 ${\mathfrak{n}}\cap{\mathcal{B}}$ contains $d$ linearly independent vectors.  \[thm0b\] Let ${\mathfrak{n}}\subset{\mathfrak{o}}$ be a nonzero ideal, and let ${\mathcal{B}}\subset k\otimes_{\mathbb{Q}}{\mathbb{R}}$ be a convex body symmetric about the origin. 