Solving zero-dimensional algebraic systems
Journal of Symbolic Computation
Efficient computation of zero-dimensional Gro¨bner bases by change of ordering
Journal of Symbolic Computation
Signature functions for algebraic numbers
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Lattices of compatibly embedded finite fields
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
On the theories of triangular sets
Journal of Symbolic Computation - Special issue on polynomial elimination—algorithms and applications
About a New Method for Computing in Algebraic Number Fields
EUROCAL '85 Research Contributions from the European Conference on Computer Algebra-Volume 2
A New Scheme for Computing with Algebraically Closed Fields
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Algebraic factoring and rational function integration
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
On the factorization of polynomials over algebraic fields
On the factorization of polynomials over algebraic fields
A modular method for computing the splitting field of a polynomial
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
Journal of Symbolic Computation
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A practical computational system is described for computing with an algebraic closure of a field. The system avoids factorization of polynomials over extension fields, but gives the illusion of a genuine field to the user. All roots of an arbitrary polynomial defined over such an algebraically closed field can be constructed and are easily distinguished within the system. The difficult case of inseparable extensions of function fields of positive characteristic is also handled properly by the system. A technique of modular evaluation into a finite field critically ensures that a unique genuine field is simulated by the system but also provides fast optimizations for some fundamental operations. Fast matrix techniques are also used for several non-trivial operations. The system has been successfully implemented within the Magma Computer Algebra System, and several examples are presented, using this implementation.