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Algebraic cryptanalysis usually requires to recover the secret key by solving polynomial equations. Grobner bases algorithm is a well-known method to solve this problem. However, a serious drawback exists in the Grobner bases based…
One of the main contributions which Volker Weispfenning made to mathematics is related to Groebner bases theory. In this paper we present an algorithm for computing all algebraic intermediate subfields in a separably generated unirational…
Our main theorems provide a single geometric setting in which polynomial representatives for Schubert classes in the integral cohomology ring of the flag manifold are determined uniquely, and have positive coefficients for geometric…
This chapter of the forthcoming Handbook of Graphical Models contains an overview of basic theorems and techniques from algebraic geometry and how they can be applied to the study of conditional independence and graphical models. It also…
Algorithms are the engine for reproducible problem-solving. We present a framework automating algorithm discovery by conceptualizing them as sequences of operations, represented as tokens. These computational tokens are chained using a…
Association schemes are combinatorial objects that allow us solve problems in several branches of mathematics. They have been used in the study of permutation groups and graphs and also in the design of experiments, coding theory, partition…
We produce algorithms to detect whether a complex affine variety computed and presented numerically by the machinery of numerical algebraic geometry corresponds to an associated component of a polynomial ideal.
We propose the convergent graph solver (CGS), a deep learning method that learns iterative mappings to predict the properties of a graph system at its stationary state (fixed point) with guaranteed convergence. CGS systematically computes…
In the era of large language models generating high quality texts, it is a necessity to develop methods for detection of machine-generated text to avoid harmful use or simply due to annotation purposes. It is, however, also important to…
We introduced the package/subsystem GeoGebra Discovery to GeoGebra which supports the automated proving or discovering of elementary geometry inequalities. In this case study, for inequality exploration problems related to isosceles and…
In the domain of geometry and topology optimization, discovering geometries that optimally satisfy specific problem criteria is a complex challenge in both engineering and scientific research. In this work, we propose a new approach for the…
In this paper, we develop a new Randomized Global Generalized Minimum Residual (RGlGMRES) algorithm for efficiently computing solutions to large scale linear systems with multiple right hand sides.The proposed method builds on a recently…
We tackle the problem of learning the geometry of multiple categories of deformable objects jointly. Recent work has shown that it is possible to learn a unified dense pose predictor for several categories of related objects. However,…
A mathematical knowledge graph (KG) presents knowledge within the field of mathematics in a structured manner. Constructing a math KG using natural language is an essential but challenging task. There are two major limitations of existing…
In the last decade, the approximate vanishing ideal and its basis construction algorithms have been extensively studied in computer algebra and machine learning as a general model to reconstruct the algebraic variety on which noisy data…
Many statistical models are algebraic in that they are defined by polynomial constraints or by parameterizations that are polynomial or rational maps. This opens the door for tools from computational algebraic geometry. These tools can be…
In this paper we consider finite-dimensional constrained Hamiltonian systems of polynomial type. In order to compute the complete set of constraints and separate them into the first and second classes we apply the modern algorithmic methods…
We present a comprehensive demonstration of how automated reasoning can assist mathematical research, both in the discovery of conjectures and in their verification. Our focus is a discrete geometry problem: What is $\mu_{5}(n)$, the…
In this paper we present an algorithm for computing Groebner bases of linear ideals in a difference polynomial ring over a ground difference field. The input difference polynomials generating the ideal are also assumed to be linear. The…
We consider the Rosenfeld-Groebner algorithm for computing a regular decomposition of a radical differential ideal generated by a set of ordinary differential polynomials in n indeterminates. For a set of ordinary differential polynomials…