FCApart[expr, {q1, q2, ...}] is an internal function
that partial fractions a loop integral (that depends on
q1,q2, …) into integrals that contain only
linearly independent propagators. The algorithm is largely based on arXiv:1204.2314 by F.Feng.
FCApart is meant to be applied to single loop integrals
only. If you need to perform partial fractioning on an expression that
contains multiple loop integrals, use ApartFF.
There is actually no reason, why one would want to apply
FCApart instead of ApartFF, except for cases,
where FCApart is called from a different package that
interacts with FeynCalc.
Overview, ApartFF, FeynAmpDenominatorSimplify.
SPD[q, q] FAD[{q, m}]
FCApart[%, {q}]\frac{q^2}{q^2-m^2}
\frac{m^2}{q^2-m^2}
SPD[q, p] SPD[q, r] FAD[{q}, {q - p}, {q - r}]
FCApart[%, {q}]\frac{(p\cdot q) (q\cdot r)}{q^2.(q-p)^2.(q-r)^2}
\frac{p^2 r^2}{4 q^2.(q-p)^2.(q-r)^2}+\frac{p^2+2 r^2}{4 q^2.(-p+q+r)^2}+\frac{q\cdot r}{2 q^2.(-p+q+r)^2}+-\frac{p^2}{4 q^2.(q-p)^2}-\frac{r^2}{4 q^2.(q-r)^2}
SPD[p, q1] SPD[p, q2]^2 FAD[{q1, m}, {q2, m}, q1 - p, q2 - p, q1 - q2]
FCApart[%, {q1, q2}]\frac{(p\cdot \;\text{q1}) (p\cdot \;\text{q2})^2}{\left(\text{q1}^2-m^2\right).\left(\text{q2}^2-m^2\right).(\text{q1}-p)^2.(\text{q2}-p)^2.(\text{q1}-\text{q2})^2}
\frac{\left(m^2+p^2\right)^3}{8 \left(\text{q1}^2-m^2\right).\left(\text{q2}^2-m^2\right).(\text{q1}-p)^2.(\text{q1}-\text{q2})^2.(\text{q2}-p)^2}-\frac{\left(m^2+p^2\right)^2}{4 \left(\text{q1}^2-m^2\right).\left(\text{q2}^2-m^2\right).(\text{q1}-p)^2.(\text{q1}-\text{q2})^2}-\frac{m^2+p^2}{4 \left(\text{q1}^2-m^2\right).(\text{q1}-\text{q2})^2.(\text{q2}-p)^2}+\frac{m^2+p^2}{8 \left(\text{q1}^2-m^2\right).\left(\text{q2}^2-m^2\right).(\text{q1}-\text{q2})^2}+\frac{\left(m^2+p^2\right) \left(m^2+2 p^2\right)}{4 \;\text{q1}^2.\text{q2}^2.\left((\text{q1}-p)^2-m^2\right).(\text{q1}-\text{q2})^2}-\frac{\left(m^2+p^2\right) (p\cdot \;\text{q1})}{4 \;\text{q1}^2.\text{q2}^2.(\text{q1}-\text{q2})^2.\left((\text{q2}-p)^2-m^2\right)}-\frac{\left(m^2+p^2\right) (p\cdot \;\text{q1})}{4 \left(\text{q1}^2-m^2\right).\left(\text{q2}^2-m^2\right).(\text{q1}-\text{q2})^2.(\text{q2}-p)^2}-\frac{p\cdot \;\text{q1}}{4 \left(\text{q1}^2-m^2\right).(\text{q1}-\text{q2})^2.(\text{q2}-p)^2}+\frac{p\cdot \;\text{q1}}{4 \left(\text{q1}^2-m^2\right).\left(\text{q2}^2-m^2\right).(\text{q1}-\text{q2})^2}-\frac{p\cdot \;\text{q1}}{4 \left(\text{q2}^2-m^2\right).(\text{q1}-p)^2.(\text{q1}-\text{q2})^2}