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ritt-wu Characteristic Set Method for Laurent Partial Differential Polynomial Systems

Journal of Systems Science & Complexity 2019年第1期32卷 62-77页

作者： HU Youren GAO Xiao-Shan KLMM Academy of Mathematics and Systems Science Chinese Academy of Sciences School of Mathematics University of Chinese Academy of Sciences Chinese Academy of Sciences

In this paper, a ritt-wu characteristic set method for Laurent partial differential polynomial systems is presented. The concept of Laurent regular differential chain is de?ned and its basic properties are proved. The authors give a partial method to decide whether a Laurent differential chain A is Laurent regular. The decision for whether A is Laurent regular is reduced to the decision of whether a univariate differential chain A1 is Laurent regular. For a univariate differential chain A1,the authors ?rst give a criterion for whether A1 is Laurent regular in terms of its generic zeros and then give partial results on deciding whether A1 is Laurent regular.

关键词： Newton polygon Laurent partial differential polynomial system Laurent regular triangular set ritt-wu characteristic set

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Hilbert Problem 15 and ritt-wu Method(Ⅰ)

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Journal of Systems Science & Complexity 2019年第1期32卷 47-61页

作者： LI Banghe KLMM Academy of Mathematics and Systems Science Chinese Academy of Sciences

Hilbert problem 15 requires to understand Schubert's book. In this book, there is a theorem in §23, about the relation of the tangent lines from a point and the singular points of cubed curves with cusp near a 3-multiple straight line, which was obtained by the so called main trunk numbers, while for these numbers, Schubert said that he obtained them by experiences. So essentially Schubert even did not give any hint for the proof of this theorem. In this paper, by using the concept of generic point in the framework of Van der Waerden and Weil on algebraic geometry, and realizing ritt-wu method on computer, the authors prove that this theorem of Schubert is completely right.

关键词： Cubed curves with cusp Hilbert Problem 15 ritt-wu Method

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