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One loop

5pt function

Scalar

(* n41 *)

n1=1;n2=1;n3=1;n4=1;n5=1;
me=1;mmu=1;
s12=-1;s13=-3;s14=-1;s15=-1;s23=-1;s24=-1;s25=-1;s34=-1;s35=-1;s45=-1;
invariants={p1^2->me^2,p2^2->me^2,p3^2->mmu^2,p4^2->mmu^2,p5^2->0,p1*p2->(s12-2*me^2)/2,p1*p3->(-s13+me^2+mmu^2)/2,p1*p4->(-s14+me^2+mmu^2)/2,p1*p5->(-s15+me^2)/2,p2*p3->(-s23+me^2+mmu^2)/2,p2*p4->(-s24+me^2+mmu^2)/2,p2*p5->(-s25+me^2)/2,p3*p4->(s34-2*mmu^2)/2,p3*p5->(s35-mmu^2)/2,p4*p5->(s45-mmu^2)/2};
DoSectors[{1},{PR[k1,mmu,n1]*PR[p4+k1,0,n2]*PR[-p2+p4+k1,me,n3]*PR[-p1-p2+p4+k1,0,n4]*PR[-p1-p2+p3+p4+k1,mmu,n5]},{k1}][-4,-1]

(* n42 *)

n1=1;n2=1;n3=1;n4=1;n5=1;
me=1;mmu=1;
s12=-1;s13=-3;s14=-1;s15=-1;s23=-1;s24=-1;s25=-1;s34=-1;s35=-1;s45=-1;
invariants={p1^2->me^2,p2^2->me^2,p3^2->mmu^2,p4^2->mmu^2,p5^2->0,p1*p2->(s12-2*me^2)/2,p1*p3->(-s13+me^2+mmu^2)/2,p1*p4->(-s14+me^2+mmu^2)/2,p1*p5->(-s15+me^2)/2,p2*p3->(-s23+me^2+mmu^2)/2,p2*p4->(-s24+me^2+mmu^2)/2,p2*p5->(-s25+me^2)/2,p3*p4->(s34-2*mmu^2)/2,p3*p5->(s35-mmu^2)/2,p4*p5->(s45-mmu^2)/2};
DoSectors[{1},{PR[k1,mmu,n1]*PR[p4+k1,0,n2]*PR[-p1+p4+k1,me,n3]*PR[-p1-p2+p4+k1,0,n4]*PR[-p1-p2+p3+p4+k1,mmu,n5]},{k1},TempFileDelete->False][-4,-1]

(* n43 *)

n1=1;n2=1;n3=1;n4=1;n5=1;
me=1;mmu=1;
s12=-1;s13=-3;s14=-1;s15=-1;s23=-1;s24=-1;s25=-1;s34=-1;s35=-1;s45=-1;
invariants={p1^2->me^2,p2^2->me^2,p3^2->mmu^2,p4^2->mmu^2,p5^2->0,p1*p2->(s12-2*me^2)/2,p1*p3->(-s13+me^2+mmu^2)/2,p1*p4->(-s14+me^2+mmu^2)/2,p1*p5->(-s15+me^2)/2,p2*p3->(-s23+me^2+mmu^2)/2,p2*p4->(-s24+me^2+mmu^2)/2,p2*p5->(-s25+me^2)/2,p3*p4->(s34-2*mmu^2)/2,p3*p5->(s35-mmu^2)/2,p4*p5->(s45-mmu^2)/2};
DoSectors[{1},{PR[k1,mmu,n1]*PR[p3+k1,0,n2]*PR[p4-k1,0,n3]*PR[-p1+p3+k1,me,n4]*PR[p2-p4+k1,me,n5]},{k1}][-4,-1]

