论文标题
算法在差分代数中产生上限
Algorithms yield upper bounds in differential algebra
论文作者
论文摘要
考虑在差分字段中具有几个通勤派生的算法计算，以便其唯一与该领域元素执行的操作是算术操作，分化和零测试。我们表明，如果保证在每个输入上终止算法，那么就输入的大小而言，对于算法的输出大小，有一个可计算的上限。我们还将其推广到使用足够好的理论模型（例如，差异字段）的算法。 然后，我们将其应用于差分代数几何形状，以表明存在一个可计算的统一上限，用于由多项式PDES系统定义的任何品种的组件数量。然后，我们使用这种界限来显示具有延迟多项式PDE系统中消除问题的可计算统一上限的存在。
Consider an algorithm computing in a differential field with several commuting derivations such that the only operations it performs with the elements of the field are arithmetic operations, differentiation, and zero testing. We show that, if the algorithm is guaranteed to terminate on every input, then there is a computable upper bound for the size of the output of the algorithm in terms of the size of the input. We also generalize this to algorithms working with models of good enough theories (including for example, difference fields). We then apply this to differential algebraic geometry to show that there exists a computable uniform upper bound for the number of components of any variety defined by a system of polynomial PDEs. We then use this bound to show the existence of a computable uniform upper bound for the elimination problem in systems of polynomial PDEs with delays.
