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Three New Methods for Computing Subresultant Polynomial Remainder Sequences (PRS’S)
| Content Provider | Semantic Scholar |
|---|---|
| Author | Akritas, Alkiviadis G. |
| Copyright Year | 2015 |
| 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 |
| Starting Page | 1 |
| Ending Page | 26 |
| Page Count | 26 |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://faculty.e-ce.uth.gr/akritas/publications/94.pdf |
| Volume Number | 9 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
