论文标题
线性方程的轨道限制系统的溶解度
Solvability of orbit-finite systems of linear equations
论文作者
论文摘要
我们在用原子的集合设置线性方程的轨道限制系统。我们的主要贡献是此类系统解决性的决策程序。该过程适用于轻度有效性假设下的每个字段（甚至是交换环），并将给定的轨道限制系统降低到许多有限的系统：总体上许多有限的系统，但是当输入系统的原子维度固定时，多数态上很多。为了获得该过程，我们进一步推动了轨道限制集合产生的向量空间理论，并表明每个矢量空间都允许轨道限制。这种基本财产是我们开发的关键工具，但也应该具有更广泛的兴趣。
We study orbit-finite systems of linear equations, in the setting of sets with atoms. Our principal contribution is a decision procedure for solvability of such systems. The procedure works for every field (and even commutative ring) under mild effectiveness assumptions, and reduces a given orbit-finite system to a number of finite ones: exponentially many in general, but polynomially many when atom dimension of input systems is fixed. Towards obtaining the procedure we push further the theory of vector spaces generated by orbit-finite sets, and show that each such vector space admits an orbit-finite basis. This fundamental property is a key tool in our development, but should be also of wider interest.
