In this paper, on the basis of the implementation of the national chemical industry standard analytical test methods and analysis of test items, a food additive quality analysis and inspection of network management ap...In this paper, on the basis of the implementation of the national chemical industry standard analytical test methods and analysis of test items, a food additive quality analysis and inspection of network management applications are developed using the development technology of Visual Basic language and computer system operating environment, to achieve a network management software for users on food additives of quality analytical testing. The software sets up an information sharing network platform for enterprise and quality management departments, which is a major innovation in the food additive quality analysis on test management methods and tools.展开更多
In 2002, Faugere presented the famous F5 algorithm for computing GrSbner basis where two cri- teria, syzygy criterion and rewritten criterion, were proposed to avoid redundant computations. He proved the correctness o...In 2002, Faugere presented the famous F5 algorithm for computing GrSbner basis where two cri- teria, syzygy criterion and rewritten criterion, were proposed to avoid redundant computations. He proved the correctness of the syzygy criterion, but the proof for the correctness of the rewritten criterion was left. Since then, F5 has been studied extensively. Some proofs for the correctness of F5 were proposed, but these proofs are valid only under some extra assumptions. In this paper, we give a proof for the correctness of F5B, an equivalent version of F5 in Buchberger＇s style. The proof is valid for both homogeneous and non-homogeneous polynomial systems. Since this proof does not depend on the computing order of the S-pairs, any strategy of selecting S-pairs could be used in F5B or F5. Furthermore, we propose a natural and non-incremental variant of F5 where two revised criteria can be used to remove almost all redundant S-pairs.展开更多
文摘In this paper, on the basis of the implementation of the national chemical industry standard analytical test methods and analysis of test items, a food additive quality analysis and inspection of network management applications are developed using the development technology of Visual Basic language and computer system operating environment, to achieve a network management software for users on food additives of quality analytical testing. The software sets up an information sharing network platform for enterprise and quality management departments, which is a major innovation in the food additive quality analysis on test management methods and tools.
基金supported by National Key Basic Research Project of China (Grant No.2011CB302400)National Natural Science Foundation of China (Grant Nos. 10971217 and 61121062)
文摘In 2002, Faugere presented the famous F5 algorithm for computing GrSbner basis where two cri- teria, syzygy criterion and rewritten criterion, were proposed to avoid redundant computations. He proved the correctness of the syzygy criterion, but the proof for the correctness of the rewritten criterion was left. Since then, F5 has been studied extensively. Some proofs for the correctness of F5 were proposed, but these proofs are valid only under some extra assumptions. In this paper, we give a proof for the correctness of F5B, an equivalent version of F5 in Buchberger＇s style. The proof is valid for both homogeneous and non-homogeneous polynomial systems. Since this proof does not depend on the computing order of the S-pairs, any strategy of selecting S-pairs could be used in F5B or F5. Furthermore, we propose a natural and non-incremental variant of F5 where two revised criteria can be used to remove almost all redundant S-pairs.
