Enter the following code into an input cell in a worksheet, and evaluate the cell:
# A problem we already know the answer to
var('a, b, c, x')
f(x) = a * x^2 + b * x + c
root_list = f.roots(x)
for root in root_list:
print("Root with multiplicity {0}:".format(root[1]))
show(root[0])
# Something more complicated
g(x) = expand((x^2 - 1)^3 * (x^2 + 1) * (x - 2));
g.show()
root_list = g.roots(x)
for root in root_list:
print("Root: {0} multiplicity: {1}".format(root[0], root[1]))
p1 = plot(g, (-2, 2))
p1.ymin(-10)
p1.show()The output is shown in the following screenshot:
We started off by finding the roots for the general second-order polynomial with the roots method. The result is a list of tuples that represent the roots. The first item in each tuple is the multiplicity, and the second item is the root. We passed the variable x to roots. If this argument is not provided, roots formulates the solution in terms of the default variable...