Simplifying and Rearranging Expressions

*To*: mathgroup at smc.vnet.net*Subject*: [mg95889] Simplifying and Rearranging Expressions*From*: "David Park" <djmpark at comcast.net>*Date*: Thu, 29 Jan 2009 05:55:14 -0500 (EST)

I want to start a thread on this because I believe many MathGroup people will have some useful things to say. A common task for Mathematica users is to obtain an expression that is in a particular form. For students and teachers this may often be a textbook form, or there may be other reasons that a particular form is desired. It might be thought that this should be an easy task but quite often it can be a very difficult task, even involving mathematical derivation and many of the capabilities of Mathematica. Not obtaining a specific form may be a matter of not knowing how to solve the problem in the first place. Nevertheless, even simple rearrangement can be difficult. I sometimes think of it as doing surgery on expressions. I believe it is generally desirable to use Mathematica to rearrange an expression and not retype the expression. Retyping is too error prone. Simplify and FullSimplify are amazingly useful but it is difficult to control them and obtain a precise result. One will often have to do additional piecemeal operations. One downside of Simplify and FullSimplify is that they can return different forms with different Mathematica versions. Then any additional operations in an old notebook may no longer work. It would be nice if there was a method of using these commands that would be more version independent. Various routines such as Together, Apart, Factor, TrigReduce, TrigFactor, TrigExpand, TrigToExp, GroebnerBasis etc., can be useful in getting a specific form. MapAt is very useful for doing surgery on specific parts of an expression. Mathematica often gets two factors that have extra minus signs. You can correct that by mapping Minus onto the two factors. For integrals in the wrong form you could cheat by trying to find the constant by which they differ by subtracting and simplifying, and then use that in the derivation. Over the years I've collected a number of routines that aid in manipulating expressions and have included them in the Presentations package. Some of these are: CompleteTheSquare, FactorOut (any 'factor' expression with ability to hold results such as factoring from a matrix), MultiplyByOne (a common mathematical technique), LinearBreakout, PushOnto (much better than Through), HoldOp (hold a specific operation but evaluate the arguments), CreateSubexpression (creates a tooltip and holds expressions together with a tag so they won't get split by routines like Simplify), ReleaseSubexpressions, MaplevelParts (apply an operation to a subset of level parts, for example Factor three out of five terms in a sum), MapLevelPatterns, EvaluateAt (evaluate specific parts of held expressions), EvaluateAtPattern. SymbolsToPatterns, LHSSymbolsToPatterns (convert specific derived rules to general patterned rules). It is very useful to get Mathematica generated expressions into the form that one wants. I believe that this is probably a sticking point with many users. In general it is not a trivial topic. Others may have some good general ideas that I don't know about. Someday someone may even write a good tutorial on it. David Park djmpark at comcast.net <http://home.comcast.net/~djmpark> http://home.comcast.net/~djmpark/

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**Re: Simplifying and Rearranging Expressions**