# Sturm Sequences and Modified Subresultant Polynomial Remainder Sequences

Akritas, Alkiviadis; Malaschonok, Gennadi; Vigklas, Panagiotis

Serdica Journal of Computing (2014)

- Volume: 8, Issue: 1, page 29-46
- ISSN: 1312-6555

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topAkritas, Alkiviadis, Malaschonok, Gennadi, and Vigklas, Panagiotis. "Sturm Sequences and Modified Subresultant Polynomial Remainder Sequences." Serdica Journal of Computing 8.1 (2014): 29-46. <http://eudml.org/doc/268663>.

@article{Akritas2014,

abstract = {ACM Computing Classification System (1998): F.2.1, G.1.5, I.1.2.In 1971 using pseudo-divisions - that is, by working in Z[x] -
Brown and Traub computed Euclid’s polynomial remainder sequences (prs’s)
and (proper) subresultant prs’s using sylvester1, the most widely known
form of Sylvester’s matrix, whose determinant defines the resultant of two
polynomials. In this paper we use, for the first time in the literature, the Pell-Gordon
Theorem of 1917, and sylvester2, a little known form of Sylvester’s matrix of 1853
to initially compute Sturm sequences in Z[x] without pseudodivisions -
that is, by working in Q[x]. We then extend our work in Q[x] and, despite
the fact that the absolute value of the determinant of
sylvester2 equals the absolute value of the resultant, we construct modified
subresultant prs’s, which may differ from the proper ones only in sign.This author is partly supported by project 2476 of the Government Task of the Russian
Ministry of Education and Science (No. 2014/285) and by project 12-07-00755 of Russian
Foundation for Basic Research.},

author = {Akritas, Alkiviadis, Malaschonok, Gennadi, Vigklas, Panagiotis},

journal = {Serdica Journal of Computing},

keywords = {Polynomials; Real Roots; Sturm Sequences; Sylvester’s Matrices; Matrix Triangularization},

language = {eng},

number = {1},

pages = {29-46},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {Sturm Sequences and Modified Subresultant Polynomial Remainder Sequences},

url = {http://eudml.org/doc/268663},

volume = {8},

year = {2014},

}

TY - JOUR

AU - Akritas, Alkiviadis

AU - Malaschonok, Gennadi

AU - Vigklas, Panagiotis

TI - Sturm Sequences and Modified Subresultant Polynomial Remainder Sequences

JO - Serdica Journal of Computing

PY - 2014

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 8

IS - 1

SP - 29

EP - 46

AB - ACM Computing Classification System (1998): F.2.1, G.1.5, I.1.2.In 1971 using pseudo-divisions - that is, by working in Z[x] -
Brown and Traub computed Euclid’s polynomial remainder sequences (prs’s)
and (proper) subresultant prs’s using sylvester1, the most widely known
form of Sylvester’s matrix, whose determinant defines the resultant of two
polynomials. In this paper we use, for the first time in the literature, the Pell-Gordon
Theorem of 1917, and sylvester2, a little known form of Sylvester’s matrix of 1853
to initially compute Sturm sequences in Z[x] without pseudodivisions -
that is, by working in Q[x]. We then extend our work in Q[x] and, despite
the fact that the absolute value of the determinant of
sylvester2 equals the absolute value of the resultant, we construct modified
subresultant prs’s, which may differ from the proper ones only in sign.This author is partly supported by project 2476 of the Government Task of the Russian
Ministry of Education and Science (No. 2014/285) and by project 12-07-00755 of Russian
Foundation for Basic Research.

LA - eng

KW - Polynomials; Real Roots; Sturm Sequences; Sylvester’s Matrices; Matrix Triangularization

UR - http://eudml.org/doc/268663

ER -

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