Minimal Degree Solutions for the Bezout Equation
We prove two results on the existence of bounds on the (global) degrees of polynomials Xt, solutions to the Bezout equation AtXt + ... + ArXr= C, with At, C, Xi in C[xlt ..., x„]. In the first theorem we require an algebraic hypothesis on the maximum degree homogeneous component of Alt ...,Ar, while the second result holds for all Bezout equations, but r = 2 is needed. Several variations and examples are discussed.
Ballico, E., & Struppa, D.C. (1987). Minimal degree solutions for the Bezout equation. Kybernetika 23(5), 360-364. Retrieved from http://dml.cz/bitstream/handle/10338.dmlcz/125882/Kybernetika_23-1987-5_2.pdf
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