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Euler's inequality $R\geq 2r$ can be investigated in a novel way by using implicit loci in GeoGebra. Some unavoidable side effects of the implicit locus computation introduce unexpected algebraic curves. By using a mixture of symbolic and…
Real algebraic geometry adapts the methods and ideas from (complex) algebraic geometry to study the real solutions to systems of polynomial equations and polynomial inequalities. As it is the real solutions to such systems modeling…
The Eureqa symbolic regression program has recently received extensive press praise. A representative quote is "There are very clever 'thinking machines' in existence today, such as Watson, the IBM computer that conquered Jeopardy! last…
Traceroutes and geolocation are two essential network measurement tools that aid applications such as network mapping, topology generation, censorship, and Internet path analysis. However, these tools, individually and when combined, have…
We resolve a longstanding open problem in the computational modeling of nonlinear plates by introducing a numerical method that exactly enforces the isometry constraint, namely, that the first fundamental form of the mid-surface coincides…
Mathematics olympiads are prestigious competitions, with problem proposing and solving highly honored. Building artificial intelligence that proposes and solves olympiads presents an unresolved challenge in automated theorem discovery and…
Symmetry in mathematical programming may lead to a multiplicity of solutions. In nonconvex optimisation, it can negatively affect the performance of the branch-and-bound algorithm. Symmetry may induce large search trees with multiple…
Many geophysical flow or wave propagation problems can be modeled with two-dimensional depth-averaged equations, of which the shallow water equations are the simplest example. We describe the GeoClaw software that has been designed to solve…
Equation discovery methods enable modelers to combine domain-specific knowledge and system identification to construct models most suitable for a selected modeling task. The method described and evaluated in this paper can be used as a…
We survey both old and new developments in the theory of algorithms in real algebraic geometry -- starting from effective quantifier elimination in the first order theory of reals due to Tarski and Seidenberg, to more recent algorithms for…
We introduce and discuss, through a computational algebraic geometry approach, the automatic reasoning handling of propositions that are simultaneously true and false over some relevant collections of instances. A rigorous, algorithmic…
This article introduces a general purpose framework and software to approximate partial differential equations (PDEs). The sparsity patterns of finite element discretized operators is identified automatically using the tools from…
Mathematical educational soft explore, investigating in a dynamical way, some algebraically, geometrically problems, the expected results being used to involve a lot of mathematical results. One such software soft is GeoGebra. The software…
Electronic Geometry Textbook is a knowledge management system that manages geometric textbook knowledge to enable users to construct and share dynamic geometry textbooks interactively and efficiently. Based on a knowledge base organizing…
Determining visibility in planar polygons and arrangements is an important subroutine for many algorithms in computational geometry. In this paper, we report on new implementations, and corresponding experimental evaluations, for two…
We give a new theoretical tool to solve sparse systems with finitely many solutions. It is based on toric varieties and basic linear algebra; eigenvalues, eigenvectors and coefficient matrices. We adapt Eigenvalue theorem and Eigenvector…
We present Tarski, a tool for specifying configurable trace semantics to facilitate automated reasoning about traces. Software development projects require that various types of traces be modeled between and within development artifacts.…
We propose GeoUni, the first unified geometry expert model capable of generating problem solutions and diagrams within a single framework in a way that enables the creation of unique and individualized geometry problems. Traditionally,…
The Ehrhard-Borell inequality is a far-reaching refinement of the classical Brunn-Minkowski inequality that captures the sharp convexity and isoperimetric properties of Gaussian measures. Unlike in the classical Brunn-Minkowski theory, the…
The effectiveness of projection methods for solving systems of linear inequalities is investigated. It is shown that they have a computational advantage over some alternatives and that this makes them successful in real-world applications.…