A.2.4 Counting Roots of Polynomials - Wolfram Research

A.2 Implementing Mathematical Algorithms 619
A.2.4 Counting Roots of Polynomials
The packages we have discussed so far implement algorithms that basically involve
only numbers or lists of numbers. You can also write Mathematica programs that
implement symbolic and algebraic algorithms.
Here is an example of a package that implements Sturm's method for counting
the real roots of a polynomial in an interval.
CountRoots::usage =
"CountRoots[f,{x,a,b}] computes the number of zeroes of the real polynomial
f on the interval a

620 A. Some Examples of Mathematica Packages
This shows that the polynomial has three
real roots in the range -2 to 2.
In[3]:= Plot[poly, {x,-2,2}]
10
7.5
5
2.5
-2 -1
-2.5
1 2
-5
You can check this result using
CountRoots.
In[4]:= CountRoots[poly, {x, -2, 2}]
Out[4]= 3
Web sample page from The Mathematica Book, First Edition, by Stephen Wolfram, published by Addison-Wesley Publishing
Company (hardcover ISBN 0-201-19334-5; softcover ISBN 0-201-19330-2). To order Mathematica or this book contact Wolfram
Research: info@wolfram.com; http://www.wolfram.com/; 1-800-441-6284.
c 1988 Wolfram Research, Inc. Permission is hereby granted for web users to make one paper copy of this page for their
personal use. Further reproduction, or any copying of machine-readable files (including this one) to any server computer, is strictly
prohibited.