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 : factor 124744878111332355674003415153753485211381849014286981744945
7
o1 = 3*5*53*2819 10861*10212222054939737109085868749
o1 : Expression of class Product
|
i2 : y = (2^15-4)/(2^15-5)
32764
o2 = -----
32763
o2 : QQ
|
i3 : x = factor y
2
2 8191
o3 = --------
3*67*163
o3 : Expression of class Divide
|
i4 : value x
32764
o4 = -----
32763
o4 : QQ
|
We may peek inside x to a high depth to see its true structure as Expression.
i5 : peek'(100,x)
o5 = Divide{Product{Power{2, 2}, Power{8191, 1}}, Product{Power{3, 1},
------------------------------------------------------------------------
Power{67, 1}, Power{163, 1}}}
|
For integers, factorization is done by FLINT, and the factors $x$ are actually just probably prime, as described in the documentation of isPseudoprime.
For multivariate polynomials the factorization is done with code of Michael Messollen (see Singular-Factory). For univariate polynomials the factorization is in turn done with code of Gert-Martin Greuel and Ruediger Stobbe (see Singular-Factory).
i6 : R = ZZ/101[u] o6 = R o6 : PolynomialRing |
i7 : factor (u^3-1)
2
o7 = (u - 1)(u + u + 1)
o7 : Expression of class Product
|
i8 : F = frac(ZZ/101[t]) o8 = F o8 : FractionField |
i9 : factor ((t^3-1)/(t^3+1))
2
(t - 1)(t + t + 1)
o9 = -------------------
2
(t + 1)(t - t + 1)
o9 : Expression of class Divide
|