Abstract A method is presented for computing the form of highest degree of the implicit equation of a rational surface, defined by means of a rational parametrization. Determining the form of highest degree is useful to study the asymptotic behavior of the surface, to perform surface recognition, or to study symmetries of surfaces, among other applications. The method is efficient, and works generally better than known algorithms for implicitizing the whole surface, in the absence of base points blowing up to a curve at infinity. Possibilities to compute the form of highest degree of the implicit equation under the presence of such base points are also discussed. We provide timings to compare our method with known methods for computing the whole implicit equation of the surface, both in absence and in presence of base points blowing up to a curve at infinity.

中文翻译：

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计算有理曲面隐式方程的最高阶形式

摘要 提出了一种计算有理曲面隐式方程最高阶形式的方法，该方程是通过有理参数化定义的。确定最高阶的形式对于研究表面的渐近行为、执行表面识别或研究表面的对称性以及其他应用非常有用。该方法是有效的，并且通常比用于隐式整个表面的已知算法更有效，因为没有基点在无穷远处炸成一条曲线。还讨论了在存在此类基点的情况下计算隐式方程最高阶形式的可能性。我们提供了时间来将我们的方法与已知的计算表面的整个隐式方程的方法进行比较，