Matroid intersection

The matroid intersection problem is a fundamental problem that has been extensively studied for half a century. In the classic version of this problem, we are given two matroids ${\mathcal{M}}_1=(V,{\mathcal{I}}_1)$ and ${\mathcal{M}}_2=(V,{\mathcal{I}}_2)$ on a comment ground set $V$ of $n$ elements, and then we have to find the largest common independent set $S\in {\mathcal{I}}_1\cap {\mathcal{I}}_2$ by making independence oracle queries of the form ''Is $S\in {\mathcal{I}}_1$?