键合多项式p-不可约的一些结果

Some results for determining p-irreducibility of binding polynomials

在生物化学研究领域,对键合多项式p-不可约性的判定是一个重要问题.已有结果主要考虑四次或四次以下多项式.应用实代数几何和多项式稳定性等理论,借助计算机代数系统Maple 9.5,对键合多项式p-不可约问题进行了进一步的研究,给出了五次键合多项式p-不可约的二组充分条件.同时,从正分解角度重新考虑了四次键合多项式,给出了四次键合多项式一种正分解的充要条件.所有条件都是用多项式的系数构成的不等式组显式表示的.

The problem of deciding whether a binding polynomial has positive decompositions is important in studying biochemistry process. Many existing results about this were confined to the polynomials with degree less than five and few were reported on the result concerning the positive polynomials with degree five. Combining the knowledge of real algebraic geometry and polynomials stability, two sets of sufficient conditions for judging the p-irreducibility are given. Moreover, the binding polynomials with degree four from the aspect of positive decomposition is reconsid- ered, and the necessary and sufficient condition for some positive decomposition are given. The main results were expressed by some inequalities composed of the coefficients of the positive polynomial.