(* n44 *)

n1=1;n2=1;n3=1;n4=1;n5=1;
me=1;mmu=1;
s12=-1;s13=-3;s14=-1;s15=-1;s23=-1;s24=-1;s25=-1;s34=-1;s35=-1;s45=-1;
invariants={p1^2->me^2,p2^2->me^2,p3^2->mmu^2,p4^2->mmu^2,p5^2->0,p1*p2->(s12-2*me^2)/2,p1*p3->(-s13+me^2+mmu^2)/2,p1*p4->(-s14+me^2+mmu^2)/2,p1*p5->(-s15+me^2)/2,p2*p3->(-s23+me^2+mmu^2)/2,p2*p4->(-s24+me^2+mmu^2)/2,p2*p5->(-s25+me^2)/2,p3*p4->(s34-2*mmu^2)/2,p3*p5->(s35-mmu^2)/2,p4*p5->(s45-mmu^2)/2};
DoSectors[{1},{PR[k1,mmu,n1]*PR[p3+k1,0,n2]*PR[-p4+k1,0,n3]*PR[p1-p4+k1,me,n4]*PR[-p2+p3+k1,me,n5]},{k1}][-4,-1]

invariants

Vector

(* 41 *)

n1=1;n2=1;n3=1;n4=1;n5=1;
me=1;mmu=1;
s12=-1;s13=-3;s14=-1;s15=-1;s23=-1;s24=-1;s25=-1;s34=-1;s35=-1;s45=-1;
invariants={p1^2->me^2,p2^2->me^2,p3^2->mmu^2,p4^2->mmu^2,p5^2->0,p1*p2->(s12-2*me^2)/2,p1*p3->(-s13+me^2+mmu^2)/2,p1*p4->(-s14+me^2+mmu^2)/2,p1*p5->(-s15+me^2)/2,p2*p3->(-s23+me^2+mmu^2)/2,p2*p4->(-s24+me^2+mmu^2)/2,p2*p5->(-s25+me^2)/2,p3*p4->(s34-2*mmu^2)/2,p3*p5->(s35-mmu^2)/2,p4*p5->(s45-mmu^2)/2};
DoSectors[{k1*p1},{PR[k1,mmu,n1]*PR[p4+k1,0,n2]*PR[-p2+p4+k1,me,n3]*PR[-p1-p2+p4+k1,0,n4]*PR[-p1-p2+p3+p4+k1,mmu,n5]},{k1}][-4,-1]

(* n42 *)

n1=1;n2=1;n3=1;n4=1;n5=1;
me=1;mmu=1;
s12=-1;s13=-3;s14=-1;s15=-1;s23=-1;s24=-1;s25=-1;s34=-1;s35=-1;s45=-1;
invariants={p1^2->me^2,p2^2->me^2,p3^2->mmu^2,p4^2->mmu^2,p5^2->0,p1*p2->(s12-2*me^2)/2,p1*p3->(-s13+me^2+mmu^2)/2,p1*p4->(-s14+me^2+mmu^2)/2,p1*p5->(-s15+me^2)/2,p2*p3->(-s23+me^2+mmu^2)/2,p2*p4->(-s24+me^2+mmu^2)/2,p2*p5->(-s25+me^2)/2,p3*p4->(s34-2*mmu^2)/2,p3*p5->(s35-mmu^2)/2,p4*p5->(s45-mmu^2)/2};
DoSectors[{k1*p1},{PR[k1,mmu,n1]*PR[p4+k1,0,n2]*PR[-p1+p4+k1,me,n3]*PR[-p1-p2+p4+k1,0,n4]*PR[-p1-p2+p3+p4+k1,mmu,n5]},{k1}][-4,-1]

(* n43 *)

n1=1;n2=1;n3=1;n4=1;n5=1;
me=1;mmu=1;
s12=-1;s13=-3;s14=-1;s15=-1;s23=-1;s24=-1;s25=-1;s34=-1;s35=-1;s45=-1;
invariants={p1^2->me^2,p2^2->me^2,p3^2->mmu^2,p4^2->mmu^2,p5^2->0,p1*p2->(s12-2*me^2)/2,p1*p3->(-s13+me^2+mmu^2)/2,p1*p4->(-s14+me^2+mmu^2)/2,p1*p5->(-s15+me^2)/2,p2*p3->(-s23+me^2+mmu^2)/2,p2*p4->(-s24+me^2+mmu^2)/2,p2*p5->(-s25+me^2)/2,p3*p4->(s34-2*mmu^2)/2,p3*p5->(s35-mmu^2)/2,p4*p5->(s45-mmu^2)/2};
DoSectors[{k1*p1},{PR[k1,mmu,n1]*PR[p3+k1,0,n2]*PR[p4-k1,0,n3]*PR[-p1+p3+k1,me,n4]*PR[p2-p4+k1,me,n5]},{k1}][-4,-1]

