# Three New Methods for Computing Subresultant Polynomial Remainder Sequences (PRS’S)

Serdica Journal of Computing (2015)

- Volume: 9, Issue: 1, page 1-26
- ISSN: 1312-6555

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topAkritas, Alkiviadis. "Three New Methods for Computing Subresultant Polynomial Remainder Sequences (PRS’S)." Serdica Journal of Computing 9.1 (2015): 1-26. <http://eudml.org/doc/281368>.

@article{Akritas2015,

abstract = {Given the polynomials f, g ∈ Z[x] of degrees n, m, respectively,
with n > m, three new, and easy to understand methods — along with
the more efficient variants of the last two of them — are presented for the
computation of their subresultant polynomial remainder sequence (prs).
All three methods evaluate a single determinant (subresultant) of an
appropriate sub-matrix of sylvester1, Sylvester’s widely known and used
matrix of 1840 of dimension (m + n) × (m + n), in order to compute the
correct sign of each polynomial in the sequence and — except for the second
method — to force its coefficients to become subresultants.
Of interest is the fact that only the first method uses pseudo remainders.
The second method uses regular remainders and performs operations
in Q[x], whereas the third one triangularizes sylvester2, Sylvester’s little
known and hardly ever used matrix of 1853 of dimension 2n × 2n.
All methods mentioned in this paper (along with their supporting functions)
have been implemented in Sympy and can be downloaded from the link
http://inf-server.inf.uth.gr/~akritas/publications/subresultants.py},

author = {Akritas, Alkiviadis},

journal = {Serdica Journal of Computing},

keywords = {Pseudo Remainders; Subresultant prs’s; Sylvester’s Matrices},

language = {eng},

number = {1},

pages = {1-26},

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

title = {Three New Methods for Computing Subresultant Polynomial Remainder Sequences (PRS’S)},

url = {http://eudml.org/doc/281368},

volume = {9},

year = {2015},

}

TY - JOUR

AU - Akritas, Alkiviadis

TI - Three New Methods for Computing Subresultant Polynomial Remainder Sequences (PRS’S)

JO - Serdica Journal of Computing

PY - 2015

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 9

IS - 1

SP - 1

EP - 26

AB - Given the polynomials f, g ∈ Z[x] of degrees n, m, respectively,
with n > m, three new, and easy to understand methods — along with
the more efficient variants of the last two of them — are presented for the
computation of their subresultant polynomial remainder sequence (prs).
All three methods evaluate a single determinant (subresultant) of an
appropriate sub-matrix of sylvester1, Sylvester’s widely known and used
matrix of 1840 of dimension (m + n) × (m + n), in order to compute the
correct sign of each polynomial in the sequence and — except for the second
method — to force its coefficients to become subresultants.
Of interest is the fact that only the first method uses pseudo remainders.
The second method uses regular remainders and performs operations
in Q[x], whereas the third one triangularizes sylvester2, Sylvester’s little
known and hardly ever used matrix of 1853 of dimension 2n × 2n.
All methods mentioned in this paper (along with their supporting functions)
have been implemented in Sympy and can be downloaded from the link
http://inf-server.inf.uth.gr/~akritas/publications/subresultants.py

LA - eng

KW - Pseudo Remainders; Subresultant prs’s; Sylvester’s Matrices

UR - http://eudml.org/doc/281368

ER -

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