On the parallel Risch Algorithm (II)
ACM Transactions on Mathematical Software (TOMS)
Liouvillian Solutions of Linear Differential Equations with Liouvillian Coefficients
Journal of Symbolic Computation
On solutions of linear ordinary differential equations in their coefficient field
Journal of Symbolic Computation
On polynomial solutions of linear operator equations
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
Asymptotic expansions of exp-log functions
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
Journal of Symbolic Computation
Symbolic integration I: transcendental functions
Symbolic integration I: transcendental functions
Solving linear ordinary differential equations over C (x, e∫ f(x)dx)
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
On rational solutions of systems of linear differential equations
Journal of Symbolic Computation - Special issue on differential algebra and differential equations
The Parallel Risch Algorithm (I)
EUROCAM '82 Proceedings of the European Computer Algebra Conference on Computer Algebra
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We propose a polynomial time algorithm to decide whether the Galois group of an irreducible polynomial ƒ ∈ Q[x] is abelian, and, if so, determine all its elements along with their action on the set of roots of ƒ. This algorithm does not require factorization of polynomials over number fields. Instead we shall use the quadratic Newton—Lifting and the truncated expressions of the roots of ƒ over a p—adic number field Qp, for an appropriate prime p in Z.