Euclid meets Bezout: Intersecting algebraic plane curves with the Euclidean algorithm
We show how the Eulcidean algorithm for polynomials can be used to find the intersection points, with multiplicities, of two plane algebraic curves.
math.AG↗
arXiv subjects
Jan Hilmar
Publications and source records attributed to Jan Hilmar.
Consequences of the Continuity of the Monic Integer Transfinite Diameter
We consider the problem of determining the monic integer transfinite diameter for real intervals $I$ of length less than 4. We show that $t_M([0,x])$, as a function in $x>0$, is continuous, therefore disproving two conjectures due to Hare and Smyth. Consequently, for $n>2\in\naturals$, we define the quantity $b_{\max}(n)&=&\sup_{b>\frac{1}{n}}\left\{b|t_M([0,b])=\tfrac{1}{n}\right.\right\}$ and give lower and upper bounds of $b_{\max}(n)$. Finally, we improve the lower bound for $b_{\max}(n)$ for $3\leq n\leq 8$.
math.NT↗