Related papers: The algebraic method in experimental design
A symbolic method is used to establish some properties of the Bernoulli-Barnes polynomials.
Computation of parallel lines (envelopes) to parabolas, ellipses, and hyperbolas is of importance in structure engineering and theory of mechanisms. Homogeneous polynomials that implicitly define parallel lines for the given offset to a…
Over the past several decades, algebraic geometry has provided innovative approaches to biological experimental design that resolved theoretical questions and improved computational efficiency. However, guaranteeing uniqueness and perfect…
Refinement based formal methods allow the modelling of systems through incremental steps via abstraction. Discovering the right levels of abstraction, formulating correct and meaningful invariants, and analysing faulty models are some of…
We provide a scheme for inferring causal relations from uncontrolled statistical data based on tools from computational algebraic geometry, in particular, the computation of Groebner bases. We focus on causal structures containing just two…
In this expositional paper, we discuss commutative algebra -- a study inspired by the properties of integers, rational numbers, and real numbers. In particular, we investigate rings and ideals, and their various properties. After, we…
We describe a type of Lie color algebra, which we call generic, whose universal enveloping algebra is a domain with finite global dimension. Moreover, it is an iterated Ore extension. We provide an application and show Grobner basis methods…
Local Fourier analysis is a strong and well-established tool for analyzing the convergence of numerical methods for partial differential equations. The key idea of local Fourier analysis is to represent the occurring functions in terms of a…
The relationship between algebraic geometry and the inferential framework of the Bayesian Networks with hidden variables has now been fruitfully explored and exploited by a number of authors. More recently the algebraic formulation of…
The set of common roots of a finite set $I$ (it is an ideal) of homogeneous polynomials is known as projective algebraic set $V$. In this article I show how to dualize such projective algebraic sets $V$ by elimination of variables from a…
Identification of fractional order systems is considered from an algebraic point of view. It allows for a simultaneous estimation of model parameters and fractional (or integer) orders from input and output data. It is exact in that no…
We use geometric algebra techniques to give a synthetic and computationally efficient approach to Fierz identities in arbitrary dimensions and signatures, thus generalizing previous work. Our approach leads to a formulation which displays…
Cylindrical algebraic decomposition (CAD) is an important tool for the study of real algebraic geometry with many applications both within mathematics and elsewhere. It is known to have doubly exponential complexity in the number of…
We associate to each synchronous game an algebra whose representations determine if the game has a perfect deterministic strategy, perfect quantum strategy or one of several other perfect strategies. when applied to the graph coloring game,…
Given finitely many consecutive terms of an infinite sequence, we discuss the construction of a polynomial difference equation that the sequence may satisfy. We also present a method to seek a candidate polynomial differential equation for…
Algorithmic computation in polynomial rings is a classical topic in mathematics. However, little attention has been given to the case of rings with an infinite number of variables until recently when theoretical efforts have made possible…
A universal analytic Gr{\"o}bner basis (UAGB) of an ideal of a Tate algebra is a set containing a local Gr{\"o}bner basis for all suitable convergence radii. In a previous article, the authors proved the existence of finite UAGB's for…
We seek to determine a real algebraic variety from a fixed finite subset of points. Existing methods are studied and new methods are developed. Our focus lies on aspects of topology and algebraic geometry, such as dimension and defining…
Standard noncommutative Gr\"obner basis procedures are used for computing ideals of free noncommutative polynomial rings over fields. This paper describes Gr\"obner basis procedures for one-sided ideals in finitely presented noncommutative…
We study the problems of testing isomorphism of polynomials, algebras, and multilinear forms. Our first main results are average-case algorithms for these problems. For example, we develop an algorithm that takes two cubic forms $f, g\in…