A set of special basis in which the elements are nonnegative is designed based on the feature of real linear space generated by bivariate symmetric form. The variant itself is nonnegative if its coordinates is nonnegative under the special basis designed. Thus the proof of nonnegativity of a variant is transformed into the proof of nonnegativity of coordinates corresponding to the variant in appointed basis. And decreasing dimension is successful, for the number of variates in coordinates is always less than the number of variants belonged to symmetric form. Furthermore, we are able to solve the nonegativity of a variant belonged to unsymmetric form by transforming the unsymmetric form into the symmetric form. Finally, the general program called Bidecomp is programmed according to the above method. The method is very efficient although it is incomplete.
CHEN Shengli
, YAO Yong
, XU Jia. , {{custom_author.name_en}}.
Method of Decreasing Dimension by Partition and Automated Proving for Algebraic Inequalities. Journal of Systems Science and Mathematical Sciences, 2009, 29(1): 26-34 https://doi.org/10.12341/jssms10121
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