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Division-free computation of subresultants using bezout matrices

Kerber, Michael

May 2006, 20 pages.

Status: available - back from printing

We present an algorithm to compute the subresultant sequence of two polynomials that completely avoids division in the ground domain, generalizing an algorithm from Abdeljaoued et al.\ (see Abdeljaoed et al.: Minors of Bezout Matrices\ldots, Int.\ J.\ of Comp.\ Math.\ 81, 2004). This is done by evaluating determinants of slightly manipulated Bezout matrices using an algorithm of Berkowitz. Experiments show that our algorithm is superior compared to pseudo-division approaches for moderate degrees if the domain contains indeterminates.

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  AUTHOR = {Kerber, Michael},
  TITLE = {Division-free computation of subresultants using bezout matrices},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Stuhlsatzenhausweg 85, 66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-2006-1-006},
  MONTH = {May},
  YEAR = {2006},
  ISSN = {0946-011X},