Vastly improved MomentumCombine to have more control over the way

expressions get combined.

FeynCalc/Documentation/Mathematica/Lorentz/MomentumCombine.m

@@ -9,6 +9,31 @@
 
 (* ::Text:: *)
 (*`MomentumCombine[expr]` is the inverse operation to `MomentumExpand` and `ExpandScalarProduct`. `MomentumCombine` combines also `Pair`s.*)
+(*Notice, that `MomentumCombine` cannot complete squares. It can, however, bring expressions containing scalar products to a suitable form that allows for a square completion using other means.*)
+
+
+(* ::Text:: *)
+(*This function offers multiple options.*)
+
+
+(* ::Text:: *)
+(*The option `NumberQ` (default is `True`) specifies whether one should only merge quantities with numerical prefactors or not. Setting it to `False` allows for symbolic prefactors.*)
+
+
+(* ::Text:: *)
+(*Setting the option `"Quadratic"` to `False` (default is `True`) effectively means that momenta squared will not be combined with anything else.*)
+
+
+(* ::Text:: *)
+(*With the option `"ExcludeScalarProducts"` we can ensure that scalar products containing any of the momenta listed are not merged with anything else. So `a.x + a.y` can be merged either if `a` contains no such momenta, or if both `x` and `y` are free of them.*)
+
+
+(* ::Text:: *)
+(*The option `Except` forbids merging the listed momenta with anything else. It is much more restrictive than `"ExcludeScalarProducts"` that allows for merging terms linear in the listed momenta.*)
+
+
+(* ::Text:: *)
+(*The option `Select` allows for gathering all terms linear in the given momenta before applying any other combining rules.*)
 
 
 (* ::Subsection:: *)
@@ -93,3 +118,37 @@
 
 
 MomentumCombine[ex,NumberQ->False,"Quadratic"->False,Except->{k,l}]
+
+
+(* ::Text:: *)
+(*Suppose that we have an expression that can be written as a square. To achieve the desired combination of momenta we need to*)
+
+
+(DataType[#,FCVariable]=True)&/@{gkin,meta,u0b};
+
+
+ex=SPD[k1,k1]-2 SPD[k1,k2]+2 gkin meta SPD[k1,n]-2 gkin meta u0b SPD[k1,n]-meta u0b SPD[k1,nb]+
+SPD[k2,k2]-2 gkin meta SPD[k2,n]+2 gkin meta u0b SPD[k2,n]+meta u0b SPD[k2,nb]
+
+
+(* ::Text:: *)
+(*The naive application of `MomentumCombine` doesn't return anything useful*)
+
+
+MomentumCombine[ex]
+
+
+(* ::Text:: *)
+(*Here we actually want to gather terms linear in `k1` and `k2`first before trying to combine them together. To that aim we can use the option `Select`.*)
+(*Employing the options `"Quadratic"` and `"ExcludeScalarProducts"` we can prevent `k1` and `k2` from getting combined with anything containing *)
+(*those momenta. Furthermore, we enable symbolical prefactor by setting `NumberQ` to false*)
+
+
+MomentumCombine[ex,Select->{k1,k2},"Quadratic"->False,"ExcludeScalarProducts"->{k1,k2},NumberQ->False]
+
+
+(* ::Text:: *)
+(*This result looks very good, but `k1` and `k2` were not combined because they are contracted to long linear combinations of 4-momenta that were not properly factorized. The option `Factoring` solves this issue*)
+
+
+res=MomentumCombine[ex,Select->{k1,k2},"Quadratic"->False,"ExcludeScalarProducts"->{k1,k2},NumberQ->False,Factoring->Factor2]