The following is the so-called Wilkinson polynomial, that has zeros at 1,
2, ..., 20 :
julia> using Polynomial
julia> pW = poly([1.0:20.0])
julia> roots(pW)
20-element Array{Complex{Float64},1}:
1.0-0.0im
2.0-0.0im
3.0-0.0im
3.99999-0.0im
5.00006-0.0im
6.00181-0.0im
6.95031-0.0im
8.09172-0.579086im
8.09172+0.579086im
9.70891-1.64679im
9.70891+1.64679im
11.7999-2.59604im
11.7999+2.59604im
14.3615-3.12883im
14.3615+3.12883im
17.1543-2.89387im
17.1543+2.89387im
19.5758-1.70785im
19.5758+1.70785im
20.6635-0.0im
Compare this with the same computation in Matlab:
>> pw = poly(1:20);
>> roots(pw)
ans =
20.0003
18.9972
18.0112
16.9711
16.0483
14.9354
14.0653
12.9491
12.0334
10.9840
10.0061
8.9984
8.0003
7.0000
6.0000
5.0000
4.0000
3.0000
2.0000
1.0000
The roots of this polynomial are known to be difficult to determine, but
the results in Julia's Polynomial package seem really far off.
