منابع مشابه
Fixed points of automorphisms of real algebraic curves
We bound the number of fixed points of an automorphism of a real curve in terms of the genus and the number of connected components of the real part of the curve. Using this bound, we derive some consequences concerning the maximum order of an automorphism and the maximum order of an abelian group of automorphisms of a real curve. We also bound the full group of automorphisms of a real hyperell...
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This thesis presents an exact and complete approach for visualization of segments and points of real plane algebraic curves given in implicit form f(x, y) = 0. A curve segment is a distinct curve branch consisting of regular points only. Visualization of algebraic curves having self-intersection and isolated points constitutes the main challenge. Visualization of curve segments involves even mo...
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Shape modeling using planar cubic algebraic curves calls for computing the real inflection points of these curves since inflection points represents important shape feature. A real inflection point is also required for transforming projectively a planar cubic algebraic curve to the normal form, in order to facilitate further analysis of the curve. However, the naive method for computing the inf...
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We study real algebraic plane curves, at an elementary level, using as little algebra as possible. Both cases, affine and projective, are addressed. A real curve is infinite, finite or empty according to the fact that a minimal polynomial for the curve is indefinite, semi–definite nondefinite or definite. We present a discussion about isolated points. By means of the operator, these points can ...
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For an integer n≥ 2, let p(z)=nk=1(z−αk) and q(z)= ∏n k=1(z−βk), where αk,βk are real. We find the number of connected components of the real algebraic curve {(x,y)∈R2 : |p(x+iy)|−|q(x+iy)| = 0} for some αk and βk. Moreover, in these cases, we show that each connected component contains zeros of p(z)+q(z), and we investigate the locus of zeros of p(z)+q(z). 2000 Mathematics Subject Classificati...
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ژورنال
عنوان ژورنال: European Journal of Mathematics
سال: 2019
ISSN: 2199-675X,2199-6768
DOI: 10.1007/s40879-019-00324-9