论文标题
原始递归有序字段和某些应用
Primitive Recursive Ordered Fields and Some Applications
论文作者
论文摘要
我们建立了有关真实和可计算真实的可计算有序字段的一些已知事实的原始递归版本，然后将它们应用于线性代数和分析中某些自然问题的原始递归性。特别是，我们发现了Ershov-Madison的局部原始递归类似物关于可计算有序场的真实封闭的定理，将相应的字段与原始递归真实物相关联，为原始的递归递归辅助辅助，计算正常矩阵的计算矩阵和计算量的计算求解器提供了足够的条件。
We establish primitive recursive versions of some known facts about computable ordered fields of reals and computable reals, and then apply them to proving primitive recursiveness of some natural problems in linear algebra and analysis. In particular, we find a partial primitive recursive analogue of Ershov-Madison's theorem about real closures of computable ordered fields, relate the corresponding fields to the primitive recursive reals, give sufficient conditions for primitive recursive root-finding, computing normal forms of matrices, and computing solution operators of some linear systems of PDE.
