低次微分多项式系统的Sibirsky理想生成元的构造

The Construction of Generators for the Sibirsky Ideals of Lower-Degree Polynomial Differential Systems

研究了低次微分多项式系统的Sibirsky理想生成元的构造问题,指出了Sibirsky理想可以由基本旋转不变量生成.通过给出一个具有12个变元的丢番图方程的基本正规解的上界,文章得到了丢番图方程的所有基本正规解,从而给出了五次多项式微分系统的所有基本旋转不变量,构造出五次多项式微分系统的Sibirsky理想生成元.最后,文章在MAPLE中实现了构造Sibirsky理想生成元的方法,将运行的结果与已知的Jarrah(2003)和刘一戎等人(1989, 2010)结论进行了比较.

In this paper, the construction of generators for the Sibirsky ideals of low degrees polynomial differential systems is investigated. It is concluded that the generators for the Sibirsky ideals can be computed by some rotational invariants.The upper bounder of the basic regular solution of a Diophantine equation with twelves variables is given. And all the basic rotational invariants of the fifth degree system are constructed. Sequently, the generators for the Sibirsky ideal of the fifth degree polynomial differential system are also constructed. Finally, the procedure of constructing generators for the Sibirsky ideal is realized in Maple and the results of the procedure are compared with the known conclusions from Jarrah and Liu, etc.