Computer algebra: symbolic and algebraic computation (2nd ed.)
Computer algebra: symbolic and algebraic computation (2nd ed.)
The Complexity of Solving Polynomial Equations by Quadrature
Journal of the ACM (JACM)
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Polynomial Time Algorithms for Galois Groups
EUROSAM '84 Proceedings of the International Symposium on Symbolic and Algebraic Computation
Lower bounds for algebraic computation trees
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Computational geometry.
Hi-index | 0.00 |
We use simple arguments from Galois theory to prove the impossibility of exact algorithms for problems under various models of computation. In particular we show that there exist applied computational problems for which there are no closed from solutions over models such as Q(+, -, *, /, √), Q(+, -, *, /, k√), and Q(+, -, *, /, k√, q(x)), where Q is the field of rationals and q(x)&egr; Q[x] are polynomials with non-solvable Galois groups.