实对称型上的Schur子空间及应用

Schur Subspace of Real Symmetric Forms and Application

本文构作了Schur型多项式,将其作为研究实对称型的基础.研究了具有零点(1,1,...,1)的实对称型形成的子空间,即Schur子空间.建立了这种子空间的构造性理论,并应用于计算(构造)实代数几何中比较关心的对称型正性判定问题,以及给出一些特殊类型的Hilbert第17问题的构造解.

Schur type polynomial which the research base for the real symmetric form is constructed. Schur subspace which is consisted of the real symmetric polynomial vanishing at （1, 1,..., 1） is also studied. And constructive theory of Suchur subspace is built. As an application, we use them to determine the definition of symmetric forms and to solve some kind of the 17th Problem of Hilbert.