Computations with parametric equations
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
A new method for solving algebraic systems of positive dimension
Discrete Applied Mathematics - Special volume on applied algebra, algebraic algorithms, and error-correcting codes
A generalized Euclidean algorithm for computing triangular representations of algebraic varieties
Journal of Symbolic Computation
On the theories of triangular sets
Journal of Symbolic Computation - Special issue on polynomial elimination—algorithms and applications
Computing triangular systems and regular systems
Journal of Symbolic Computation
Lifting techniques for triangular decompositions
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Some properties of triangular sets and improvement upon algorithm charser
AISC'06 Proceedings of the 8th international conference on Artificial Intelligence and Symbolic Computation
Comprehensive triangular decomposition
CASC'07 Proceedings of the 10th international conference on Computer Algebra in Scientific Computing
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Given a regular set T in K[x], Lemaire et al. in ISSAC'08 give a nice algebraic property: the regular set T generates its saturated ideal if and only if it is primitive. We firstly aim at giving a more direct proof of the above result, generalizing the concept of primitivity of polynomials and regular sets and presenting a new result which is equivalent to the above property. On the other hand, based upon correcting an error of the definition of U-set in AISC'06, we further develop some geometric properties of triangular sets. To a certain extent, the relation between the primitivity of T and its U-set is also revealed in this paper.