(* n44 *)

n1=1;n2=1;n3=1;n4=1;n5=1;
me=1;mmu=1;
s12=-1;s13=-3;s14=-1;s15=-1;s23=-1;s24=-1;s25=-1;s34=-1;s35=-1;s45=-1;
invariants={p1^2->me^2,p2^2->me^2,p3^2->mmu^2,p4^2->mmu^2,p5^2->0,p1*p2->(s12-2*me^2)/2,p1*p3->(-s13+me^2+mmu^2)/2,p1*p4->(-s14+me^2+mmu^2)/2,p1*p5->(-s15+me^2)/2,p2*p3->(-s23+me^2+mmu^2)/2,p2*p4->(-s24+me^2+mmu^2)/2,p2*p5->(-s25+me^2)/2,p3*p4->(s34-2*mmu^2)/2,p3*p5->(s35-mmu^2)/2,p4*p5->(s45-mmu^2)/2};
DoSectors[{k1*p1},{PR[k1,mmu,n1]*PR[p3+k1,0,n2]*PR[-p4+k1,0,n3]*PR[p1-p4+k1,me,n4]*PR[-p2+p3+k1,me,n5]},{k1}][-4,-1]

me=1;mmu=2;
s12=-1;s13=-3;s14=-1;s15=-1;s23=-1;s24=-1;s25=-1;s34=-1;s35=-1;s45=-1;
invariants={p1^2->me^2,p2^2->me^2,p3^2->mmu^2,p4^2->mmu^2,p5^2->0,p1*p2->(s12-2*me^2)/2,p1*p3->(-s13+me^2+mmu^2)/2,p1*p4->(-s14+me^2+mmu^2)/2,p1*p5->(-s15+me^2)/2,p2*p3->(-s23+me^2+mmu^2)/2,p2*p4->(-s24+me^2+mmu^2)/2,p2*p5->(-s25+me^2)/2,p3*p4->(s34-2*mmu^2)/2,p3*p5->(s35-mmu^2)/2,p4*p5->(s45-mmu^2)/2};
DoSectors[{k1*p1},{PR[-k1,mmu,1]PR[k1+p3,0,1]PR[k1-p2+p3,me,1]PR[k1+p1-p4,me,1]PR[-k1+p4,0,1]},{k1}][-4,0]

me=1;mmu=2;
s12=-1;s13=-3;s14=-1;s15=-1;s23=-1;s24=-1;s25=-1;s34=-1;s35=-1;s45=-1;
invariants={p1^2->me^2,p2^2->me^2,p3^2->mmu^2,p4^2->mmu^2,p5^2->0,p1*p2->(s12-2*me^2)/2,p1*p3->(-s13+me^2+mmu^2)/2,p1*p4->(-s14+me^2+mmu^2)/2,p1*p5->(-s15+me^2)/2,p2*p3->(-s23+me^2+mmu^2)/2,p2*p4->(-s24+me^2+mmu^2)/2,p2*p5->(-s25+me^2)/2,p3*p4->(s34-2*mmu^2)/2,p3*p5->(s35-mmu^2)/2,p4*p5->(s45-mmu^2)/2};
DoSectors[{k1*p1},{PR[k1,mmu,1]PR[k1+p3,0,1]PR[k1-p2+p3,me,1]PR[k1+p1-p4,me,1]PR[k1-p4,0,1]},{k1},TempFileDelete->False][-4,0]

me=1;mmu=2;
s12=-1;s13=-3;s14=-1;s15=-1;s23=-1;s24=-1;s25=-1;s34=-1;s35=-1;s45=-1;
invariants={p1^2->me^2,p2^2->me^2,p3^2->mmu^2,p4^2->mmu^2,p5^2->0,p1*p2->(s12-2*me^2)/2,p1*p3->(-s13+me^2+mmu^2)/2,p1*p4->(-s14+me^2+mmu^2)/2,p1*p5->(-s15+me^2)/2,p2*p3->(-s23+me^2+mmu^2)/2,p2*p4->(-s24+me^2+mmu^2)/2,p2*p5->(-s25+me^2)/2,p3*p4->(s34-2*mmu^2)/2,p3*p5->(s35-mmu^2)/2,p4*p5->(s45-mmu^2)/2};
DoSectors[{k1*p1},{PR[k1,mmu,1]PR[k1+p3,0,1]PR[k1-p2+p3,me,1]PR[k1+p1-p4,me,1]PR[k1-p4,0,1]},{k1},TempFileDelete->False][-4,0]

