The conic h(x, y) = [x.sup.2] + [cy.sup.2] -1 = 0, c [member of] R, is an invariant
algebraic curve of system (1).
5.1 General position with respect to
algebraic curvesFor example, Bezout's theorem, that the number of points of intersection of two
algebraic curves is equal to the product of their degrees, would obviously suffer greatly if restricted to the real affine plane."
Although we have presented an algorithm to compute singular points of irreducible
algebraic curves in [17], the algorithm is almost experimental and related analysis of the algorithm is not provided, for instance, the feasibility and complexity.
[1] Bix, R., Conics and Cubics: A Concrete Introduction to
Algebraic Curves, Springer, 2006.
Via the correspondence between
algebraic curves and floor diagrams [BM09, Theorem 2.5] these notions correspond literally to the respective analogues for
algebraic curves.
A selection of 10 papers from it consider such topics as self-dual codes and invariant theory; vector bundles in error-correcting for geometric Goppa codes; combinatorial designs and code synchronization; real and imaginary hyper-elliptic curve cryptography; divisibility, smoothness, and cryptographic applications; a variant of the Reidemeister-Schreier algorithm for the fundamental groups of Riemann surfaces; theta functions and
algebraic curves with automorphisms; enumerative geometry and string theory; and the cryptographical properties of extremal algebraic graphs.
Ramanathan: Moduli for principal bundles over
algebraic curves. I, Proc.
DEMMEL, Algorithms for intersecting parametric and
algebraic curves I.