Journal of Symbolic Computation
Gro¨bner bases: a computational approach to commutative algebra
Gro¨bner bases: a computational approach to commutative algebra
Solving the load flow problem using Gröbner basis
ACM SIGSAM Bulletin
Involution approach to investigating polynomial systems
Selected papers presented at the international IMACS symposium on Symbolic computation, new trends and developments
Involutive bases of polynomial ideals
Mathematics and Computers in Simulation - Special issue: Simplification of systems of algebraic and differential equations with applications
A new algorithm for discussing Gröbner bases with parameters
Journal of Symbolic Computation
A criterion for detecting unnecessary reductions in the construction of Groebner bases
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
An alternative approach to comprehensive Gröbner bases
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
Canonical comprehensive Gröbner bases
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
A simple algorithm to compute comprehensive Gröbner bases using Gröbner bases
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Minimal canonical comprehensive Gröbner systems
Journal of Symbolic Computation
Detecting unnecessary reductions in an involutive basis computation
Journal of Symbolic Computation
Involution: The Formal Theory of Differential Equations and its Applications in Computer Algebra
Involution: The Formal Theory of Differential Equations and its Applications in Computer Algebra
A new algorithm for computing comprehensive Gröbner systems
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Gröbner bases for polynomial systems with parameters
Journal of Symbolic Computation
Involutive division generated by an antigraded monomial ordering
CASC'11 Proceedings of the 13th international conference on Computer algebra in scientific computing
Computation of full comprehensive gröbner bases
CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
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In this paper we consider parametric ideals and introduce a notion of comprehensive involutive system. This notion plays the same role in theory of involutive bases as the notion of comprehensive Gröbner system in theory of Gröbner bases. Given a parametric ideal, the space of parameters is decomposed into a finite set of cells. Each cell yields the corresponding involutive basis of the ideal for the values of parameters in that cell. Using the Gerdt---Blinkov algorithm described in [6] for computing involutive bases and also the Montes DisPGB algorithm for computing comprehensive Gröbner systems [13], we present an algorithm for construction of comprehensive involutive systems. The proposed algorithm has been implemented in Maple, and we provide an illustrative example showing the step-by-step construction of comprehensive involutive system by our algorithm.