Tensor rank 2

(* 41 *)

n1=1;n2=1;n3=1;n4=1;n5=1;
me=1;mmu=1;
s12=-1;s13=-3;s14=-1;s15=-1;s23=-1;s24=-1;s25=-1;s34=-1;s35=-1;s45=-1;
invariants={p1^2->me^2,p2^2->me^2,p3^2->mmu^2,p4^2->mmu^2,p5^2->0,p1*p2->(s12-2*me^2)/2,p1*p3->(-s13+me^2+mmu^2)/2,p1*p4->(-s14+me^2+mmu^2)/2,p1*p5->(-s15+me^2)/2,p2*p3->(-s23+me^2+mmu^2)/2,p2*p4->(-s24+me^2+mmu^2)/2,p2*p5->(-s25+me^2)/2,p3*p4->(s34-2*mmu^2)/2,p3*p5->(s35-mmu^2)/2,p4*p5->(s45-mmu^2)/2};
DoSectors[{k1*p1,k1*p2},{PR[k1,mmu,n1]*PR[p4+k1,0,n2]*PR[-p2+p4+k1,me,n3]*PR[-p1-p2+p4+k1,0,n4]*PR[-p1-p2+p3+p4+k1,mmu,n5]},{k1}][-4,-1]

(* n42 *)

n1=1;n2=1;n3=1;n4=1;n5=1;
me=1;mmu=1;
s12=-1;s13=-3;s14=-1;s15=-1;s23=-1;s24=-1;s25=-1;s34=-1;s35=-1;s45=-1;
invariants={p1^2->me^2,p2^2->me^2,p3^2->mmu^2,p4^2->mmu^2,p5^2->0,p1*p2->(s12-2*me^2)/2,p1*p3->(-s13+me^2+mmu^2)/2,p1*p4->(-s14+me^2+mmu^2)/2,p1*p5->(-s15+me^2)/2,p2*p3->(-s23+me^2+mmu^2)/2,p2*p4->(-s24+me^2+mmu^2)/2,p2*p5->(-s25+me^2)/2,p3*p4->(s34-2*mmu^2)/2,p3*p5->(s35-mmu^2)/2,p4*p5->(s45-mmu^2)/2};
DoSectors[{k1*p1,k1*p2},{PR[k1,mmu,n1]*PR[p4+k1,0,n2]*PR[-p1+p4+k1,me,n3]*PR[-p1-p2+p4+k1,0,n4]*PR[-p1-p2+p3+p4+k1,mmu,n5]},{k1}][-4,-1]

(* 43 *)

n1=1;n2=1;n3=1;n4=1;n5=1;
me=1;mmu=1;
s12=-1;s13=-3;s14=-1;s15=-1;s23=-1;s24=-1;s25=-1;s34=-1;s35=-1;s45=-1;
invariants={p1^2->me^2,p2^2->me^2,p3^2->mmu^2,p4^2->mmu^2,p5^2->0,p1*p2->(s12-2*me^2)/2,p1*p3->(-s13+me^2+mmu^2)/2,p1*p4->(-s14+me^2+mmu^2)/2,p1*p5->(-s15+me^2)/2,p2*p3->(-s23+me^2+mmu^2)/2,p2*p4->(-s24+me^2+mmu^2)/2,p2*p5->(-s25+me^2)/2,p3*p4->(s34-2*mmu^2)/2,p3*p5->(s35-mmu^2)/2,p4*p5->(s45-mmu^2)/2};
DoSectors[{k1*p1,k1*p2},{PR[k1,mmu,n1]*PR[p3+k1,0,n2]*PR[p4-k1,0,n3]*PR[-p1+p3+k1,me,n4]*PR[p2-p4+k1,me,n5]},{k1}][-4,-1]

