论文标题
签名基础理论的公理
Axioms for a theory of signature bases
论文作者
论文摘要
发现F5算法二十年后，具有签名的Gröbner基地仍然具有挑战性地了解和适应不同的环境。这与Buchberger的算法形成鲜明对比，我们可以在许多方向上弯曲正确的正确性和终止。我提出了一种具有签名的Gröbner基础的公理方法，目的是解开理论和算法，并给出适用于许多不同不同设置的一般结果（例如，gröbner用于子模块，F4风格的还原，非交换环，非交换环，非零环，非零环的设置等）。
Twenty years after the discovery of the F5 algorithm, Gröbner bases with signatures are still challenging to understand and to adapt to different settings. This contrasts with Buchberger's algorithm, which we can bend in many directions keeping correctness and termination obvious. I propose an axiomatic approach to Gröbner bases with signatures with the purpose of uncoupling the theory and the algorithms, and giving general results applicable in many different settings (e.g. Gröbner for submodules, F4-style reduction, noncommutative rings, non-Noetherian settings, etc.).
