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0

Tensor indices: T^{\alpha\beta}{}_{\gamma\delta}: $T^{\alpha\beta}{}_{\gamma\delta}$ T^{\alpha \beta}{}_{\gamma\delta}{}^{\lambda}: $T^{\alpha \beta}{}_{\gamma\delta}{}^{\lambda}$ So for instance, a $(2,2)$-tensor would act on two covectors ($\omega$, $\varphi$) and two vectors ($v$,$w$) to produce a real number like this: $$[T^{\alpha \beta}{}_{\...


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$$\overset{C\hspace{-2px}R\style{zoom:1.1}{T}}{\iff}$$ \overset{C\hspace{-3px}R\style{zoom:1.1}{T}}{\iff} Works in my browser currently ( with htmlcss or SVG renderer, all of common html,preview html makes the T bigger) but seems a little annoying to type out. chrome version 76 something at my local library.


16

Since you asked about some specific meanings when the vertical line appears: For divisibility, you use \mid (and \nmid) for "does not divide". For example, $a\mid b$ $a\mid b$, $4\mid8$ $4\mid8$, $4\nmid7$ $4\nmid7$. The advantage over typing just $4|8$ $4|8$ is that \mid yields extra spacing (but some authors prefer $4|8$). For conditions in set notation, ...


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I believe the word "pipe" is used more in computer science than in mathematics. Unlike the strict syntax requirement in programming languages, how to type out this vertical bar in mathematical writing is mostly about typographical consideration. There are discussions regarding different commands in this question at https://tex.stackexchange.com. ...


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$$\underset{\underset{\hspace{-20px}l_k}\searrow}{y\overset{f}\longrightarrow}\underset{\hspace{-20px}X_{l_K}}{\underset{\downarrow P_{r_k}}{\hspace{-20px}X}}$$ I mostly used underset and overset: \underset{\underset{\hspace{-20px}l_k}\searrow}{y\overset{f}\longrightarrow}\underset{\hspace{-20px}X_{l_K}}{\underset{\downarrow P_{r_k}}{\hspace{-20px}X}} ...


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