Horner’s rule¶
Here we show how to use the function horner to evaluate a polynomial. It’s not a part of core Julia, so you need to download and install this text’s package once, and load it for each new Julia session. The download is done with the following lines–but the second one is commented out here to avoid dumping a lot of irrelevant output into this notebook.
import Pkg
#Pkg.add(Pkg.PackageSpec(url="https://github.com/fncbook/fnc.git"));
Once installed, any package (including a standard library that comes with Julia) can be loaded with the using command, as follows. (Sometimes a using or import statement can take a few seconds or even minutes to execute. This book depends on a large package that must be compiled on first use and after every update.)
using FundamentalsNumericalComputation
For your convenience, this package also loads and imports all the packages used throughout the book.
Now let us define a vector of the coefficients of \(p(x)=(x-1)^3=x^3-3x^2+3x-1\), in ascending degree order.
c = [-1,3,-3,1]
4-element Array{Int64,1}:
-1
3
-3
1
In order to avoid clashes between similarly named functions, Julia has sandboxed all the book functions into a namespace called FNC. We use this namespace whenever we invoke one of the functions.
FNC.horner(c,1.6)
0.21600000000000041
The above is the value of \(p(1.6)\).
While the namespace does lead to a little extra typing, a nice side effect of using this paradigm is that if you type FNC. (including the period) and hit the Tab key, you will see a list of all the functions known in that namespace.