2018/01/30 by Juan Gerardo Alcázar, Alcázar, Juan Gerardo, Miroslav Lávička +3
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #FOS: Computer and information sciences #FOS: Mathematics #Polynomial and algebraic computation #Symbolic Computation (cs.SC)
paper · pdf · doi:10.48550/arxiv.1801.09962
openalex publication_date 2018/01/30 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
We present novel, deterministic, efficient algorithms to compute the\nsymmetries of a planar algebraic curve, implicitly defined, and to check\nwhether or not two given implicit planar algebraic curves are similar, i.e.\nequal up to a similarity transformation. Both algorithms are based on the fact,\nwell-known in Harmonic Analysis, that the Laplacian operator commutes with\northogonal transformations, and on efficient algorithms to find the\nsymmetriessimilarities of a harmonic algebraic curvetwo given harmonic\nalgebraic curves. In fact, we show that in general the problem can be reduced\nto the harmonic case, except for some special cases, easy to treat.\n