(* n44 *)

n1=1;n2=1;n3=1;n4=1;n5=1;
me=1;mmu=1;
s12=-1;s13=-3;s14=-1;s15=-1;s23=-1;s24=-1;s25=-1;s34=-1;s35=-1;s45=-1;
invariants={p1^2->me^2,p2^2->me^2,p3^2->mmu^2,p4^2->mmu^2,p5^2->0,p1*p2->(s12-2*me^2)/2,p1*p3->(-s13+me^2+mmu^2)/2,p1*p4->(-s14+me^2+mmu^2)/2,p1*p5->(-s15+me^2)/2,p2*p3->(-s23+me^2+mmu^2)/2,p2*p4->(-s24+me^2+mmu^2)/2,p2*p5->(-s25+me^2)/2,p3*p4->(s34-2*mmu^2)/2,p3*p5->(s35-mmu^2)/2,p4*p5->(s45-mmu^2)/2};
DoSectors[{k1*p1,k1*p2},{PR[k1,mmu,n1]*PR[p3+k1,0,n2]*PR[-p4+k1,0,n3]*PR[p1-p4+k1,me,n4]*PR[-p2+p3+k1,me,n5]},{k1}][-4,-1]

Tensor rank 3

(* 41 *)

n1=1;n2=1;n3=1;n4=1;n5=1;
me=1;mmu=1;
s12=-1;s13=-3;s14=-1;s15=-1;s23=-1;s24=-1;s25=-1;s34=-1;s35=-1;s45=-1;
invariants={p1^2->me^2,p2^2->me^2,p3^2->mmu^2,p4^2->mmu^2,p5^2->0,p1*p2->(s12-2*me^2)/2,p1*p3->(-s13+me^2+mmu^2)/2,p1*p4->(-s14+me^2+mmu^2)/2,p1*p5->(-s15+me^2)/2,p2*p3->(-s23+me^2+mmu^2)/2,p2*p4->(-s24+me^2+mmu^2)/2,p2*p5->(-s25+me^2)/2,p3*p4->(s34-2*mmu^2)/2,p3*p5->(s35-mmu^2)/2,p4*p5->(s45-mmu^2)/2};
DoSectors[{k1*p1,k1*p2,k1*p3},{PR[k1,mmu,n1]*PR[p4+k1,0,n2]*PR[-p2+p4+k1,me,n3]*PR[-p1-p2+p4+k1,0,n4]*PR[-p1-p2+p3+p4+k1,mmu,n5]},{k1}][-4,-1]

(* n42 *)

n1=1;n2=1;n3=1;n4=1;n5=1;
me=1;mmu=1;
s12=-1;s13=-3;s14=-1;s15=-1;s23=-1;s24=-1;s25=-1;s34=-1;s35=-1;s45=-1;
invariants={p1^2->me^2,p2^2->me^2,p3^2->mmu^2,p4^2->mmu^2,p5^2->0,p1*p2->(s12-2*me^2)/2,p1*p3->(-s13+me^2+mmu^2)/2,p1*p4->(-s14+me^2+mmu^2)/2,p1*p5->(-s15+me^2)/2,p2*p3->(-s23+me^2+mmu^2)/2,p2*p4->(-s24+me^2+mmu^2)/2,p2*p5->(-s25+me^2)/2,p3*p4->(s34-2*mmu^2)/2,p3*p5->(s35-mmu^2)/2,p4*p5->(s45-mmu^2)/2};
DoSectors[{k1*p1,k1*p2,k1*p3},{PR[k1,mmu,n1]*PR[p4+k1,0,n2]*PR[-p1+p4+k1,me,n3]*PR[-p1-p2+p4+k1,0,n4]*PR[-p1-p2+p3+p4+k1,mmu,n5]},{k1}][-4,-1]

(* 43 *)

n1=1;n2=1;n3=1;n4=1;n5=1;
me=1;mmu=1;
s12=-1;s13=-3;s14=-1;s15=-1;s23=-1;s24=-1;s25=-1;s34=-1;s35=-1;s45=-1;
invariants={p1^2->me^2,p2^2->me^2,p3^2->mmu^2,p4^2->mmu^2,p5^2->0,p1*p2->(s12-2*me^2)/2,p1*p3->(-s13+me^2+mmu^2)/2,p1*p4->(-s14+me^2+mmu^2)/2,p1*p5->(-s15+me^2)/2,p2*p3->(-s23+me^2+mmu^2)/2,p2*p4->(-s24+me^2+mmu^2)/2,p2*p5->(-s25+me^2)/2,p3*p4->(s34-2*mmu^2)/2,p3*p5->(s35-mmu^2)/2,p4*p5->(s45-mmu^2)/2};
DoSectors[{k1*p1,k1*p2,k1*p3},{PR[k1,mmu,n1]*PR[p3+k1,0,n2]*PR[p4-k1,0,n3]*PR[-p1+p3+k1,me,n4]*PR[p2-p4+k1,me,n5]},{k1}][-4,-1]

