论文信息 - On the representation of constructible sets

On the representation of constructible sets

The occurrence of redundant components is a natural phenomenon when computing with constructible sets. We present different algorithms for computing an irredundant representation of a constructible set or a family thereof. We provide a complexity analysis and report on an experimental comparison.

[1] Hoon Hong,et al. Simple solution formula construction in cylindrical algebraic decomposition based quantifier elimination , 1992, ISSAC '92.

[2] M. M. Maza,et al. Well known theorems on triangular systems and the D5 principle , 2006 .

[3] Changbo Chen,et al. Comprehensive Triangular Decomposition , 2007, CASC.

[4] Changbo Chen,et al. The ConstructibleSetTools and ParametricSystemTools Modules of the RegularChains Library in Maple , 2008, 2008 International Conference on Computational Sciences and Its Applications.

[5] Marc Moreno Maza,et al. Polynomial Gcd Computations over Towers of Algebraic Extensions , 1995, AAECC.

[6] Joachim von zur Gathen,et al. Modern Computer Algebra , 1998 .

[7] Marc Moreno Maza,et al. On the complexity of the D5 principle , 2005, SIGS.

[8] Dominique Duval,et al. About a New Method for Computing in Algebraic Number Fields , 1985, European Conference on Computer Algebra.

[9] Jeffrey Shallit,et al. Factor refinement , 1993, SODA '90.

[10] Antonio Montes,et al. Minimal canonical comprehensive Gröbner systems , 2006, J. Symb. Comput..