0). References: [1] Alfred V. Aho, John E. Hopcroft, and Jeffrey D. Ullman, The design and analysis of computer algorithms, Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1975. Second printing; Addison-Wesley Series in Computer Science and Information Processing. · Zbl 0326.68005 [2] R. Fricke, Die elliptischen Funktionen und ihre Anwendungen, Vol. 2, Teubner, Leipzig, 1922. · JFM 48.0432.01 [3] Joseph H. Silverman, The arithmetic of elliptic curves, Graduate Texts in Mathematics, vol. 106, Springer-Verlag, New York, 1986. · Zbl 0585.14026 [4] H. Weber, Lehrbuch der Algebra. III, 3rd ed., Chelsea, New York, 1961. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.