Displaying similar documents to “Edge-orthogonal patches through a given rational Bézier curve.”

The real field with the rational points of an elliptic curve

Ayhan Günaydın, Philipp Hieronymi (2011)

Fundamenta Mathematicae

Similarity:

We consider the expansion of the real field by the group of rational points of an elliptic curve over the rational numbers. We prove a completeness result, followed by a quantifier elimination result. Moreover we show that open sets definable in that structure are semialgebraic.

On triple curves through a rational triple point of a surface

M. R. Gonzalez-Dorrego (2006)

Annales Polonici Mathematici

Similarity:

Let k be an algebraically closed field of characteristic 0. Let C be an irreducible nonsingular curve in ℙⁿ such that 3C = S ∩ F, where S is a hypersurface and F is a surface in ℙⁿ and F has rational triple points. We classify the rational triple points through which such a curve C can pass (Theorem 1.8), and give an example (1.12). We only consider reduced and irreducible surfaces.