Mathematica Cookbook

Chapter 10. Algebra

When a problem comes along You must whip it Before the cream sits out too long You must whip it When something’s going wrong You must whip it

Now whip it Into shape Shape it up Get straight Go forward Move ahead Try to detect it It’s not too late To whip it Whip it good

—Devo, “Whip It”

10.0 Introduction

Algebra can be divided into elementary algebra and abstract algebra. Elementary algebra is the kind we all learned in high school. Mathematica is well equipped to solve problems in elementary algebra, and many of the recipes in this chapter show you how to leverage these features. Mathematica does not presently have deep support for abstract algebra, which is concerned with constructs such as groups, rings, and fields. However, there are third-party packages available for exploring abstract algebra, and I provide references for those.

Mathematica’s ability to do algebraic manipulation is important for two reasons. First, many problems, although conceptually easy to solve by hand, are tedious, and it makes sense to have Mathematica relieve you of this drudgery. 10.1 Solving Algebraic Equations shows you how to solve algebraic equations; 10.2 Finding a Polynomial from a Given Root shows how to work backward from a root to a polynomial. However, helping you solve algebraic equations is not the most important part of this chapter. Rather, you will often find that Mathematica will not automatically give you an answer in the form you desire. Knowing how to coax expressions ...