Matrix invariants of binary forms

Invariants of Polynomials and Binary Forms

We survey various classical results on invariants of polynomials, or equivalently, of binary forms, focussing on explicit calculations for invariants of polynomials of degrees 2, 3, 4.

Joint Differential Invariants of Binary and Ternary Forms

We construct and classify the joint invariants and joint differential invariants of binary and ternary forms. In particular, we prove that the differential invariant algebra of ternary forms is generated by a single third order differential invariant. To connect our results with earlier analysis of Kogan, we develop a general method for relating differential invariants associated with different...

Invariants of Binary Bilinear Forms Modulo Two Larry

Smallest Reduction Matrix of Binary Quadratic Forms And Cryptographic Applications

We present a variant of the Lagrange-Gauss reduction of quadratic forms designed to minimize the norm of the reduction matrix within a quadratic complexity. The matrix computed by our algorithm on the input f has norm O f 1 2 Δ 4 f , which is the square root of the best previously known bounds using classical algorithms. This new bound allows us to fully prove the heuristic lattice based attack...

Equivariant -invariants and -forms

Let a Lie group G act isometrically on an odd dimensional Riemannian manifold M and let D be a G-equivariant operator of Dirac type on M. We construct a formal power series X (D) in X 2 g, which can be interpreted as a universal-form for families of Dirac operators induced by D over brations with bres isometric to M and with structure group G. For a Killing eld X 2 g without zeroes, rX (D) is t...