Factor3[exp] factors a rational function
exp over the field of complex numbers.
Factor3 is primarily meant to be used on matrices from
differential equations and Feynman parametric representations of loop
integrals. Its main goal is to rewrite all denominators such, that they
can be integrated in terms of HPLs or GPLs (when possible).
To avoid performance bottlenecks, in the case of rational functions
only the denominator will be factored by default. This can be changed by
setting the option Numerator to True.
Overview, FCPartialFractionForm.
Factor3[(1 - 4 x) (1 + 3 y)]-12 \left(x-\frac{1}{4}\right) \left(y+\frac{1}{3}\right)
Factor3[16*(1 - 2*eps)^2*x^2]64 \left(\text{eps}-\frac{1}{2}\right)^2 x^2
Factor3[2*(32904490323 + 164521613783*eps + 1256744*eps^2)*(11 - 5*eps - 47*eps^2 + 44*eps^3)]110593472 \left(\text{eps}+\frac{1}{264} \left(1-i \sqrt{3}\right) \sqrt[3]{-137143+198 i \sqrt{122615}}+\frac{2869 \left(1+i \sqrt{3}\right)}{264 \sqrt[3]{-137143+198 i \sqrt{122615}}}-\frac{47}{132}\right) \left(\text{eps}+\frac{1}{264} \left(1+i \sqrt{3}\right) \sqrt[3]{-137143+198 i \sqrt{122615}}+\frac{2869 \left(1-i \sqrt{3}\right)}{264 \sqrt[3]{-137143+198 i \sqrt{122615}}}-\frac{47}{132}\right) \left(\text{eps}-\frac{628374}{-1570927-\sqrt{2467796558401}}\right) \left(\text{eps}-\frac{104729 \left(-1570927-\sqrt{2467796558401}\right)}{2513488}\right) \left(\text{eps}+\frac{1}{132} \left(-47-\frac{2869}{\sqrt[3]{-137143+198 i \sqrt{122615}}}-\sqrt[3]{-137143+198 i \sqrt{122615}}\right)\right)
mat = {{(2 - 2*eps)/x, 0, 0, 0, 0}, {0, (2 - 2*eps)/(2*x), 0, 0, 0},
{0, (-2 + 2*eps)/(x - 4*x^2), (6 - 2*(4 - 2*eps))/(1 - 4*x), 0, 0},
{(-2 + 2*eps)/(x - 4*x^2), 0, 0, (2 - 2*eps + 4*(5 - 2*(4 - 2*eps))*x)/(2*(1 -
4*x)*x), 0}, {(2 - 2*eps)^2/(16*(1 - x)*x^2), -1/8*(2 - 2*eps)^2/((1 - x)*x^2),
0, 0, -((7 - 2*(4 - 2*eps) - 13*x + 4*(4 - 2*eps)*x)/(2*x - 2*x^2))}};Factor3[mat]\left( \begin{array}{ccccc} \frac{2-2 \;\text{eps}}{x} & 0 & 0 & 0 & 0 \\ 0 & \frac{2-2 \;\text{eps}}{2 x} & 0 & 0 & 0 \\ 0 & -\frac{2 \;\text{eps}-2}{4 \left(x-\frac{1}{4}\right) x} & -\frac{6-2 (4-2 \;\text{eps})}{4 \left(x-\frac{1}{4}\right)} & 0 & 0 \\ -\frac{2 \;\text{eps}-2}{4 \left(x-\frac{1}{4}\right) x} & 0 & 0 & -\frac{4 (5-2 (4-2 \;\text{eps})) x-2 \;\text{eps}+2}{8 \left(x-\frac{1}{4}\right) x} & 0 \\ -\frac{(2-2 \;\text{eps})^2}{16 (x-1) x^2} & \frac{(2-2 \;\text{eps})^2}{8 (x-1) x^2} & 0 & 0 & -\frac{-4 (4-2 \;\text{eps}) x+2 (4-2 \;\text{eps})+13 x-7}{2 (x-1) x} \\ \end{array} \right)