factoring polynomials

factoring polynomials

Polynomials can be factored with factor. Factorization works in polynomial rings over prime finite fields, ZZ, or QQ.

i1 : R = ZZ/10007[a,b];

i2 : f = (2*a+3)^4 + 5



        4      3       2

o2 = 16a  + 96a  + 216a  + 216a + 86



o2 : R

i3 : g = (2*a+b+1)^3



       3      2        2    3      2             2

o3 = 8a  + 12a b + 6a*b  + b  + 12a  + 12a*b + 3b  + 6a + 3b + 1



o3 : R

i4 : S = factor f



       2

o4 = (a  + 3a - 2301)(a + 405)(a - 402)(16)



o4 : Product

i5 : T = factor g



                       3

o5 = (a - 5003b - 5003) (8)



o5 : Product

The results have been packaged for easy viewing. The number of factors is obtained using

i6 : #T



o6 = 2

Each factor is represented as a power (exponents equal to 1 don't appear in the display.) The parts can be extracted with #.

i7 : T#0



                       3

o7 = (a - 5003b - 5003)



o7 : Power

i8 : T#0#0



o8 = a - 5003b - 5003



o8 : R

i9 : T#0#1



o9 = 3