Greatest common divisors from generalized sylvester resultant matrices

1980 ◽  
Vol 8 (4) ◽  
pp. 271-279 ◽  
Author(s):  
Stephen Barnett
Keyword(s):  
Sylvester Resultant ◽  
Greatest Common Divisors

scholarly journals Weighted greatest common divisors and weighted heights

2020 ◽  
Vol 213 ◽  
pp. 319-346
Author(s):  
L. Beshaj ◽  
J. Gutierrez ◽  
T. Shaska
Keyword(s):  
Greatest Common Divisors

Some Interesting Mathematics about Prime Factorization

1975 ◽  
Vol 68 (1) ◽  
pp. 73-74
Author(s):  
Joe Tom Rodgers
Keyword(s):  
Prime Factorization ◽  
Factoring Polynomials ◽  
Greatest Common Divisors ◽  
School Careers

Throughout their school careers, students are taught how to find the prime factorization of numbers. Most students readily learn the technique and find the process interesting. Most teachers then teach the ways in which prime factorizations can aid in factoring polynomials and finding greatest common divisors as well as least common multiples.

GREATEST COMMON DIVISORS OF EUCLIDEAN DOMAIN MATRICES

2017 ◽  
Vol 101 (4) ◽  
pp. 855-872
Author(s):  
Nur Erawaty ◽  
Mawardi Bahri ◽  
Loecky Haryanto ◽  
Amir Kamal Amir
Keyword(s):  
Euclidean Domain ◽  
Greatest Common Divisors

scholarly journals Ordered groups with greatest common divisors theory

2000 ◽  
Vol 24 (7) ◽  
pp. 469-479
Author(s):  
Jiří Močkoř
Keyword(s):  
Abelian Group ◽  
Ordered Groups ◽  
Greatest Common Divisors

An embedding (called aGCD theory) of partly ordered abelian groupGinto abelian l-groupΓis investigated such that any element ofΓis an infimum of a subset (possible non-finite) fromG. It is proved that a GCD theory need not be unique. Acomplete GCD theoryis introduced and it is proved thatGadmits a complete GCD theory if and only if it admits a GCD theoryG→Γsuch thatΓis an Archimedean l-group. Finally, it is proved that a complete GCD theory is unique (up too-isomorphisms) and that a po-group admits the complete GCD theory if and only if anyv-ideal isv-invertible.

scholarly journals Greatest common divisors of iterates of polynomials

2017 ◽  
Vol 11 (6) ◽  
pp. 1437-1459 ◽  
Author(s):  
Liang-Chung Hsia ◽  
Thomas Tucker
Keyword(s):  
Greatest Common Divisors

The Position Analysis of Spherical Seven-Bar Mechanism

2011 ◽  
Vol 101-102 ◽  
pp. 193-196
Author(s):  
Zhao Feng Zhang ◽  
Zhi Huan Zhang
Keyword(s):  
Mathematical Model ◽  
Analytical Solutions ◽  
Polynomial Equation ◽  
Constraint Equations ◽  
Position Analysis ◽  
Numerical Example ◽  
Location Parameters ◽  
Sylvester Resultant ◽  
Univariate Polynomial

In this paper, we turn plane seven-bar mechanism into spherical seven-bar mechanism, using quaternion to construct mathematical model for spherical seven-bar mechanism. Three constraint equations are obtained according to the angles constraint. Using Sylvester resultant elimination by two steps, a 32 degree univariate polynomial equation can be obtained. A numerical example confirms that analytical solutions of spherical seven-bar mechanism are 32 and with the help of Mathematic software to solve the location parameters.

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