Algorithms in invariant theory
Algorithms in invariant theory
Dynamics of Feedback Systems
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
ASP-DAC '07 Proceedings of the 2007 Asia and South Pacific Design Automation Conference
A Singular Introduction to Commutative Algebra
A Singular Introduction to Commutative Algebra
An Algebraic Approach to Guarantee Harmonic Balance Method Using Gröbner Base
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
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This paper presents efficient applications of invariants to harmonic balance (HB) methods using Gröbner base. The Gröbner base is a powerful tool based on ideal theory. Using the Gröbner base, we can obtain the solutions of the HB equation. However, its computation is very time-consuming when the equation has equivalent different solutions based on symmetries of the system. We show that invariants enable to transpose the equivalent different solutions to a unique solution. The bifurcation diagram of the invariant is simpler than the original bifurcation diagram, and its computation is considerably decreased. Further, we can obtain the relation among the amplitudes of each frequency component using the invariants. We propose a method for finding the circuit parameters using the amplitude relation.