MEGA 2007Effective Methods in Algebraic Geometry Strobl, Austria, June 25th - 29th |
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Electronic Proceedings
Abstract
| Title | The number of real roots of a bivariate polynomial on a line. |
| Keywords | fewnomials, Descartes' rule of signs, algorithms. |
| Abstract | We prove that a polynomial f in R[x,y] with t non-zero terms, restricted on a real line y=ax+b, either has at most 6t-4 zeroes or vanishes over the whole line. As a consequence, we derive an alternative algorithm to decide whether a linear polynomial y-ax-b in K[x,y] divides a sparse polynomial f in K[x,y] with t terms in [log(H(f)H(a)H(b))[K:Q]log(deg(f))t^O(1) bit operations, where K is a real number field. |
The Institute is named after the famous Austrian mathematician Johann Radon (1887-1956)
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Österreichische Akademie der Wissenschaften
Juristische Person öffentlichen Rechts (BGBl 569/1921 idF BGBl I 130/2003)
Dr. Ignaz Seipel-Platz 2, 1010 Wien
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