# Invariant Methods in Discrete and Computational Geometry

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Invariant, or coordinate-free methods provide a natural framework for many geometric questions. Invariant Methods in Discrete and Computational Geometry provides a basic introduction to several aspects of invariant theory, including the supersymmetric algebra, the Grassmann-Cayler algebra, and Chow forms. It also presents a number of current research papers on invariant theory and its applications to problems in geometry, such as automated theorem proving and computer vision. Audience: Researchers studying mathematics, computers and robotics.We take the ideal generated by the three polynomials uoofo-Huoi fi +uo2 f2+ u03 fa, ulofo + u11.fi + u12 f2 + u13.f3, and u20fo + u21f1 + ... As the result we get the expansion of the Chow form R X = [123]a a [023]* + [013]. ... example, if A = {(3, 0), (2, 1), (1, 2), (0, 3)} then the toric variety XA is the twisted cubic curve and the A- resultant is the resultant of two binary cubic forms. ... fixed Le G(n a d a 2, n), the expression Rx (span(p, L)) is a polynomial in p = (po, p1, ..., pn) of degree deg(X).

 Title : Invariant Methods in Discrete and Computational Geometry Author : Neil L. White Publisher : Springer Science & Business Media - 2013-03-09