Groebner Basis for Polynomials with Parametric Exponents

2008 ◽  
Author(s):  
Tadashi Takahashi
Keyword(s):  
Groebner Basis

Groebner-basis solution of the three-dimensional resection problem (P4P)

2003 ◽  
Vol 77 (5-6) ◽  
pp. 327-337 ◽  
Author(s):  
J. L. Awange ◽  
E. W. Grafarend
Keyword(s):  
Three Dimensional ◽  
Groebner Basis ◽  
Basis Solution

SOLVING THE INVERSE KINEMATICAL PROBLEM OF A ROBOT ARM BY USING GROEBNER BASIS

2021 ◽  
Vol 13 (1) ◽  
pp. 15
Author(s):  
Alisya Masturoh ◽  
Bambang Hendriya Guswanto ◽  
Triyani Triyani
Keyword(s):  
Robot Hand ◽  
Polynomial Equations ◽  
Robot Arm ◽  
Groebner Basis

The inverse kinematical problem of a robot arm is a problem to find some appropriate joint configurations for a pair of position and direction of a robot hand which is represented by a polynomial equations system. The system is solved by employing Groebner basis notion. Thus, the appropriate joint configurations for a pair of position and direction of the robot hand are obtained.

scholarly journals Satisfying positivity requirement in the Beyond Complex Langevin approach

2018 ◽  
Vol 175 ◽  
pp. 11026 ◽  
Author(s):  
Adam Wyrzykowski ◽  
Błażej Ruba Ruba
Keyword(s):  
Exact Solution ◽  
Approximate Solutions ◽  
Groebner Basis ◽  
Matching Conditions ◽  
Quadratic Equations ◽  
Positive Distribution ◽  
Langevin Approach ◽  
Basis Method ◽  
Special Case ◽  
Complex Density

The problem of finding a positive distribution, which corresponds to a given complex density, is studied. By the requirement that the moments of the positive distribution and of the complex density are equal, one can reduce the problem to solving the matching conditions. These conditions are a set of quadratic equations, thus Groebner basis method was used to find its solutions when it is restricted to a few lowest-order moments. For a Gaussian complex density, these approximate solutions are compared with the exact solution, that is known in this special case.

Application of Groebner Basis Methodology to Nonlinear Static Cable Analysis

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
Y. Jane Liu ◽  
George R. Buchanan ◽  
John Peddieson
Keyword(s):  
Nonlinear Analysis ◽  
Analytical Solutions ◽  
Geometrically Nonlinear ◽  
Large Deflections ◽  
Groebner Basis ◽  
Governing Equations ◽  
Geometrically Nonlinear Analysis ◽  
Exact Analytical Solutions ◽  
Highly Nonlinear ◽  
Nonlinear Static

The governing equations for large deflections of cables have a highly nonlinear and coupled nature, which precludes exact analytical solutions except in a few simplified cases. The present study demonstrates the utility of Groebner Basis methodology in facilitating the construction of approximate analytical and semianalytical Galerkin solutions in the geometrically nonlinear analysis of cable statics.

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