FCLoopFactorizingSplit[int, topo] checks whether the
given loop integral factorizes and separates it into factorizing
integrals if it is the case. The input can be made integrals in the
GLI or FAD notation.
Notice that the output is always given in the FAD
notation even if the input was provided using GLIs.
Overview, FCLoopFactorizingQ, FCLoopCreateFactorizingRules.
FCReloadFunctionFromFile[FCLoopFactorizingSplit]FCLoopFactorizingSplit[{FAD[{k, m}]}, {k}]\left( \begin{array}{c} \left\{\frac{1}{k^2-m^2},\{k\},\{\}\right\} \\ \end{array} \right)
FCLoopFactorizingSplit[FAD[{k1, m1}, {k2, m2}, {k1 - k2}], {k1, k2}]\left( \begin{array}{ccc} \frac{1}{\left(\text{k1}^2-\text{m1}^2\right) \left(\text{k2}^2-\text{m2}^2\right) (\text{k1}-\text{k2})^2} & \{\text{k1},\text{k2}\} & \{\} \\ \end{array} \right)
FCLoopFactorizingSplit[FAD[{k1, m1}, {k2, m2}], {k1, k2}]\left( \begin{array}{ccc} \frac{1}{\text{k1}^2-\text{m1}^2} & \{\text{k1}\} & \{\} \\ \frac{1}{\text{k2}^2-\text{m2}^2} & \{\text{k2}\} & \{\} \\ \end{array} \right)
int = FAD[{k1, m1}, {k1 - p1}, {k2, m2}, {k2 - p2}] /. k1 -> k1 + k2\frac{1}{\left((\text{k1}+\text{k2})^2-\text{m1}^2\right).(\text{k1}+\text{k2}-\text{p1})^2.\left(\text{k2}^2-\text{m2}^2\right).(\text{k2}-\text{p2})^2}
FCLoopFactorizingSplit[int, {k1, k2}]\left( \begin{array}{ccc} \frac{1}{\left(\text{k1}^2-\text{m1}^2\right) (\text{k1}-\text{p1})^2} & \{\text{k1}\} & \{\} \\ \frac{1}{\left(\text{k2}^2-\text{m2}^2\right) (\text{k2}-\text{p2})^2} & \{\text{k2}\} & \{\} \\ \end{array} \right)