Related papers: Automatic Deduction in Dynamic Geometry using Sage
Cylindrical algebraic decomposition (CAD) is an important tool for working with polynomial systems, particularly quantifier elimination. However, it has complexity doubly exponential in the number of variables. The base algorithm can be…
This paper is a sequel to "Computing diagonal form and Jacobson normal form of a matrix using Groebner bases", J. of Symb. Computation, 46 (5), 2011. We present a new fraction-free algorithm for the computation of a diagonal form of a…
We are concerned with the problem of decomposing the parameter space of a parametric system of polynomial equations, and possibly some polynomial inequality constraints, with respect to the number of real solutions that the system attains.…
The Shapley Additive Global Importance (SAGE) value is a theoretically appealing interpretability method that fairly attributes global importance to a model's features. However, its exact calculation requires the computation of the…
A unified method for extracting geometric shape features from binary image data using a steady state partial differential equation (PDE) system as a boundary value problem is presented in this paper. The PDE and functions are formulated to…
Background: Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models, with the goal to gain a better understanding of the system. The…
This paper introduces an algebraic combinatorial approach to simplicial cone decompositions, a key step in solving inhomogeneous linear Diophantine systems and counting lattice points in polytopes. We use constant term manipulation on the…
It has been discovered that linear codes may be described by binomial ideals. This makes it possible to study linear codes by commutative algebra and algebraic geometry methods. In this paper, we give a decoding algorithm for binary linear…
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…
The introduction of automated deduction systems in secondary schools face several bottlenecks. Beyond the problems related with the curricula and the teachers, the dissonance between the outcomes of the geometry automated theorem provers…
Over the past decade, the Gr\"obner basis theory and automatic solver generation have lead to a large number of solutions to geometric vision problems. In practically all cases, the derived solvers apply a fixed elimination template to…
Geometric involutive bases for polynomial systems of equations have their origin in the prolongation and projection methods of the geometers Cartan and Kuranishi for systems of PDE. They are useful for numerical ideal membership testing and…
Sampling-based algorithms are classical approaches to perform Bayesian inference in inverse problems. They provide estimators with the associated credibility intervals to quantify the uncertainty on the estimators. Although these methods…
Boolean algebraic manipulation is at the core of logic synthesis in Electronic Design Automation (EDA) design flow. Existing methods struggle to fully exploit optimization opportunities, and often suffer from an explosive search space and…
We introduce a new dynamic analysis technique to discover invariants in separation logic for heap-manipulating programs. First, we use a debugger to obtain rich program execution traces at locations of interest on sample inputs. These…
Multiplication by the pseudoscalar $\mathbf{I}$ has been traditionally used in geometric algebra to perform non-metric operations such as calculating coordinates and the regressive product. In algebras with degenerate metrics, such as…
Automatic extraction of road networks from aerial imagery is a fundamental task, yet prevailing methods rely on polylines that struggle to model curvilinear geometry. We maintain that road geometry is inherently curve-based and introduce…
Designing software systems for Geometric Computing applications can be a challenging task. Software engineers typically use software abstractions to hide and manage the high complexity of such systems. Without the presence of a unifying…
Recent advances in generative networks have enabled new approaches to subsurface velocity model synthesis, offering a compelling alternative to traditional methods such as Full Waveform Inversion. However, these approaches predominantly…
We propose a geometric algorithm for topic learning and inference that is built on the convex geometry of topics arising from the Latent Dirichlet Allocation (LDA) model and its nonparametric extensions. To this end we study the…