On the multiplicative complexity of polynomials
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Igor S. Sergeev
Abstract
We study the multiplicative (nonscalar) complexity μ(Md,n) for the class Md,n of complex polynomials in n variables of degree at most d. It is shown that the relation μ(Md,n) ≍ n⌈d/2⌉ holds for any constant d ≥ 2. The lower bound for odd values of d in this relation is new. For the case of cubic polynomials we prove more accurate bounds n2/18 ≲ μ(M3,n) ≲ n2/4.
Originally published in Diskretnaya Matematika (2022) 34, №3, 85–89 (in Russian).
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Articles in the same Issue
- Frontmatter
- Weakly supercritical branching process in unfavourable environment
- Classes of piecewise quasiaffine transformations on dihedral, quasidihedral and modular maximal-cyclic 2-groups
- On the multiplicative complexity of polynomials
- On the complexity of realizations of Boolean functions in some classes of hypercontact circuits
- On the rate of convergence of quasigroup convolutions of probability distributions
Articles in the same Issue
- Frontmatter
- Weakly supercritical branching process in unfavourable environment
- Classes of piecewise quasiaffine transformations on dihedral, quasidihedral and modular maximal-cyclic 2-groups
- On the multiplicative complexity of polynomials
- On the complexity of realizations of Boolean functions in some classes of hypercontact circuits
- On the rate of convergence of quasigroup convolutions of probability distributions
