Volume 23, Issue 5
Piecewise Semialgebraic Sets

Chun-Gang Zhu & Ren-Hong Wang

DOI:

J. Comp. Math., 23 (2005), pp. 503-512

Published online: 2005-10

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  • Abstract

Semialgebraic sets are objects which are truly a special feature of real algebraic geometry. This paper presents the piecewise semialgebraic set, which is the subset of $R^n$ satisfying a boolean combination of multivariate spline equations and inequalities with real coefficients. Moreover, the stability under projection and the dimension of $C^{\mu}$ piecewise semialgebraic sets are also discussed.

  • Keywords

Algebraic geometry Semialgebraic geometry Tarski-Seidenberg Principle Multivariate splines Piecewise semialgebraic sets

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@Article{JCM-23-503, author = {}, title = {Piecewise Semialgebraic Sets}, journal = {Journal of Computational Mathematics}, year = {2005}, volume = {23}, number = {5}, pages = {503--512}, abstract = { Semialgebraic sets are objects which are truly a special feature of real algebraic geometry. This paper presents the piecewise semialgebraic set, which is the subset of $R^n$ satisfying a boolean combination of multivariate spline equations and inequalities with real coefficients. Moreover, the stability under projection and the dimension of $C^{\mu}$ piecewise semialgebraic sets are also discussed. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8835.html} }
TY - JOUR T1 - Piecewise Semialgebraic Sets JO - Journal of Computational Mathematics VL - 5 SP - 503 EP - 512 PY - 2005 DA - 2005/10 SN - 23 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8835.html KW - Algebraic geometry KW - Semialgebraic geometry KW - Tarski-Seidenberg Principle KW - Multivariate splines KW - Piecewise semialgebraic sets AB - Semialgebraic sets are objects which are truly a special feature of real algebraic geometry. This paper presents the piecewise semialgebraic set, which is the subset of $R^n$ satisfying a boolean combination of multivariate spline equations and inequalities with real coefficients. Moreover, the stability under projection and the dimension of $C^{\mu}$ piecewise semialgebraic sets are also discussed.
Chun-Gang Zhu & Ren-Hong Wang. (1970). Piecewise Semialgebraic Sets. Journal of Computational Mathematics. 23 (5). 503-512. doi:
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