Andradas Heranz, Carlos and Recio, Tomás and Sendra, J. Rafael (1999) Base field restriction techniques for parametric curves. ISSAC 99: PROCEEDINGS OF THE 1999 INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION . pp. 17-22.
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Given a variety V, implicitly defined over an algebraic separable field extension k(alpha), A. Weil  developed a restriction technique (called by him a descente method),that associates to V a suitable k-variety W, such that many properties of V can be analyzed by merely looking at W, that is, by descending to the base field k. In this paper we present a parametric counterpart, for curves, of Weil's construction. As an application, we state some simple algorithmic criteria over the variety W that translate, for instance, the k-definability of a parametric curve V, or the existence of an infinite number of L-rational points in V.
|Additional Information:||International Symposium on Symbolic and Algebraic Computation, JUL 29-31, 1999 Vancouver,Canada|
|Uncontrolled Keywords:||Computer Science; Theory & Methods; Mathematica; Applied; Mathematics|
|Subjects:||Sciences > Mathematics > Algebraic geometry|
|Deposited On:||20 Apr 2012 11:42|
|Last Modified:||06 Feb 2014 10:12|
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