Minimal polynomial from the markov parameters of a system

1976 ◽  
Vol 21 (1) ◽  
pp. 133-134 ◽  
Author(s):  
Quang Tham
Keyword(s):  
Minimal Polynomial ◽  
Markov Parameters

scholarly journals DIOPHANTINE SETS OF POLYNOMIALS OVER ALGEBRAIC EXTENSIONS OF THE RATIONALS

2014 ◽  
Vol 79 (3) ◽  
pp. 733-747
Author(s):  
CLAUDIA DEGROOTE ◽  
JEROEN DEMEYER
Keyword(s):  
Minimal Polynomial ◽  
Finite Extension ◽  
Algebraic Extension ◽  
Recursively Enumerable

AbstractLet L be a recursive algebraic extension of ℚ. Assume that, given α ∈ L, we can compute the roots in L of its minimal polynomial over ℚ and we can determine which roots are Aut(L)-conjugate to α. We prove that there exists a pair of polynomials that characterizes the Aut(L)-conjugates of α, and that these polynomials can be effectively computed. Assume furthermore that L can be embedded in ℝ, or in a finite extension of ℚp (with p an odd prime). Then we show that subsets of L[X]k that are recursively enumerable for every recursive presentation of L[X], are diophantine over L[X].

scholarly journals Digital Identification and Control of Multivariable Plants Using Markov Parameters

2020 ◽  
Vol 53 (2) ◽  
pp. 3847-3853
Author(s):  
Anatoly R. Gaiduk ◽  
Vyacheslav Kh. Pshikhopov ◽  
Mikhail Yu. Medvedev
Keyword(s):  
Markov Parameters ◽  
Digital Identification ◽  
And Control

An extension of the Cobham-Semënov Theorem

2000 ◽  
Vol 65 (1) ◽  
pp. 201-211 ◽  
Author(s):  
Alexis Bès
Keyword(s):  
Characteristic Polynomial ◽  
Minimal Polynomial ◽  
Pisot Numbers ◽  
Numeration Systems

AbstractLet θ, θ′ be two multiplicatively independent Pisot numbers, and letU,U′ be two linear numeration systems whose characteristic polynomial is the minimal polynomial of θ and θ′, respectively. For everyn≥ 1, ifA⊆ ℕnisU-andU′ -recognizable thenAis definable in 〈ℕ: + 〉.

On the degree of the minimal polynomial of the Lyapunov operator

1974 ◽  
Vol 78 (3) ◽  
pp. 229-236 ◽  
Author(s):  
Marvin Marcus ◽  
M. Shafqat Ali
Keyword(s):  
Minimal Polynomial ◽  
Lyapunov Operator
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