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Each point \(p \in \mathbb{H}^n\) has tangent vectors \(\frac{\partial}{\partial x^i} in T_p M\) (which we write as the partial derivatives) at \(p\) given local coordinates (i.e. a basis \(\text{span}\{x^1,\dots,x^n\} = T_p M\)). The collection \(\bigl\{\frac{\partial}{\partial x^1}\big|_p,\dots,\frac{\partial}{\partial x^n}\big|_p\bigr\}\) forms a basis of \(T_pM\).
The main lesson I learnt from working on these projects is that agents work best when you have approximate knowledge of many things with enough domain expertise to know what should and should not work. Opus 4.5 is good enough to let me finally do side projects where I know precisely what I want but not necessarily how to implement it. These specific projects aren’t the Next Big Thing™ that justifies the existence of an industry taking billions of dollars in venture capital, but they make my life better and since they are open-sourced, hopefully they make someone else’s life better. However, I still wanted to push agents to do more impactful things in an area that might be more worth it.，这一点在雷电模拟器官方版本下载中也有详细论述
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