The Algebra of Invariants

By T. A. Springer. 2007

241 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/bb06905bf8f32cec9063dee5d6884c35f8616327

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Citations in the corpus

Hyperelliptic curves and their invariants: geometric, arithmetic and algorithmic aspects (2011, background): “Thanks to the so-called Clebsch-Gordan formula, one can even prove that Cn is generated by a finite number of iterations of transvectants starting from the single covariant f (see [25]).”
Integrals and Phase Portraits of Planar Quadratic Differential Systems With Invariant Lines of at Least Five Total Multiplicity (2008, background): “as well as the classical differential operator (f, φ)(k) acting on R[x, y]2 which is called transvectant of index k (see, for example, [9, 12]):”
Topics in classical algebraic geometry (2006, background): “It is proven in [140] that any covariant of C,S is given by a polynomial in homogeneous forms defining C,S, F, J(C,S, F ).”
Classical Algebraic Geometry: A Modern View (2012, background): “One can find an exposition on the theory of invariants of ternary cubics in classical books on the invariant theory [259], [213].”
Linear scale-space (1994, methodology): “( 1991 ) , who makes use of classical techniques from diierential geometry ( Spivak 1975 ; Koenderink 1990 ) , algebraic geometry , and invariant theory ( Grace and Young 1965 ; Weyl 1946 ) for classifying geometric properties of the N - jet of a signal at a given scale in scale - space .”
The invariants of a genus one curve (2006, methodology): “One of the tools of classical invariant theory is the so-called symbolic notation, as described in [ 14 ].”
Planar quadratic differential systems with invariant straight lines of total multiplicity four (2008, unknown): “(f, g) (k) ∈ R[a, x, y] is called the transvectant of index k of (f, g) (cf. [ 8 ], [13])”
Integral Invariants for Shape Matching (2006, background): “Consequently, a number of features that are invariant under specific transformations have been investigated [24], [39], [25], [ 33 ], [56], [81], [74].”
The Full Study of Planar Quadratic Differential Systems Possessing a Line of Singularities at Infinity (2008, background): “transvectant of index k (see, for example, [ 9 ,14]):”