[HTML][HTML] Communication: Fitting potential energy surfaces with fundamental invariant neural network

K Shao, J Chen, Z Zhao, DH Zhang - The Journal of Chemical Physics, 2016 - pubs.aip.org
A more flexible neural network (NN) method using the fundamental invariants (FIs) as the
input vector is proposed in the construction of potential energy surfaces for molecular …

[图书][B] Computational invariant theory

H Derksen, G Kemper - 2015 - books.google.com
This book is about the computational aspects of invariant theory. Of central interest is the
question how the invariant ring of a given group action can be calculated. Algorithms for this …

Primary decomposition: algorithms and comparisons

W Decker, GM Greuel, G Pfister - … Number Theory: Selected Papers From a …, 1999 - Springer
The Hilbert series and degree bounds play significant roles in computational invariant
theory. In the modular case, neither of these tools is avrulable in general. In this article three …

Arjeh M. Cohen Henri Cohen

DEB Sturmfels - 2006 - Springer
Systems of polynomial equations are central to mathematics and its application to science
and engineering. Their solution sets, called algebraic sets, are studied in algebraic …

[图书][B] Computer algebra methods for equivariant dynamical systems

K Gatermann - 2007 - books.google.com
This book starts with an overview of the research of Gröbner bases which have many
applications in various areas of mathematics since they are a general tool for the …

Invariant Theory

W Decker, L Ramesh, J Schmitt - The Computer Algebra System OSCAR …, 2025 - Springer
This is a tutorial on invariant theory in OSCAR. We begin by introducing some of the basic
notions and results of invariant theory in their historical context. Then we discuss relevant …

Galois group computation for rational polynomials

K Geissler, J Klüners - Journal of Symbolic Computation, 2000 - Elsevier
We describe methods for the computation of Galois groups of univariate polynomials over
the rationals which we have implemented up to degree 15. These methods are based on …

On the Cohen–Macaulay property of modular invariant rings

G Kemper - Journal of Algebra, 1999 - Elsevier
IfVis a faithful module for a finite groupGover a field of characteristicp, then the ring of
invariants need not be Cohen–Macaulay ifpdivides the order ofG. In this article the …

Computation of Galois groups of rational polynomials

C Fieker, J Klüners - LMS Journal of Computation and Mathematics, 2014 - cambridge.org
Computational Galois theory, in particular the problem of computing the Galois group of a
given polynomial, is a very old problem. Currently, the best algorithmic solution is …

Symmetric powers of modular representations, Hilbert series and degree bounds

I Hughes, G Kemper - Communications in Algebra, 2000 - Taylor & Francis
Let G= Z p be a cyclic group of prime order p with a representation G→ GL (V) over a field K
of characteristic p. In 1976, Almkvist and Fossum gave formulas for the decomposition of the …