Moving Frames and Invariants in the Differential and Algebraic Settings
  • Hong, H. and Kogan, I. A.
    Equi-affine minimal-degree moving frames for polynomial curves,     Maple code and examples.

  • Agudelo, J., Dippold. B., Klein, I., Kokot, A., Geiger, E., and Kogan, I.
    Euclidean and Affine Curve Reconstruction. accepted to Involve.

  • Kogan, I. A.
    Invariants: Computation and Applications
    Proceedings of the 2023 International Symposium on Symbolic and Algebraic Computation, (2023) 31 - 40.
    Maple Codes     Tutorial Slides

  • Geiger, E. and Kogan, I. A.
    Non-congruent non-degenerate curves with identical signatures.
    Journal of Mathematical Imaging and Vision (JMIV) 63 (5), (2021) 601 - 625
    Online version     ArXiv preprint

  • Kogan I.A., Ruddy, M. and Vinzant C.
    Differential signatures of algebraic curves
    SIAM Journal on Applied Algebra and Geometry (SIAGA) 4(1), 185 - 226. (42 pages)
    ArXiv preprint

  • Hong, H., Hough, Z., Kogan I. A. and Li, Z.
    Degree-optimal moving frames for rational curves,     Maple code and examples.

  • Kogan I. A. and Olver P. J.
    Invariants of objects and their images under surjective maps
    Lobachevskii J. Math., Vol. 36, No 3, (2015), 260 - 285.
    Corrections and additions to the published version
    ArXiv (with correction and additions)

  • Burdis, J. M., Kogan, I. A. and Hong, H.
    Object-image correspondence for algebraic curves under projections.
    SIGMA. Symmetry, Integrability and Geometry. Methods and Applications, Vol. 9, (2013), 31 pp.
    ArXiv preprint

  • Burdis, J. M. and Kogan, I. A.
    Object-image correspondence for curves under central and parallel projections.
    Proceedings of the Symposium on Computational Geometry (SoCG), ACM, New York (2012), 373 - 382.
    Maple code and supplementary materials     preprint

  • Feng, S., Kogan, I. A. and Krim, H.
    Classification of curves in 2D and 3D via affine integral signatures.
    Acta Applicandae Mathematicae, Vol. 109, No. 3, (2010), 903 - 937
    arXiv preprint.

  • Hubert, E. and Kogan, I. A.
    Smooth and algebraic invariants of a group action. Local and global constructions.
    Foundations of Computational Math. J., Vol. 7, No. 4 (2007), 345 - 383.
    preprint

  • Hubert, E. and Kogan, I. A.
    Rational invariants of a group action. Construction and rewriting.
    J. of Symbolic Comput., Vol 42, No 1-2, (2007) 203 - 217.
    preprint     earlier (2005) arXiv version

  • Kogan, I. A.
    Two algorithms for a moving frame construction.
    Canadian Journal of Math., Vol. 55, No. 2, (2003), 266 - 291.
    preprint

  • Kogan, I. A. and Moreno Maza, M.
    Computation of canonical forms for ternary cubics.
    Proceedings of International Symposium on Symbolic and Algebraic Computation (ISSAC), ACM, (2002), 151 - 160.
    Corrected version     Corrections to published version     Maple worksheet


    Invariant Euler-Lagrange equations and the invariant variational bicomplex.
    Acta Applicandae Mathematicae, Vol. 76, No. 2, (2003), 137 - 193.
    Corrected version     Corrections to published version.     Maple worksheet: iVB

  • Kogan, I. A. and Olver, P.
    The invariant variational bicomplex.
    Contemporary Mathematics, AMS, Vol. 285, (2001), 131 - 144.
    Corrected version     Corrections to published version

  • Kogan, I. A.
    Inductive construction of moving frames.
    Contemporary Mathematics, AMS, Vol. 285, (2001), 157 - 170.
    preprint

  • Kogan, I. A.
    Inductive Approach to Cartan's Moving Frame Method with Applications to Classical Invariant Theory
    Ph.D. Thesis, University of Minnesota, 2000.

  • Berchenko (Kogan), I. A. and Olver, P.
    Symmetries of polynomials.
    J. of Symbolic Comput., Vol. 29, No 4-5, (2000), 485 - 514.
    Maple worksheet in html format     Maple worksheet in mws format