Example#1, calculation in d=6-2*eps

<<AMBREv3.1.m

<<PlanarityTestv1.2.m

invariants={p1^2->0,p2^2->0,p1*p2->s/2};

d=6-2 eps;(* by default d=4-2 eps *)

ex1=PR[k1,0,n1] PR[k1-k2,0,n2] PR[k2,0,n3] PR[k1-k2+p1,m,n4] PR[k2+p2,0,n5] PR[k1+p1+p2,0,n6];

PlanarityTest[{ex1},{k1,k2},DrawGraph->True];

res=MBreprNP[{1},{ex1},{k1,k2}]

finres = res /.{n1->1,n2->1,n3->1,n4->1,n5->1,n6->1}

<<MB.m

<<MBresolve.m

step1=MBresolve[#,eps]&/@finres//Flatten;

step2=MBexpand[step1,Exp[2*eps*EulerGamma],{eps,0,0}];
MBanalytic=MBmerge[step2]

MBintegrate[MBanalytic,{s->-1,m->1}]

Quit[]

<<../../FIESTA3.2/FIESTA3.m

UsingQLink=False;UsingC=False;

d0=6;

SDEvaluate[UF[{k1,k2},{-k1^2,-(k1-k2)^2,-k2^2,-(k1-k2+p1)^2+m^2,-(k2+p2)^2,-(k1+p1+p2)^2},{p1^2->0,p2^2->0,p1*p2->s/2,
s->-1,m->1}],{1,1,1,1,1,1},0]

Quit[]

Example#2, 3-loop non-planar box (arXiv:1312.2588)

<<AMBREv3.1.m

<<PlanarityTestv1.2.m

invariants={p1^2->0,p2^2->0,p3^2->0,p4^2->0,p1*p2->1/2*s,p3*p4->1/2 s,p1*p3->1/2*t,p2*p4->1/2*t,p2*p3->1/2*u,p1*p4->1/2*u};

ex2=PR[k1,0,n1] PR[k2,0,n2] PR[k3,0,n3] PR[k1-k2-p1,0,n4]PR[k2-k3-p4,0,n5] PR[k1-k2+k3+p2+p4,0,n6];

PlanarityTest[{ex2},{k1,k2,k3},DrawGraph->True];

SimplifyFpoly[{s+t+u->0}];

res=MBreprNP[{1},{ex2},{k1,k2,k3}]

fin = BarnesLemma[#,1]&/@res

finres = fin /.{n1->1,n2->1,n3->1,n4->1,n5->1,n6->1}

<<MB.m

<<MBresolve.m

step1=MBresolve[#,eps]&/@finres//Flatten;

step2=MBexpand[step1,Exp[3*eps*EulerGamma],{eps,0,0}];
MBanalytic=MBmerge[step2]

MBintegrate[MBanalytic,{s->-1,t->-1,u->-1}]

Quit[]

<<../../FIESTA3.2/FIESTA3.m

UsingQLink=False;UsingC=False;

UFpoly=UF[{k1,k2,k3},{-k1^2,-k2^2,-k3^2,-(k1-k2-p1)^2,-(k2-k3-p4)^2,-(k1-k2+k3+p2+p4)^2},{p1^2->0,p2^2->0,p3^2->0,p4^2->0,p1*p2->1/2*s,p3*p4->1/2 s,p1*p3->1/2*t,p2*p4->1/2*t,p2*p3->1/2*u,p1*p4->1/2*u}]//.{s x_. + t x_. + u x_. -> 0}/.{s->-1,t->-1,u->-1}

SDEvaluate[UFpoly,{1,1,1,1,1,1},0]

Quit[]

Example#3, 3-loop non-planar massless vertex

To run this example, please modify the MBresolve.m file:
in the line 60 must be
point=NMinimize[function,vars,Method -> “DifferentialEvolution”, MaxIterations->1000];
(be aware, it may take several hours to get the result)

<<AMBREv3.1.m

<<PlanarityTestv1.2.m

invariants={p1^2->0,p2^2->0,p1*p2->s/2};

ex4=PR[k1,0,n1] PR[k2,0,n2] PR[k3,0,n3] PR[k2-k1,0,n4]PR[k2-k1-p1,0,n5] PR[k2-p1-p2,0,n6] PR[k2-k3-p1-p2,0,n7] PR[k2-k1-k3-p1,0,n8];

PlanarityTest[{ex4},{k1,k2,k3},DrawGraph->True];

res=MBreprNP[{1},{ex4},{k1,k2,k3}]

fin = BarnesLemma[#,1]&/@res

finres = fin /.{n1->1,n2->1,n3->1,n4->1,n5->1,n6->1,n7->1,n8->1}

<<MB.m

<<MBresolve.m

step1=MBresolve[#,eps]&/@finres//Flatten;

step2=MBexpand[step1,Exp[3*eps*EulerGamma],{eps,0,0}];
MBanalytic=MBmerge[step2]

MBintegrate[MBanalytic,{s->-1},MaxPoints->10^7]

Quit[]

<<../../FIESTA3.2/FIESTA3.m

UsingQLink=False;UsingC=False;

CurrentIntegratorOptions={{"maxeval","5000000"}};

SDEvaluate[UF[{k1,k2,k3},{-k1^2,-k2^2,-k3^2,-(k2-k1)^2,-(k2-k1-p1)^2,-(k2-p1-p2)^2,-(k2-k3-p1-p2)^2,-(k2-k1-k3-p1)^2},{p1^2->0,p2^2->0,p1*p2->s/2,
s->-1}],{1,1,1,1,1,1,1,1},0]

Quit[]

Example#4, limitations 1

Present version cannot generate representation for planar diagrams and non-planar
diagrams with a planar subloop like in this example (this possibility will be added in a future release)

<<AMBREv3.1.m

<<PlanarityTestv1.2.m

invariants={p1^2->0,p2^2->0,p3^2->0,p4^2->0,p1*p2->1/2*s,p3*p4->1/2 s,p1*p3->1/2*t,p2*p4->1/2*t,p2*p3->1/2*u,p1*p4->1/2*u};

ex3=PR[k1,0,n1] PR[k1+p1,0,n2] PR[k1+p1+p2,0,n3] PR[k1-k2,0,n4]PR[k2,0,n5] PR[k2+p1+p2,0,n6] PR[p1+p2+p4+k2-k3,0,n7] PR[k2-k3,0,n8] PR[k3,0,n9] PR[p4-k3,0,n10];

PlanarityTest[{ex3},{k1,k2,k3},DrawGraph->True];

res=MBreprNP[{1},{ex3},{k1,k2,k3}]

Quit[]

Example#5, limitations 2

too high dimensionality of the result
(will be improved in a future release)

<<AMBREv3.1.m

<<PlanarityTestv1.2.m

invariants={p1^2->0,p2^2->0,p1*p2->s/2};

ex5=PR[k1,0,n1] PR[k2,0,n2] PR[k3,0,n3] PR[k1-k2,0,n4]PR[k2-k3,0,n5] PR[k1-p1-p2,0,n6] PR[k1-k2+k3-p1-p2,0,n7] PR[k3-p1,0,n8] PR[k3-p1-p2,0,n9];

PlanarityTest[{ex5},{k1,k2,k3},DrawGraph->True];

res=MBreprNP[{1},{ex5},{k1,k2,k3}]

fin = BarnesLemma[#,1]&/@res

finres = fin /.{n1->1,n2->1,n3->1,n4->1,n5->1,n6->1,n7->1,n8->1,n9->1}

Quit[]