Analysis of Geometrical Theorems in Coordinate-Free Form by Using Anticommutative Gröbner Bases Method
نویسنده
چکیده
In this paper we consider the Gröbner bases of Grassman algebra and their application to the algebraic geometry. Geometrical statements of constructive type should be given in the coordinate-free form.
منابع مشابه
Application of the Noncommutative Gröbner Bases Method for Proving Geometrical Statements in Coordinate-free Form
In this paper we consider the application of the noncommutative Gröbner bases method for proving theorems in algebraic geometry. Geometrical statements of constructive type should be given in the coordinate-free form. 1. Coordinate-free representation of points and statements We consider theorems of elementary geometry (two-dimensional and three-dimensional). Let A1, A2, A3, . . . , An be point...
متن کاملar X iv : 1 50 2 . 06 47 2 v 1 [ m at h . R A ] 8 N ov 2 01 4 Gröbner - Shirshov bases and PBW theorems ∗
We review some applications of Gröbner-Shirshov bases, including PBW theorems, linear bases of free universal algebras, normal forms for groups and semigroups, extensions of groups and algebras, embedding of algebras.
متن کاملStiffness Synthesis of a Variable Geometry Six-Degrees-of-Freedom Double Planar Parallel Robot
In this paper, we address the stiffness synthesis problem of variable geometry double planar parallel robots. For a desired stiffness matrix, the free geometrical variables are calculated as a solution of a corresponding polynomial system. Since in practice the set of free geometrical variables might be deficient, the suggested solution addresses also the case where not all stiffness matrix ele...
متن کاملConnecting Gröbner Bases Programs with Coq to do Proofs in Algebra, Geometry and Arithmetics
We describe how we connected three programs that compute Gröbner bases [1] to Coq [11], to do automated proofs on algebraic, geometrical and arithmetical expressions. The result is a set of Coq tactics and a certificate mechanism 1. The programs are: F4 [5], GB [4], and gbcoq [10]. F4 and GB are the fastest (up to our knowledge) available programs that compute Gröbner bases. Gbcoq is slow in ge...
متن کاملSome Geometrical Bases for Incremental-Iterative Methods (RESEARCH NOTE)
Finding the equilibrium path by non-linear structural analysis is one of the most important subjects in structural engineering. In this way, Incremental-Iterative methods are extremely used. This paper introduces several factors in incremental steps. In addition, it suggests some control criteria for the iterative part of the non-linear analysis. These techniques are based on the geometric of e...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2002