Journal of Symbolic Computation

In recent years there has been increased use of machine learning (ML) techniques within mathematics, including symbolic computation where it may be applied safely to optimise or select algorithms. This paper explores whether using explainable AI (...

We study linear PDE with constant coefficients. The constant rank condition on a system of linear PDEs with constant coefficients is often used in the theory of compensated compactness. While this is a purely linear algebraic condition, the ...

In a series of papers we develop symbolic computation algorithms to investigate finiteness of central configurations for the planar n-body problem. Our approach is based on Albouy-Kaloshin's work on finiteness of central configurations for the 5-...

We propose a two-step Newton's method for refining an approximation of a singular zero whose deflation process terminates after one step, also known as a deflation-one singularity. Given an isolated singular zero of a square analytic system, our ...

Satisfiability modulo theories (SMT) solvers check the satisfiability of quantifier-free first-order logic formulae over different theories. We consider the theory of non-linear real arithmetic where the formulae are logical combinations of ...

In this paper, we compute an algebraic decomposition of black-box rings in the generic ring model. More precisely, we explicitly decompose a black-box ring as a direct product of a nilpotent black-box ring and unital local black-box rings, by ...

Let G be a permutation group acting on a set Ω. Best known algorithms for computing the centralizer of G in the symmetric group on Ω are all based on the same general approach that involves solving the following two fundamental problems: given a ...

Twenty years after the discovery of the F5 algorithm, Gröbner bases with signatures are still challenging to understand and to adapt to different settings. This contrasts with Buchberger's algorithm, which we can bend in many directions keeping ...

In this note, we precisely elaborate the connection between recognisable series (in the sense of Berstel and Reutenauer) and q-regular sequences (in the sense of Allouche and Shallit) via their linear representations. In particular, we show that ...

Let η be a polarization with connected kernel on a superspecial abelian variety E g. We give a sufficient criterion which allows the computation of the theta nullvalues of any quotient of E g by a maximal isotropic subgroup scheme of ker ⁡ ( η ) ...