SOLVING SYSTEMS OF POLYNOMIAL EQUATIONS

By Dinesh Manocha. 2002

1,064 citations recorded by the source corpus.

Subfields: Computational Mathematics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/b03e0b7a9075c37f9c3b6a90e6cc36e1e35ee843

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Citations in the corpus

Linear Fitted-Q Iteration with Multiple Reward Functions (2012, methodology): “The system (10) of polynomial equations can be solved by computer algebra systems or using numerical approximation techniques (Cox et al., 1997; Sturmfels, 2002).”
On the frontiers of polynomial computations in tropical geometry (2004, background): “From the viewpoint of polynomial equations, the modern birth of tropical geometry originates in the book [20] which pinpoints the central role of tropical geometry as a link between algebraic geometry, symbolic computation , and discrete geometry, thus providing computationally-accessible methods…”
One-, Two-, and Multi-Fold Origami Axioms (2006, neutral): “[30]) in the program Magma.”
Patchworking singular algebraic curves, non-Archimedean amoebas and enumerative geometry (2002, background): “rreducible curves and irreducible amoebas One can speak on non-Archimedean amoebas as corner loci of all possible convex piece-wise linear functions, whose generic gradients are integral vectors (cf. [28]). In such a sense, an amoeba is called reducible if it is the union of two proper sub-amoebas. ”
Mixed multiplicities of ideals versus mixed volumes of polytopes (2005, background): “n (−1)n−hV n(Q i1 +···+Q i h ). Here V n denotes the n-dimensional Euclidean volume. Mixed volumes play an important role in convex geometry (see [BF], [Ew]) and elimination theory (see [GKZ], [CLO], [Stu]). Our interest in mixed volumes arises from the following result of Bernstein [Be] which relat”
Log-concavity of characteristic polynomials and the Bergman fan of matroids (2011, background): “yperplanes on an r-dimensional projective subspace V ⊂ Pn realizing M. We can identify ∆M as the tropicalization of the complement V◦ := V \A = V ∩ T. LOG-CONCAVITY AND THE BERGMAN FAN 7 Theorem 4.2. [16] The tropicalization of V ◦ is ∆M. Let Ve denote the closure of V ◦ in X = X(∆U n). Since the un”
The Tropical Totally Positive Grassmannian (2003, background): “Finally, we suggest a general conjecture about the positive part of the tropicalization of a cluster algebra.”
Matroid Theory for Algebraic Geometers (2014, background): “Sturmfels gave a combinatorial definition [92] which was elaborated by Ardila-Klivans [3].”
Algebraic Solution of GPS Pseudo-Ranging Equations (2002, methodology): “It should be pointed out that there exist several procedures for computing the resultants as exemplified in the works of Manocha (1992, 1993, 1994a, 1994b, 1994c) , who solved the Multipolynomial resultants using the eigenvalue-eigenvector approach, Canny (1988), who solved the resultant using the ”
Eigenvalues and invariants of tensors (2007, background): “According to the resultant theory [5,8,22], the resultant of F(x) is an irreducible polynomial of the coefficient of F(x), i.”
Ideals of adjacent minors (2003, background): “ probability distributions of these random variables (the so-called no dway interaction models [8]) gives rise to a toric variety whose set of deﬁning equations may be extremely large and complicated [1, 15]. However, the positive probability distributions are described precisely by the simple multi”
Parametric optimization and optimal control using algebraic geometry methods (2006, methodology): “Various methods have been proposed in the literature for solving systems of polynomial equations, both numerical and symbolic (Manocha 1994, Parrilo and Sturmfels 2000 and Sturmfels 2002).”
On the rank of a tropical matrix (2003, background): “We review the basic setup from [24, 26].”