In the following example, we will see how Sage can be used to simplify expressions that involve exponentials, logarithms, rational functions, and square roots:
var('x')
# Logs
f(x) = log(x^2 * sin(x) / sqrt(1 + x))
print("Original function:")
f.show()
print("This form is easier to work with:")
show(f.expand_log())
print("Simplify expanded form:")
show(f.expand_log().simplify_log())
# Rational functions
f(x) = (x + 1) / (x^2 + x)
print("Original function:")
f.show()
print("Simplified:")
show(f.simplify_rational())
# Radicals
f(x) = sqrt(x^2+x)/sqrt(x)
print("Original function:")
f.show()
print("Simplified:")
show(f.simplify_radical())The output is shown in the following screenshot:
