Factorization : collect

collect takes as argument a polynomial or a list of polynomials and optionnaly an algebraic extension like sqrt(n) (for $\sqrt{{n}}$).
collect factorizes the polynomial (or the polynomials of the list) on the field of it's coefficient (for example $\mathbb {Q}$) or on the smallest extension containing the optional second argument (e.g. $\mathbb {Q}$[$\sqrt{{n}}$]). In complex mode, the field is complexified.
Examples :

• Factorize x2 - 4 over the integers, input :
  collect(x^2-4)
  Output in real mode :
  (x-2)*(x+2)
• Factorize x2 + 4 over the integers, input :
  collect(x^2+4)
  Output in real mode :
  x^2+4
  Output in complex mode :
  (x+2*i)*(x-2*i)
• Factorize x2 - 2 over the integers, input :
  collect(x^2-2)
  Output in real mode :
  x^2-2
  But if you input :
  collect(sqrt(2)*(x^2-2))
  Output :
  sqrt(2)*(x-sqrt(2))*(x+sqrt(2))
• Factorize over the integers :
  x3 - 2x2 + 1 and x2 - x
  Input :
  collect([x^3-2*x^2+1,x^2-x])
  Output :
  [(x-1)*(x^2-x-1),x*(x-1)]
  But, input :
  collect((x^3-2*x^2+1)*sqrt(5))
  Output :
  ((19*sqrt(5)-10)*((sqrt(5)+15)*x+7*sqrt(5)-5)* ((sqrt(5)+25)*x-13*sqrt(5)-15)*(x-1))/6820
  Or, input :
  collect(x^3-2*x^2+1,sqrt(5))
  Output :
  ((2*sqrt(5)-19)*((sqrt(5)+25)*x-13*sqrt(5)-15)*(-x+1)*((sqrt(5)+15)*x+7*sqrt(5)-5))/6820