A.2.4 Counting Roots of Polynomials - Wolfram Research
A.2.4 Counting Roots of Polynomials - Wolfram Research
A.2.4 Counting Roots of Polynomials - Wolfram Research
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A.2 Implementing Mathematical Algorithms 619<br />
<strong>A.2.4</strong> <strong>Counting</strong> <strong>Roots</strong> <strong>of</strong> <strong>Polynomials</strong><br />
The packages we have discussed so far implement algorithms that basically involve<br />
only numbers or lists <strong>of</strong> numbers. You can also write Mathematica programs that<br />
implement symbolic and algebraic algorithms.<br />
Here is an example <strong>of</strong> a package that implements Sturm's method for counting<br />
the real roots <strong>of</strong> a polynomial in an interval.<br />
Count<strong>Roots</strong>::usage =<br />
"Count<strong>Roots</strong>[f,{x,a,b}] computes the number <strong>of</strong> zeroes <strong>of</strong> the real polynomial<br />
f on the interval a
620 A. Some Examples <strong>of</strong> Mathematica Packages<br />
This shows that the polynomial has three<br />
real roots in the range -2 to 2.<br />
In[3]:= Plot[poly, {x,-2,2}]<br />
10<br />
7.5<br />
5<br />
2.5<br />
-2 -1<br />
-2.5<br />
1 2<br />
-5<br />
You can check this result using<br />
Count<strong>Roots</strong>.<br />
In[4]:= Count<strong>Roots</strong>[poly, {x, -2, 2}]<br />
Out[4]= 3<br />
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