require "algebra"

PQ = Polynomial(Rational, "x")
x = PQ.var
f = x**4 + 2
p f #=> x^4 + 2
field, modulus, facts = f.decompose
p modulus #=> [a^4 + 2, b^2 + a^2]
p facts #=> (x - a)(x + a)(x - b)(x + b)

fp = Polynomial(field, "x")
x = fp.var
facts = Factors.new(facts.collect{|g, n| [g.evaluate(x), n]})
p facts.pi == f.convert_to(fp) #=> true