Factoring sparse multivariate polynomials
Journal of Computer and System Sciences
Complexity of deciding Tarski algebra
Journal of Symbolic Computation
Algebraic solution of systems of polynomial equations using Groebner bases
Proceedings of the 5th international conference, AAECC-5 on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Complexity of factoring and calculating the GCD of linear ordinary differential operators
Journal of Symbolic Computation
Fast parallel algorithms for sparse multivariate polynomial interpolation over finite fields
SIAM Journal on Computing
The membership problem for unmixed polynomial ideals is solvable in single exponential time
Discrete Applied Mathematics - Special volume on applied algebra, algebraic algorithms, and error-correcting codes
Efficient computation of zero-dimensional Gro¨bner bases by change of ordering
Journal of Symbolic Computation
Zeros, multiplicities, and idempotents for zero-dimensional systems
Algorithms in algebraic geometry and applications
Subresultants and Reduced Polynomial Remainder Sequences
Journal of the ACM (JACM)
Complexity of Quantifier Elimination in the Theory of Algebraically Closed Fields
Proceedings of the Mathematical Foundations of Computer Science 1984
Constructing Universal Groebner Bases
AAECC-5 Proceedings of the 5th International Conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Some New Effectivity Bounds in Computational Geometry
AAECC-6 Proceedings of the 6th International Conference, on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Generalized Characteristic Polynomials
ISAAC '88 Proceedings of the International Symposium ISSAC'88 on Symbolic and Algebraic Computation
Solving Systems of Algebraic Equations
ISAAC '88 Proceedings of the International Symposium ISSAC'88 on Symbolic and Algebraic Computation
Complexity of quantifier elimination in the theory of ordinary differential equations
EUROCAL '87 Proceedings of the European Conference on Computer Algebra
Properties of Gröbner bases under specializations
EUROCAL '87 Proceedings of the European Conference on Computer Algebra
Solving systems of algebraic equations by using Gröbner bases
EUROCAL '87 Proceedings of the European Conference on Computer Algebra
EUROCAL '85 Research Contributions from the European Conference on Computer Algebra-Volume 2
Algebraic Complexity Theory
Complexity of the resolution of parametric systems of polynomial equations and inequations
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Solving parametric polynomial systems
Journal of Symbolic Computation
Hi-index | 0.00 |
Let F be an algebraically closed field of zero characteristic, a polynomial @@@@ ∈ F[X1, … , Xn have a multiplicative complexity r and ƒ1, … ƒk ∈ F[X1, … , Xn] be some polynomials of degrees not exceeding d, such that @@@@ = ƒ1 = ··· = ƒk = 0 has a finite number of roots. We show that the number of possible distinct vectors of multiplicities of these roots is small when r, d and k are small. As technical tools we design algorithms which produce Gröbner bases and vectors of multiplicities of the roots for a parametric zero-dimensional system. The complexities of these algorithms are singly exponential. We also describe an algorithm for parametric absolute factorization of multivariate polynomials. This algorithm has subexponential complexity in the case of a small (relative to the number of variables) degree of the polynomials.