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Mathematica is very useful and powerful in symbol compute, but some output isn’t concise if we didn’t simplify.

Can i predefined some operator? eg. Lie bracket. Here is a minimum example.

Suppose bracket operator is $[x, y]= xy-yx$, and $\hat{a} b= a \times b$ (Hat operator). Here $x,y,a, b$ are vector (fields).

If some output in Mathematica is

2*X[t]*y[t]-2*y[t]*x[t] + CrossProduct[3*a,b]

Can i simplify it as $2[x,y]+3\hat{a} b$, the form in most Math books?

I find a lots of similar discussion (It use self-defined Functions to simplify the expression by FullSimplify), but i think it’s important in symbol computing and simplifying by self-defined operators. In this way, output will not the function Name eg. liebracket[x_,y_]=x y - y x , we may let symbol operator appear in formula, eg [x,y].

Any comments will be much appreciate!

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