منابع مشابه
Computation of Galois groups over function fields
Symmetric function theory provides a basis for computing Galois groups which is largely independent of the coefficient ring. An exact algorithm has been implemented over Q(t1, t2, . . . , tm) in Maple for degree up to 8. A table of polynomials realizing each transitive permutation group of degree 8 as a Galois group over the rationals is included.
متن کاملTechniques for the Computation of Galois Groups
This note surveys recent developments in the problem of computing Galois groups. Galois theory stands at the cradle of modern algebra and interacts with many areas of mathematics. The problem of determining Galois groups therefore is of interest not only from the point of view of number theory (for example see the article [39] in this volume), but leads to many questions in other areas of mathe...
متن کاملInvariants for the computation of intransitive and transitive Galois groups
One hard step in the computation of Galois groups by Stauduhar’s method is the construction of relative invariants. In this note, a representationtheoretic approach is given for the construction in the case of an intransitive group. In the second part of the article, it is shown that the construction can be used for groups that have a suitable intransitive subgroup. The construction solves an o...
متن کاملAround the numeric-symbolic computation of differential Galois groups
Let L∈K(z)[∂] be a linear differential operator, where K is an effective algebraically closed subfield of C. It can be shown that the differential Galois group of L is generated (as a closed algebraic group) by a finite number of monodromy matrices, Stokes matrices and matrices in local exponential groups. Moreover, there exist fast algorithms for the approximation of the entries of these matri...
متن کاملFormal Computation of Galois Groups with Relative Resolvents
We propound a systematic and formal method to compute the Galois group of a non-necessarily irreducible polynomial: we proceed by successive inclusions, using mostly computations on scalars (and very few on polynomials). It is based on a formal method of specialization of relative resolvents: it consists in expressing the generic coeecients of the resolvent using the powers of a primitive eleme...
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ژورنال
عنوان ژورنال: Foundations of Computational Mathematics
سال: 2017
ISSN: 1615-3375,1615-3383
DOI: 10.1007/s10208-017-9356-x