Is it possible with sage to use some type of shorthand notation to 

> denote the first or second time derivative? 
>
>
Hi,

That's a good question, but Sage does not currently support the greatest 
short notation for derivatives, either differential-style or fluxion-style. 
 The problem is the ambiguity that can arise, among others.  However, in 
principle one could customize the string-creating or LaTeX methods for 
derivatives if one wanted to, though it could be tricky to do so 
consistently.

Craig Finch, who is not affiliated with Sage but wrote a pretty good 
introductory (non-free) book about it, has a good explanation 
at http://www.shocksolution.com/2012/03/partial-derivative-notation-in-sage/ 
and there is something kind of like what you want in the comments (I 
think), and he also links to a very long discussion 
at https://groups.google.com/forum/#!topic/sage-devel/LIBo8nwftkI You can 
see some noble attempts at this at http://trac.sagemath.org/ticket/6756 .

Good luck!
- kcrisman

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