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## Factorization : collect

collect takes as argument a polynomial or a list of polynomials and optionnaly an algebraic extension like sqrt(n) (for ).
collect factorizes the polynomial (or the polynomials of the list) on the field of it's coefficient (for example ) or on the smallest extension containing the optional second argument (e.g. []). 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

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giac documentation written by Renée De Graeve and Bernard Parisse