Symbolic calculation of greatest common divisor of 2D polynomial matrices

1995 ◽  
Vol 12 (1) ◽  
pp. 5-15
Author(s):  
D. S. JOHNSON ◽  
A. C. PUGH ◽  
G. E. HAYTON
Keyword(s):  
Greatest Common Divisor ◽  
Polynomial Matrices ◽  
Symbolic Calculation

scholarly journals Minor Prime Factorization for n-D Polynomial Matrices over Arbitrary Coefficient Field

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Jinwang Liu ◽  
Dongmei Li ◽  
Licui Zheng
Keyword(s):  
Computational Methods ◽  
Maximal Order ◽  
Greatest Common Divisor ◽  
Polynomial Matrices ◽  
Prime Factorization

In this paper, we investigate two classes of multivariate (n-D) polynomial matrices whose coefficient field is arbitrary and the greatest common divisor of maximal order minors satisfy certain condition. Two tractable criterions are presented for the existence of minor prime factorization, which can be realized by programming and complexity computations. On the theory and application, we shall obtain some new and interesting results, giving some constructive computational methods for carrying out the minor prime factorization.

Regular greatest common divisor of two polynomial matrices

1972 ◽  
Vol 72 (2) ◽  
pp. 161-165 ◽  
Author(s):  
S. Barnett
Keyword(s):  
Full Rank ◽  
Greatest Common Divisor ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Polynomial Matrices ◽  
Linearly Independent ◽  
The Matrix ◽  
Necessary And Sufficient

AbstractLet T(λ) and V(λ) be two polynomial matrices having dimensions l x l and m x l respectively, with T(λ) regular and of degree n and V(λ) of degree at most n – 1. It has recently been shown that a necessary and sufficient condition for T and V to be relatively right prime is that a certain nlm x nl matrix R(T, V) have full rank. It is shown here that if T and V have a greatest common right divisor D(λ), then provided D is regular, its degree k is equal to n – (1/l) rank R. Furthermore, if R˜. denotes the matrix of the first (n – k) lm rows of R, then it is shown that the last (n – k) l columns of R˜ are linearly independent and that the coefficient matrices of D can be obtained by expressing the remaining columns of R˜ in terms of this basis.

Approximate greatest common divisor of many polynomials and generalised resultants

2003 ◽  
Author(s):  
N. Karcanias ◽  
S. Fatouros ◽  
M. Mitrouli ◽  
G. Halikias
Keyword(s):  
Greatest Common Divisor

Interpolation algorithm of Leverrier–Faddev type for polynomial matrices

2006 ◽  
Vol 42 (3-4) ◽  
pp. 345-361 ◽  
Author(s):  
Marko D. Petković ◽  
Predrag S. Stanimirović
Keyword(s):  
Interpolation Algorithm ◽  
Polynomial Matrices
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