Admissible orders and linear forms
ACM SIGSAM Bulletin
Bifurcations and transitions to chaos in the three-dimensional Lotka-Volterra map
SIAM Journal on Applied Mathematics
Admissible term orderings used in computer algebra systems
ACM SIGSAM Bulletin
On mechanical quantifier elimination for elementary algebra and geometry
Journal of Symbolic Computation
Gröbner bases and primary decomposition of polynomial ideals
Journal of Symbolic Computation
Journal of Symbolic Computation
On an installation of Buchberger's algorithm
Journal of Symbolic Computation
Some comments on term-ordering in Gröbner basis computations
ACM SIGSAM Bulletin
On radical zero-dimensional ideals
Journal of Symbolic Computation
Decomposing algebraic sets using Gro¨bner bases
Computer Aided Geometric Design
Algebraic Solution of Systems of Polynomial Equations Using Groebner Bases
AAECC-5 Proceedings of the 5th International Conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
On Goldman's Algorithm for Solving First-Order Multinomial Autonomous Systems
AAECC-6 Proceedings of the 6th International Conference, on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Computer and Commutative Algebra
AAECC-6 Proceedings of the 6th International Conference, on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
On the implementation of dynamic evaluation
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
About the polynomial solutions of homogeneous linear differential equations depending on parameters
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
A new algorithm for discussing Gröbner bases with parameters
Journal of Symbolic Computation
Computer algebra handbook
Non-linear loop invariant generation using Gröbner bases
Proceedings of the 31st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Decomposition of ordinary difference polynomials
Journal of Symbolic Computation
Hilbert stratification and parametric gröbner bases
CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
| Hi-index | 0.00 |
We present a theoretical foundation for studying parametric systems of linear equations and prove an efficient algorithm for identifying all parametric values (including degenerate cases) for which the system is consistent. The algorithm gives a small set of regimes where for each regime, the solutions of the specialized systems may be given uniformly. For homogeneous linear systems, or for systems where the right hand side Is arbitrary, this small set is irredundant. We discuss in detail practical issues concerning implementations, with particular emphasis on simplification of results, Examples are given based on a close implementation of the algorithm in SCRATCHPAD II. We also give a complexity analysis of the Gaussian elimination method and compare that with our algorithm.