In[]:=
ClearAll["Global`*"]

Code

In[]:=

Exampes

Simple Example

u=
5-d
4
rho3[2]
X32
rho3[3]
X33
1
2
(-5+d)
(t(
4
m1
t+
4
m2
t+t
2
(s+X32)
-2
2
m2
(st-(t-2X32)(X32-X33))-2
2
m1
(
2
m2
t+st+(t-2X33)(X32-X33))+2stX33-2(2s+t)X32X33+t
2
X33
))
;​​u=u/.{s-17,t-23,m131,m251,d1/67};​​vars={X32,X33};​​omega=Table[Simplify[D[Log[u],vars[[i]]]],{i,Length[vars]}];​​phiL=1/(X32*X33);​​phiR=1/(X32*X33);​​e={1,1/X32};​​h=e;
(Debug) In[]:=
res=IntersecRec[phiL,phiR,{e},{h},omega,vars];

Example cut box:

In[]:=
ureg3c2=
5-d
4
rho3[1]
X32
rho3[2]
X33
1
2
(-5+d)
(t(
4
m1
t+
4
m2
t+t
2
(s+X32)
-2
2
m2
(st-(t-2X32)(X32-X33))-2
2
m1
(
2
m2
t+st+(t-2X33)(X32-X33))+2stX33-2(2s+t)X32X33+t
2
X33
))
;​​u=ureg3c2/.{s-17,t-23,m131,m251,d1/67};​​vars={X32,X33};​​omega=Table[Simplify[D[Log[u],vars[[i]]]],{i,Length[vars]}];​​phileftlist={1,1/X32,1/X33,1/(X32*X33)};​​phirightlist=phileftlist;​​phileftlistuse=Join[phileftlist,ML3];​​e={1,1/X32};​​h=e;

Monomial Decomposition:

T=Expand
1
2
2
(-2+D)
X32*X33
(-2+D)-
1
2
X32(2(
2
m1
+
2
m2
-s)-X33)+(
2
m1
+
2
m2
-s)(
2
m1
+
2
m2
-s-X33)-(2
2
m1
-X32)(2
2
m2
-X33)(-2(2
2
m1
-X32)(2
2
m2
-X33)+(-2+D)((
2
m1
+
2
m2
-s)(
2
m1
+
2
m2
-s-X32-X33)+(-
2
m1
-
2
m2
+s+X32)(-
2
m1
-
2
m2
+s+X33)))//.{s-17,t-23,m131,m251,d1/67};
In[]:=
Variables[T]
Out[]=
{X32,X33}
In[]:=
fn[x_,{var__}]:=List@@Pick[x,x,Alternatives[var]^_.]​​A33=fn[T,{X32,X33}];
In[]:=
R1=
1
X32
:>a,X32:>b,
1
X33
:>c,
1
X32X33
:>z,
X32
X33
:>g,X33:>j,
X33
X32
:>k,X32X33:>l;​​R2=a:>
1
X32
,b:>X32,c:>
1
X33
,z:>
1
X32X33
,g:>
X32
X33
,j:>X33,k:>
X33
X32
,l:>X32X33;
q=FactorTermsT,
1
X32
,X32,
1
X33
,
1
X32X33
,
X32
X33
,X33,
X33
X32
,X32X33//.R1;​​ML2=MonomialList[q,{a,b,c,z,g,j,k,l}];​​ML3=ML2//.R2;
Out[]=
-
2870909197216362
17689X32
,-
220152447X32
17689
,-
3914114928183882
17689X33
,
5633556370676982801
17689X32X33
,
679867860681X32
17689X33
,-
161476527X33
17689
,
365760057961X33
17689X32
,
71289X32X33
70756
,
1631061005109
17689

phileftlistuseTab=Join[phileftlist,ML3];
Out[]=
1,
1
X32
,
1
X33
,
1
X32X33
,-
2870909197216362
17689X32
,-
220152447X32
17689
,-
3914114928183882
17689X33
,
5633556370676982801
17689X32X33
,
679867860681X32
17689X33
,-
161476527X33
17689
,
365760057961X33
17689X32
,
71289X32X33
70756
,
1631061005109
17689

In[464]:=​​result=​​Table[Table[0,{Length[phirightlist]}],{Length[phileftlistuse]}];​​Do[​​Do[​​result[[i,j]]=​​IntersecRec[phileftlistuse[[i]],phirightlist[[j]],{e},{h},​​omega,vars];​​,{j,Length[phirightlist]}]​​,{i,Length[phileftlistuse]}];​​​​