A new algorithm for discussing Gröbner bases with parameters

A Montes - Journal of Symbolic Computation, 2002 - Elsevier
Let F be a set of polynomials in the variables __x= x1,..., xnwith coefficients in R [__ a],
where R is a UFD and __ a= a1,..., am a set of parameters. In this paper we present a new …

Fundamentals of the holomorphic embedding load-flow method

A Trias - ar** computational
methods to solve load flow equations where a key question is the maximum number of …

Improving the DISPGB algorithm using the discriminant ideal

M Manubens, A Montes - Journal of Symbolic Computation, 2006 - Elsevier
In 1992, V. Weispfenning proved the existence of Comprehensive Gröbner Bases (CGB)
and gave an algorithm for computing one. That algorithm was not very efficient and not …

Convexification of power flow equations in the presence of noisy measurements

R Madani, J Lavaei, R Baldick - IEEE Transactions on …, 2019 - ieeexplore.ieee.org
This paper is concerned with the power system state estimation (PSSE) problem that aims to
find the unknown operating point of a power network based on a given set of measurements …

HELM: The holomorphic embedding load-flow method. Foundations and implementations

A Trias - Foundations and Trends® in Electric Energy …, 2018 - nowpublishers.com
Abstract The Holomorphic Embedding Load-Flow Method (HELM) was recently introduced
as a novel technique to constructively solve the power flow equations in power networks …

Gröbner bases for families of affine or projective schemes

M Wibmer - Journal of Symbolic Computation, 2007 - Elsevier
Let I be an ideal of the polynomial ring A [x]= A [x1,…, xn] over the commutative, Noetherian
ring A. Geometrically, I defines a family of affine schemes, parameterized by Spec (A): For …

[HTML][HTML] Parametric FGLM algorithm

MD Darmian, A Hashemi - Journal of Symbolic Computation, 2017 - Elsevier
In this paper, we consider the non-trivial problem of converting a zero-dimensional
parametric Gröbner basis wrt a given monomial ordering to a Gröbner basis wrt any other …

Gröbner systems conversion

A Hashemi, M Dehghani Darmian… - Mathematics in Computer …, 2017 - Springer
In this paper, we consider the problem of converting parametric Gröbner bases. More
precisely, given a (comprehensive) Gröbner system wrt a given monomial ordering, we …