Results 231 to 240 of about 6,569 (263)

The Complexity of the Minimal Polynomial

2001
We investigate the computational complexity of the minimal polynomial of an integer matrix. We show that the computation of the minimal polynomial is in AC0(GapL), the AC0-closure of the logspace counting class GapL, which is contained in NC2. Our main result is that the problem is hard for GapL (under AC0 many-one reductions). The result extends to
Thanh Minh Hoang, Thomas Thierauf
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Minimal polynomial realizations

Mathematics of Control, Signals, and Systems, 1988
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Minimal ⁎-varieties and minimal supervarieties of polynomial growth

Journal of Algebra, 2020
Let \(\mathfrak M\) be variety of algebras. Consider a space \(V_n\) of multilinear words of length \(n\) over alphabet \(x_1,\dots,x_n\) in relatively free algebra in \(\mathfrak M\), \(n_k=\dim(V_k)\). The sequence \(\{n_k\}\) is a \textit{codimension sequence} of the variety \(\mathfrak M\). Codimension sequence was introduced by \textit{A.
Tatiana Aparecida Gouveia, Rafael Bezerra dos Santos, Ana Cristina Vieira   +2 more
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A Method to Compute Minimal Polynomials

SIAM Journal on Algebraic Discrete Methods, 1985
Let f(X) and g(X) be polynomials with coefficients in an arbitrary field K. Assume that f(X) is irreducible and let r be a root of f(X). We describe a new algorithm for computing the minimal polynomial of g(r) over K. The novelty of our algorithm is that it begins by computing the polynomial p(X,Y) of smallest degree such that \(p(f,g)=0\).
Peskin, Barbara R., Richman, David R.
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Minimal degrees for polynomial reducibilities

Journal of the ACM, 1987
The existence of minimal degrees is investigated for several polynomial reducibilities. It is shown that no set has minimal degree with respect to polynomial many-one or Turing reducibility. This extends a result of Ladner in which only recursive sets are considered. A polynomial reducibility ≤ h
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The RCH method for computing minimal polynomials of polynomial matrices

Journal of Systems Science and Complexity, 2014
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Bo Yu 0003, Jintao Zhang, Yanyan Xu
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Minimal Balanced Neighborly Polynomials

Acta Mathematica Vietnamica
The study of balanced neighborly polynomials (BNPs) was initiated motivated by an existence problem of balanced neighborly simplicial spheres. The existence of balanced neighborly simplicial spheres is an interesting problem in a combinatorial study of face numbers of simplicial complexes, since if a balanced neighborly simplicial spheres of type \((d,\
Satoshi Murai, Nguyen Thi Thanh Tam
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On Interpolating Polynomials of Minimal Degree

SIAM Review, 1977
Given an incidence matrix E, the general problem of interpolating data on E is investigated. The objective of determining the polynomials of minimal degree satisfying the data is solved by consider...
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On multivariate minimal polynomials

Mathematical Proceedings of the Cambridge Philosophical Society, 2000
Let \(E\) be a compact subset of \({\mathbb C}^n\) and let \(\alpha \in {\mathbb Z}^n_+\) be a multiindex of length \(d:=|\alpha|\). Consider the classes of polynomials \(\mathbb P (\alpha):= \{p; p(z) = z^{\alpha}+\sum_{|\beta \leq d-1}c_{\beta}z^{\beta}\}\) and \(\mathcal P(\alpha):= \{p; p(z):= z^{\alpha}+\sum_{\beta \prec \alpha} c_{\beta}z^{\beta}\
Bloom, Thomas, Calvi, Jean-Paul
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FACTORING VARIANTS OF CHEBYSHEV POLYNOMIALS WITH MINIMAL POLYNOMIALS OF

Bulletin of the Australian Mathematical Society, 2022
AbstractWe solve the problem of factoring polynomials $V_n(x) \pm 1$ and $W_n(x) \pm 1$ , where $V_n(x)$ and $W_n(x)$ are Chebyshev polynomials of the third and fourth kinds, in terms of the minimal polynomials of $\cos ({2\pi }{/d})$ . The method of proof is based on earlier work, D. A. Wolfram, [‘Factoring variants of Chebyshev polynomials of
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