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A generalized criterion for signature related algorithms to compute Gröbner basis is proposed in this paper. Signature related algorithms are a popular kind of algorithms for computing Gröbner basis, including the famous F5 algorithm, the extended F5 algorithm and the GVW algorithm. The main purpose of current paper is to study in theory what kind of(More)
To provide an insight into the mechanism of interspecific interactions mediated by allelochemicals, cucumber and figleaf gourd seedlings were compared on their response to cinnamic acid, an autotoxin from root exudates of cucumber. Reactive oxygen species metabolism and plasma membrane H(+)-ATPase activity were examined in roots upon exposure to cinnamic(More)
This assignment covers material from the first week of class lecture and reading. If is very important that you know what the class website contains. So, for this first fun problem you are to go on a frog hunt. There are images of frogs hidden on one, or more, page(s) that I have created found somewhere on, or linked to, the class website. So, go find the(More)
A new algorithm for computing a comprehensive Gröbner system of a parametric polynomial ideal over k[U ][X] is presented. This algorithm generates fewer branches (segments) compared to Suzuki and Sato's algorithm as well as Nabeshi-ma's algorithm, resulting in considerable efficiency. As a result , the algorithm is able to compute comprehensive Gröb-ner(More)
The F5 algorithm is presented by Faugère in 2002. However, Faugère have not provide the rigorous proofs so far. In this paper, we will give a new complete proof and hence reveal the essence of this algorithm. The proof consists of the correctness and termination of the algorithm and the correctness of two criteria in it.