Pan and Wang presented a method for computing uniform GrSbner bases for certain ide- als generated by polynomials with parametric exponents in 2006, and two criteria were proposed to determine if a uniform GrSbner bas...Pan and Wang presented a method for computing uniform GrSbner bases for certain ide- als generated by polynomials with parametric exponents in 2006, and two criteria were proposed to determine if a uniform GrSbner basis can be obtained. This paper gives a new algorithmic approach for computing tile uniform GrSbner basis such that Pan and Wang＇s method could be concluded as a special case. The authors use the method of reduced term order under ring homomorphisnl to get the reduced uniform GrSbner basis. Also the authors point and correct a mistake in Pan and Wang＇s method. The result is a generalization of approach of Pan and Wang and one could compute the uniform GrSbner basis more efficiently by the new approach.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.11271040Science and Technology Foundation of Gui Zhou Province LKM[2013]16
文摘Pan and Wang presented a method for computing uniform GrSbner bases for certain ide- als generated by polynomials with parametric exponents in 2006, and two criteria were proposed to determine if a uniform GrSbner basis can be obtained. This paper gives a new algorithmic approach for computing tile uniform GrSbner basis such that Pan and Wang＇s method could be concluded as a special case. The authors use the method of reduced term order under ring homomorphisnl to get the reduced uniform GrSbner basis. Also the authors point and correct a mistake in Pan and Wang＇s method. The result is a generalization of approach of Pan and Wang and one could compute the uniform GrSbner basis more efficiently by the new approach.
