We examine quadratic surfaces in 3-space that are tangent to nine given figures. These figures can be points, lines, planes or quadrics. The numbers of tangent quadrics were determined by Hermann Schubert in 1879. We study the associated systems of polynomial equations, also in the space of complete quadrics, and we solve them using certified numerical methods. Our aim is to show that Schubert's problems are fully real.

中文翻译：

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实 3 空间中的切线二次曲线

我们检查与九个给定图形相切的 3 空间中的二次曲面。这些图形可以是点、线、平面或二次曲面。Hermann Schubert 于 1879 年确定了切线二次方程的数量。我们研究多项式方程的关联系统，也在完全二次方程的空间中，我们使用经过认证的数值方法求解它们。我们的目标是证明舒伯特的问题是完全真实的。