What do we mean when we say a expression is simplified. Should we define some kind of metric that says one expression is more simplified than another. My dumb suggestion would be the simplification of an expression would be the string that contains the fewest characters. Could simplification methods be defined in some kind of multidimensional space that could be searched for the simplest final expression. The main problem I have with computer algebra is that in simplifying an express It is obvious to my brain what should be done, but the program requires step by step instructions and the instructions are usually different for each expression. What is the current standard for automatic simplification of finite algebraic/trigonometric/hyperbolic expressions and how is it implemented?
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