A combined method for enclosing all solutions of nonlinear systems of polynomial equations

1995 ◽  
Vol 1 (1) ◽  
pp. 41-64 ◽  
Author(s):  
Christine Jäger ◽  
Dietmar Ratz ◽  
К. йегер ◽  
Л. Рац
Keyword(s):  
Nonlinear Systems ◽  
Polynomial Equations ◽  
Combined Method ◽  
All Solutions ◽  
Systems Of Polynomial Equations

Numerical Continuation Methods for Solving Polynomial Systems Arising in Kinematics

1990 ◽  
Vol 112 (1) ◽  
pp. 59-68 ◽  
Author(s):  
C. W. Wampler ◽  
A. P. Morgan ◽  
A. J. Sommese
Keyword(s):  
Polynomial Systems ◽  
Numerical Continuation ◽  
Continuation Methods ◽  
Basic Material ◽  
Polynomial Equations ◽  
All Solutions ◽  
Recent Developments ◽  
Position Problem ◽  
Main Ideas ◽  
Systems Of Polynomial Equations

Many problems in mechanism design and theoretical kinematics can be formulated as systems of polynomial equations. Recent developments in numerical continuation have led to algorithms that compute all solutions to polynomial systems of moderate size. Despite the immediate relevance of these methods, they are unfamiliar to most kinematicians. This paper attempts to bridge that gap by presenting a tutorial on the main ideas of polynomial continuation along with a section surveying advanced techniques. A seven position Burmester problem serves to illustrate the basic material and the inverse position problem for general six-axis manipulators shows the usefulness of the advanced techniques.

Construction of systems of polynomial equations with exact p-Divisibility via the covering method

2014 ◽  
Vol 13 (06) ◽  
pp. 1450013 ◽  
Author(s):  
Francis N. Castro ◽  
Ivelisse M. Rubio
Keyword(s):  
Exponential Sums ◽  
Polynomial Equations ◽  
Prime Field ◽  
Elementary Method ◽  
Covering Method ◽  
Systems Of Polynomial Equations

We present an elementary method to compute the exact p-divisibility of exponential sums of systems of polynomial equations over the prime field. Our results extend results by Carlitz and provide concrete and simple conditions to construct families of polynomial equations that are solvable over the prime field.

scholarly journals Linear Network Codes and Systems of Polynomial Equations

2008 ◽  
Vol 54 (5) ◽  
pp. 2303-2316 ◽  
Author(s):  
Randall Dougherty ◽  
Chris Freiling ◽  
Kenneth Zeger
Keyword(s):  
Polynomial Equations ◽  
Linear Network ◽  
Network Codes ◽  
Systems Of Polynomial Equations

scholarly journals Bivariate systems of polynomial equations with roots of high multiplicity

2021 ◽  
Author(s):  
I. Nikitin
Keyword(s):  
High Multiplicity ◽  
Polynomial Equations ◽  
Support Sets ◽  
Multiplicity Formula ◽  
System Of Polynomial Equations ◽  
Systems Of Polynomial Equations

Given a bivariate system of polynomial equations with fixed support sets [Formula: see text] it is natural to ask which multiplicities its solutions can have. We prove that there exists a system with a solution of multiplicity [Formula: see text] for all [Formula: see text] in the range [Formula: see text], where [Formula: see text] is the set of all integral vectors that shift B to a subset of [Formula: see text]. As an application, we classify all pairs [Formula: see text] such that the system supported at [Formula: see text] does not have a solution of multiplicity higher than [Formula: see text].

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