A quasioptimal lower bound for skew polynomial multiplication
Abstract
We establish a lower bound for the complexity of multiplying two skew polynomials. The lower bound coincides with the upper bound conjectured by Caruso and Borgne in 2017, up to a log factor. We present algorithms for three special cases, indicating that the aforementioned lower bound is quasioptimal. In fact, our lower bound is quasioptimal in the sense of bilinear complexity. In addition, we discuss the average bilinear complexity of simultaneous multiplication of skew polynomials and the complexity of skew polynomial multiplication in the case of towers of extensions.
 Publication:

arXiv eprints
 Pub Date:
 February 2024
 DOI:
 10.48550/arXiv.2402.04134
 arXiv:
 arXiv:2402.04134
 Bibcode:
 2024arXiv240204134C
 Keywords:

 Computer Science  Computational Complexity;
 Computer Science  Symbolic Computation;
 Mathematics  Rings and Algebras