Corrigendum to "A long note on Mulders' short product" [J. Symb. Comput 37 (3) (2004) 391-401]
نویسندگان
چکیده
In Algorithm ShortProduct (Hanrot and Zimmermann, 2004, pp. 394–395), at the final step, read return ( ( x2 + xmx2+ x2hx2 mod x. In the printed version, the result might have degree n: if n is odd from the term xm(x2), or if n is even from x2h(x2). The proof of Theorem 2 actually only proves that the result of Algorithm ShortProduct is congruent to f g modulo xn , not that it has degree < n. With the correction above, this is obvious. Note that it does not change the number of ring operations as it is merely a truncation step. DOI of original article: http://dx.doi.org/10.1016/j.jsc.2003.03.001. E-mail addresses: [email protected] (G. Hanrot), [email protected] (P. Zimmermann). URLs: http://perso.ens-lyon.fr/guillaume.hanrot (G. Hanrot), http://www.loria.fr/~zimmerma (P. Zimmermann). http://dx.doi.org/10.1016/j.jsc.2014.02.002 0747-7171/© 2014 Elsevier Ltd. All rights reserved. 112G. Hanrot, P. Zimmermann / Journal of Symbolic Computation 66 (2015) 111–112 AcknowledgementsThe authors would like to thank Bill Allombert and Karim Belabas for pointing this mistake.ReferencesHanrot, G., Zimmermann, P., 2004. A long note on Mulders’ short product. J. Symb. Comput. 37, 391–401.
منابع مشابه
A long note on Mulders' short product
The short product of two power series is the meaningful part of the product of these objects, i.e., ∑ i+ j<n ai b j xi+ j . Mulders (AAECC 11 (2000) 69) gives an algorithm to compute a short product faster than the full product in the case of Karatsuba’s multiplication (Karatsuba and Ofman, Dokl. Akad. Nauk SSSR 145 (1962) 293). This algorithm works by selecting a cutoff point k and performing ...
متن کاملA Note on Subresultants and the Lazard/Rioboo/Trager Formula in Rational Function Integration
An ambiguity in a formula of Lazard, Rioboo and Trager, connecting subresultants and rational function integration, is indicated and examples of incorrect interpretations are given.
متن کاملOn lattice reduction for polynomial matrices
A simple algorithm for lattice reduction of polynomial matrices is described and analysed. The algorithm is adapted and applied to various tasks, including rank profile and determinant computation, transformation to Hermite and Popov canonical form, polynomial linear system solving and short vector computation. © 2003 Elsevier Science Ltd. All rights reserved.
متن کاملNote on Jacobi's method for approximating dominant roots
In 1834 C. G. J. Jacobi gave a method for approximating dominant roots of a polynomial. In 2002 M. Mignotte and D. Stefanescu showed that Jacobi’s method works only when the dominant roots are simple. In this note, we show that Jacobi’s method can be still useful even when the dominant roots are not simple, if we use it for approximating the “distinct” dominant roots.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Symb. Comput.
دوره 66 شماره
صفحات -
تاریخ انتشار 2015