factor

factor x -- factors x.

The result is a Product each of whose factors is a Power whose base is one of the factors found and whose exponent is an integer.

i1 : y = (2^15-4)/(2^15-5)



     32764

o1 = -----

     32763



o1 : QQ

i2 : x = factor y



       2

      2 8191

o2 = --------

     3*67*163



o2 : Divide

i3 : value x



     32764

o3 = -----

     32763



o3 : QQ

We may peek inside x to a high depth to see its true structure as Expression.

i4 : peek2(x,100)



o4 = Divide{Product{Power{2,2},Power{8191,1}},Product{Power{3,1},Power{67,1},Power{163,1}}}



o4 : Net

For small integers factorization is done by trial division. Eventually we will have code for large integers. For multivariate polynomials the factorization is done with code of Michael Messollen (see Factorization and characteristic sets library). For univariate polynomials the factorization is in turn done with code of Gert-Martin Greuel and Ruediger Stobbe (see Factory library).

i5 : R = ZZ/101[u]



o5 = R



o5 : PolynomialRing

i6 : factor (u^3-1)



       2

o6 = (u  + u + 1)(u - 1)(1)



o6 : Product

The constant term is provided as the last factor.

i7 : F = frac(ZZ/101[t])



o7 = F



o7 : FractionField

i8 : factor ((t^3-1)/(t^3+1))



       2

     (t  + t + 1)(t - 1)(1)

o8 = ----------------------

       2

     (t  - t + 1)(t + 1)(1)



o8 : Divide

The code for factoring in a fraction field is easy to read:

i9 : code(factor,F)



o9 = -- ../../m2/enginering.m2:172

               factor F := options -> f -> factor numerator f / factor denominator f;



o9 : Net