Often I wish to simplify an expression f(x,y,z) with constraint g(x,y,z) 
= 0.  That is to say f(x,y,z)+lamda*g(x,y,z) is a simplified expression 
(sort of looks like lagrange multipliers).  Many times just looking at 
the expressions tell you what lamda should be, but is there any way to 
automate the process in a more general way?

On simplification in general.  I have noticed that artificial 
intelligence modules exist for python.  Have any symbolic algebra 
programs used artificial intelligence for the simplification of 
expressions or is everything alway hardwired into the code?

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