论文信息 - On the Relation Between Matrices and the Greatest Common Divisor of Polynomials

On the Relation Between Matrices and the Greatest Common Divisor of Polynomials

Following the Barnett’s approach to gcd(a(x),b(x)) based on the use of companion matrix we develop an extended algorithm that gives effectively \(d(x),\ u(x),\ v(x),\ a_1(x)\) and \(b_1(x)\), where \(a_1(x)=a(x)/d(x), b_1(x)=b(x)/d(x)\) and \(d(x)=u(x)a(x)+v(x)b(x).\) The algorithm is suitable for parallel realization on GPU, FPGA, and smart cards.

Nikolai L. Manev

[1] L. González-Vega. An elementary proof of Barnett's theorem about the greatest common divisor of several univarlate polynomials , 1996 .

[2] C. Macduffee. Some Applications of Matrics in the Theory of Equations , 1950 .

[3] M. Laidacker. Another Theorem Relating Sylvester's Matrix and the Greatest Common Divisor , 1969 .

[4] S. Barnett,et al. Greatest common divisor of two polynomials , 1970 .

[5] C. Macduffee. Some Applications of Matrices in the Theory of Equations , 1950 .

[6] Laureano Gonzalez-Vega,et al. Computing greatest common divisors and squarefree decompositions through matrix methods: The parametric and approximate cases , 2006 .