Manipulating algebraic expressions

Manipulation of numbers, polynomials, rational expressions, and RootOf expressions is discussed in Chapter 2, Numbers and algebraic operators, in Chapter 13, Polynomials and rational expressions, and in Chapter 14, Polynomial equations and factoring polynomials. This chapter continues discussing manipulation, but extends to more general types of algebraic expressions. The usual goal of manipulating algebraic expressions is conversion of an expression to a “simple” expression. but what is “simple” depends on what you want to do with the expression. Therefore, inverse actions are shown for most of the actions discussed. The first section on using options for simplify and combine is followed by sections on manipulating powers and radicals, expressions with exp and In, and trigonometric expressions. Although there are facilities for using properties of several other mathematicalfunctions, we do not try to cover them all; if you have seen these cases, you will be able to find your way yourself. Restricting the action of manipulations to a part of an expression is discussed extensively in a special section. 1fyou want to see if an equality is true, you might use other methods than symbolic manipulation. These are shown in a special section on this subject. Examples are kept as small as possible. For such cases, manipulating by hand is much simpler. But the same ideas can be usedfor manipulating very largeformulas and then using these tools can pay the efforts. Two sections each give an example of manipulating a not so simple expression. 1n the Short Reference List at the start of this book is a survey of the main manipulation tools.