Symbolic Computation Papers of the Week

All the results in this paper, concerning the wave amplitude, are dependent on the variable coefficients in that extension, while those coefficients respectively lead the nonlinearity, dispersion and transverse variations of the wave in the three directions, employed to suggest the function of dispersion in the emergence of patterns.

We introduce ALBI (Agent for Learning By Induction), a neuro-symbolic ILP framework that replaces the ASP-based hypothesis generator in the Learning from Failures (LFF) paradigm with a Large Language Model (LLM), while retaining SWI-Prolog as a formal verifier.

Using Pan's approximate factorization theorem, we give a deterministic algorithm that finds all distinct integer roots of $f$ in $\widetilde O(nb)$ bit operations.

Given a rational point of the moduli space of cubic rational maps, we seek a map in its class with the smallest integer coefficients.

We propose to instead use a transformer pre-trained on readily available random percept-action data.

We prove that for $6\le n\le9$ the maximum is $(n-1)^{n-1}r_n^{n(n-1)}$, where $r_n=\sqrt{n/(n-1)}$.

We consider linear conic problems whose cone is a product of truncated quadratic modules, the sum-of-squares (SOS) side of the moment-SOS hierarchy.

We extend the standard definition of relevance from the legal theory of evidence: An answer is relevant if and only if it is both probative and material for the matter at hand given the knowledge available.

An algorithm is presented for computing the determinant and the characteristic polynomial of a matrix $A$ over an arbitrary commutative ring R.

This work provides a comprehensive analytical and computational investigation of the Riemann coupled wave system, which serves as a prototypical model for the propagation and interaction of nonlinear waves in dispersive and dissipative media.

In this work, we study the computational complexity of computing equidimensional components of algebraic varieties, represented via Chow forms.