Thanks! That makes much more sense and seems simpler, I'm glad I know that 
now!

Side note:  Never use += on a string in a loop.  Here it's even worse, 
> since you are concatenating strings on the right hand side as well. 
>
>
Is it because it's slow? 

Also, do you think I should have the to_sage function automatically convert 
it to a symbolic function or fracfield, or should I just leave it as 
outputting the string version? 

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