Journal of Systems Science and Complexity

, Volume 30, Issue 6, pp 1470–1482

# A simplified rational representation for positive-dimensional polynomial systems and SHEPWM equations solving

• Baoxin Shang
• Shugong Zhang
• Chang Tan
• Peng Xia
Article

## Abstract

The paper is concerned with the improvement of the rational representation theory for solving positive-dimensional polynomial systems. The authors simplify the expression of rational representation set proposed by Tan and Zhang (2010), obtain the simplified rational representation with less rational representation sets, and hence reduce the complexity for representing the variety of a positive-dimensional ideal. As an application, the authors compute a “nearly” parametric solution for the SHEPWM problem with a fixed number of switching angles.

## Keywords

Positive-dimensional polynomial system solving rational univariate representation SHEPWM simplified rational representation

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© Institute of Systems Science, Academy of Mathematics and Systems Science, CAS and Springer-Verlag GmbH Germany, part of Springer Nature 2017

## Authors and Affiliations

• Baoxin Shang
• 1
• 2
• Shugong Zhang
• 1
Email author
• Chang Tan
• 3
• Peng Xia
• 4
1. 1.School of Mathematics, Key Laboratory of Symbolic Computation and Knowledge Engineering (Ministry of Education)Jilin UniversityChangchunChina
2. 2.College of ScienceNortheast Electric Power UniversityJilinChina
3. 3.College of ScienceNortheast Forestry UniversityHarbinChina
4. 4.School of MathematicsLiaoning UniversityShenyangChina