„Szerkesztő:05storm26/Faktorizálás véges test felett” változatai közötti eltérés

This algorithm works also over a field of [[characteristic (algebra)|characteristic]] zero, with the only difference that it never enters in the blocks of instructions where ''p''th roots are computed. However, in this case, [[Square-free polynomial#Yun's algorithm|Yun's algorithm]] is much more efficient because it computes the greatest common divisors of polynomials of lower degrees. A consequence is that, when factoring a polynomial over the integers, the algorithm which follows is not used: one compute first the square-free factorization over the integers, and to factor the resulting polynomials, one chooses a ''p'' such that they remain square-free modulo ''p''.
 
'''AlgorithmAlgoritmus''': '''SFF ('''Négyzetmentes (Square-Free Factorizationfaktorizáció''')'''
'''Input''': A [[monic polynomial]] ''f'' inEgy '''F'''<sub>''q''</sub>[''x''] beli [[főpolinom]].
'''Output''': Square-free factorization of ''f ''négyzetmentes faktorizációja.
 
''i''←1; ''R'' ← 1; ''g'' ← ''f''&prime;;
''c'' ← ''c''<sup>1/''p''</sup>;
'''Output'''(''R''·'''SFF'''(''c'')<sup>''p''</sup>) }
'''else''' '''Output'''(''R'')
'''else''' {
''f'' ← ''f''<sup>1/''p''</sup>;