Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In 1965 Buchberger introduced an algorithmic approach to compute Grobner bases. Later on, he and many others presented various attempts to improve the computation by removing useless elements a priori. One approach, initiated by Gebauer, Moller, Mora and Traverso in the 1990s, is to keep track of the corresponding syzygies which is related to the topic of this survey: signature-based algorithms for Grobner bases. This area was initiated by Faugere's  F5  algorithm in 2002. The general idea of signatures is to keep track of the history of the computation with a minimal overhead and to exploit this information to detect redundant elements. Here  give a summary of the literature on signature-based algorithms and show how to classify known algorithms by 3 different orderings. For this  give translations beten different notations and show the relationships (differences and similarities) among many approaches. Moreover,  give a general description of how the idea of signatures is quite natural when performing the reduction process using linear algebra.  hope that this survey would help to outline this field of active research.
['Christian Eder', 'Jean-Charles Faugère']
I am writing a research paper on a idea A survey on signature-based algorithms for computing Gröbner bases ☆
[{"from": "human", "value": "I am writing a research paper on a idea A survey on signature-based algorithms for computing Gr\u00f6bner bases \u2606"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In 1965 Buchberger introduced an algorithmic approach to compute Grobner bases. Later on, he and many others presented various attempts to improve the computation by removing useless elements a priori. One approach, initiated by Gebauer, Moller, Mora and Traverso in the 1990s, is to keep track of the corresponding syzygies which is related to the topic of this survey: signature-based algorithms for Grobner bases. This area was initiated by Faugere's  F5  algorithm in 2002. The general idea of signatures is to keep track of the history of the computation with a minimal overhead and to exploit this information to detect redundant elements. Here  give a summary of the literature on signature-based algorithms and show how to classify known algorithms by 3 different orderings. For this  give translations beten different notations and show the relationships (differences and similarities) among many approaches. Moreover,  give a general description of how the idea of signatures is quite natural when performing the reduction process using linear algebra.  hope that this survey would help to outline this field of active research."}]