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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 …
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 …
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 …
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
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 …
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 …
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 …
ring A. Geometrically, I defines a family of affine schemes, parameterized by Spec (A): For …
[HTML][HTML] Parametric FGLM algorithm
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 …
parametric Gröbner basis wrt a given monomial ordering to a Gröbner basis wrt any other …
Gröbner systems conversion
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 …
precisely, given a (comprehensive) Gröbner system wrt a given monomial ordering, we …