Related papers: Automated Generation of Triangle Geometry Theorems
We provide a framework connecting several well known theories related to the linearity of graded modules over graded algebras. In the first part, we pay a particular attention to the tensor products of graded bimodules over graded algebras.…
The purpose of this paper is to make the theory of vertex algebras trivial. We do this by setting up some categorical machinery so that vertex algebras are just ``singular commutative rings'' in a certain category. This makes it easy to…
We provide a new algorithm (called the grid algorithm) designed to generate the image of the attractor of a generalized iterated function system on a finite dimensional space and we compare it with the deterministic algorithm regarding…
We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…
Plotting solution sets for particular equations may be complicated by the existence of turning points. Here we describe an algorithm which not only overcomes such problematic points, but does so in the most general of settings. Applications…
This report presents a new, algorithmic approach to the distributions of the distance between two points distributed uniformly at random in various polygons, based on the extended Kinematic Measure (KM) from integral geometry. We first…
We describe a simple algorithm based on a Markov chain process to generate simply connected acyclic directed graphs over a fixed set of vertices. This algorithm is an extension of a previous one, designed to generate acyclic digraphs, non…
In this article we will represent some ideas and a lot of new theorems in Euclidean plane geometry.
We address generating theorems from a given set of axioms, without proof goal, aiming at value from a mathematical point of view or as lemmas for automated proving. As benchmark, we convert a fragment of the Metamath database set.mm. Our…
In this article we determine several theorems and methods for solving linear congruences and systems of linear congruences, and we find the number of distinct solutions. Many examples of solving congruences are given.
This extended abstract is about an effort to build a formal description of a triangulation algorithm starting with a naive description of the algorithm where triangles, edges, and triangulations are simply given as sets and the most complex…
To generate a triangle of unit perimeter, break a stick of length 1 in two places at random, with the condition that triangle inequalities are satisfied. Is there a similarly natural method for generating triangles of unit area? Study of a…
This paper explores the application of automated planning to automated theorem proving, which is a branch of automated reasoning concerned with the development of algorithms and computer programs to construct mathematical proofs. In…
We describe an algorithm that takes as input an open book decomposition of a closed oriented 4-manifold and outputs an explicit trisection diagram of that 4-manifold. Moreover, a slight variation of this algorithm also works for open books…
In this study we consider the problem of triangulated graphs. Precisely we give a necessary and sufficient condition for a graph to be triangulated. This give an alternative characterization of triangulated graphs. Our method is based on…
We present a multiplication algorithm to recursively construct vertices for the Schroedinger functional in the abelian background field case. The algorithm is suited for automatic perturbative calculations with a variety of actions. As…
We describe a number of geometric contexts where categorification appears naturally: coherent sheaves, constructible sheaves and sheaves of modules over quantizations. In each case, we discuss how "index formulas" allow us to easily perform…
Special orthogonal matrices with rational elements form the group SO(n,Q), where Q is the field of rational numbers. A theorem describing the structure of an arbitrary matrix from this group is proved. This theorem yields an algorithm for…
The purpose of this article is to introduce a new iterative algorithm with properties resembling real life bipartite graphs. The algorithm enables us to generate wide range of random bigraphs, which features are determined by a set of…
An algorithm is presented that generates sets of size equal to the degree of a given variety defined by a homogeneous ideal. This algorithm suggests a versatile framework to study various problems in combinatorial algebraic geometry and…