Automorphisms of certain forms of higher degree over ordered fields

Chlebowicz, Agnieszka; Sładek, Andrzej; Wołowiec-Musiał, Małgorzata

doi:10.1016/s0024-3795(01)00272-5

Cited by 5 publications

(4 citation statements)

References 8 publications

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“…The main idea to speed up the identity test is that if the degree d of a diagonal circuit C is large compared to fanin k then C = 0 only in "trivial" ways. This is formalized by the following result (also see Theorem 2 of [CSWM01] Theorem 23. Let F be a finite field with d < char(F).…”

Section: A Faster Identity Test For Diagonal Circuitsmentioning

confidence: 98%

Diagonal Circuit Identity Testing and Lower Bounds

Saxena¹

2008

Automata, Languages and Programming

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In this paper we give the first deterministic polynomial time algorithm for testing whether a diagonal depth-3 circuit C(x 1 ,. .. , x n) (i.e. C is a sum of powers of linear functions) is zero. We also prove an exponential lower bound showing that such a circuit will compute determinant or permanent only if there are exponentially many linear functions. Our techniques generalize to the following new results: 1. Suppose we are given a depth-3 circuit (over any field F) of the form:

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Section: A Faster Identity Test For Diagonal Circuitsmentioning

confidence: 98%

Diagonal Circuit Identity Testing and Lower Bounds

Saxena¹

2008

Automata, Languages and Programming

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“…An alternative presentation of the foregoing can be made using "Serret's Theorem" (see [1] or [11, p.26…”

Section: Example 1 (Part Two)mentioning

confidence: 99%

“…An alternative presentation of the foregoing can be made using "Serret's Theorem" (see [1] or [11, p.26]): given α j ∈ C n , 1 ≤ j ≤ r, α j = (α j1 , . .…”

Section: T (R N D) For Small R N Dmentioning

confidence: 99%

Patterns of dependence among powers of polynomials

Reznick¹

2003

Algorithmic and Quantitative Real Algebraic Geometry

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“…Sometimes this group is called the orthogonal group of (V , Θ) in analogy with the quadratic case. The orthogonal group of a higher degree form has been studied by several authors, for instance see [2][3][4][5][6][7]18].…”

Section: Introductionmentioning

confidence: 99%

The automorphism group of certain higher degree forms

O'Ryan

Ryom-Hansen

2009

Journal of Pure and Applied Algebra

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a b s t r a c tWe consider symmetric indecomposable d-linear (d > 2) spaces of dimension n over an algebraically closed field k of characteristic 0, whose center (the analog of the space of symmetric matrices of a bilinear form) is cyclic, as introduced by Reichstein [B. Reichstein, On Waring's problem for cubic forms, Linear Algebra Appl. 160 (1992) 1-61]. The automorphism group of these spaces is determined through the action on the center and through the determination of the Lie algebra. Furthermore, we relate the Lie algebra to the Witt algebra.

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Automorphisms of certain forms of higher degree over ordered fields

Cited by 5 publications

References 8 publications

Diagonal Circuit Identity Testing and Lower Bounds

Diagonal Circuit Identity Testing and Lower Bounds

Patterns of dependence among powers of polynomials

The automorphism group of certain higher degree forms

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