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Volume 26, Issue 2
Computation of the Rational Representation for Solutions of High-Dimensional Systems

Chang Tan & Shugong Zhang

Commun. Math. Res., 26 (2010), pp. 119-130.

Published online: 2021-05

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  • Abstract

This paper deals with the representation of the solutions of a polynomial system, and concentrates on the high-dimensional case. Based on the rational univariate representation of zero-dimensional polynomial systems, we give a new description called rational representation for the solutions of a high-dimensional polynomial system and propose an algorithm for computing it. By this way all the solutions of any high-dimensional polynomial system can be represented by a set of so-called rational-representation sets.

  • Keywords

rational univariate representation, high-dimensional ideal, maximally independent set, rational representation, irreducible component.

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COPYRIGHT: © Global Science Press

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@Article{CMR-26-119, author = {Tan , Chang and Zhang , Shugong}, title = {Computation of the Rational Representation for Solutions of High-Dimensional Systems}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {26}, number = {2}, pages = {119--130}, abstract = {

This paper deals with the representation of the solutions of a polynomial system, and concentrates on the high-dimensional case. Based on the rational univariate representation of zero-dimensional polynomial systems, we give a new description called rational representation for the solutions of a high-dimensional polynomial system and propose an algorithm for computing it. By this way all the solutions of any high-dimensional polynomial system can be represented by a set of so-called rational-representation sets.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19166.html} }
TY - JOUR T1 - Computation of the Rational Representation for Solutions of High-Dimensional Systems AU - Tan , Chang AU - Zhang , Shugong JO - Communications in Mathematical Research VL - 2 SP - 119 EP - 130 PY - 2021 DA - 2021/05 SN - 26 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19166.html KW - rational univariate representation, high-dimensional ideal, maximally independent set, rational representation, irreducible component. AB -

This paper deals with the representation of the solutions of a polynomial system, and concentrates on the high-dimensional case. Based on the rational univariate representation of zero-dimensional polynomial systems, we give a new description called rational representation for the solutions of a high-dimensional polynomial system and propose an algorithm for computing it. By this way all the solutions of any high-dimensional polynomial system can be represented by a set of so-called rational-representation sets.

Tan , Chang and Zhang , Shugong. (2021). Computation of the Rational Representation for Solutions of High-Dimensional Systems. Communications in Mathematical Research . 26 (2). 119-130. doi:
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