(* n44 *)

n1=1;n2=1;n3=1;n4=1;n5=1;
me=1;mmu=1;
s12=-1;s13=-3;s14=-1;s15=-1;s23=-1;s24=-1;s25=-1;s34=-1;s35=-1;s45=-1;
invariants={p1^2->me^2,p2^2->me^2,p3^2->mmu^2,p4^2->mmu^2,p5^2->0,p1*p2->(s12-2*me^2)/2,p1*p3->(-s13+me^2+mmu^2)/2,p1*p4->(-s14+me^2+mmu^2)/2,p1*p5->(-s15+me^2)/2,p2*p3->(-s23+me^2+mmu^2)/2,p2*p4->(-s24+me^2+mmu^2)/2,p2*p5->(-s25+me^2)/2,p3*p4->(s34-2*mmu^2)/2,p3*p5->(s35-mmu^2)/2,p4*p5->(s45-mmu^2)/2};
DoSectors[{k1*p1,k1*p2,k1*p3},{PR[k1,mmu,n1]*PR[p3+k1,0,n2]*PR[-p4+k1,0,n3]*PR[p1-p4+k1,me,n4]*PR[-p2+p3+k1,me,n5]},{k1}][-4,-1]

n1=n2=n3=n4=n5=1;
me=1;s12=-3;s23=-6;s34=-5;s45=-7;s15=-2;
invariants={p1^2->me^2,p2^2->me^2,p3^2->me^2,p4^2->0,p5^2->me^2,p1 p2->(1/2) (-2 (me^2)+s12),p2 p3->(1/2) (-2 (me^2)+s23),p3 p4->(1/2) (-(me^2)+s34),p4 p5->(1/2) (-(me^2)+s45),p1 p5->(1/2) (-2 (me^2)+s15),p3 p5->(1/2) (s12-s34-s45),p1 p4->(1/2) ((me^2)-s15+s23-s45),p2 p5->(1/2) ((me^2)-s12-s15+s34),p1 p3->(1/2) ((me^2)-s12-s23+s45),p2 p4->(1/2) ((me^2)+s15-s23-s34)};
DoSectors[{k1*p1,k1*p2,k1*p3},{PR[k1,0,n1]PR[k1+p1,me,n2]PR[k1+p1+p2,0,n3]PR[k1+p1+p2+p3,me,n4]PR[k1+p1+p2+p3+p4,me,n5]},{k1}][-2,0]

(* AMBRE OK *)

(* LoopTools OK *)

6pt function

Scalar

n1=n2=n3=n4=n5=n6=1;
m1=m2=m3=m4=m5=m6=1;
s12=-1/2;s23=-1;s34=-1;s45=-1;s56=-1;s16=-1;s123=-1;s234=-10;s345=-5/2;
p1s=-1;p2s=-1;p3s=-1;p4s=-1;p5s=-1;p6s=-1;
invariants={p1^2->p1s,p2^2->p2s,p3^2->p3s,p4^2->p4s,p5^2->p5s,p6^2->p6s,p1*p2->(-p1s-p2s+s12)/2,p2*p3->(-p2s-p3s+s23)/2,p3*p4->(-p3s-p4s+s34)/2,p4*p5->(-p4s-p5s+s45)/2,p5*p6->(-p5s-p6s+s56)/2,p1*p6->(-p1s-p6s+s16)/2,p1*p3->(p2s-s12+s123-s23)/2,p2*p4->(p3s-s23+s234-s34)/2,p3*p5->(p4s-s34+s345-s45)/2,p1*p4->(-s123+s23-s234+s56)/2,p1*p5->(p6s-s16+s234-s56)/2,p2*p5->(s16-s234+s34-s345)/2,p2*p6->(p1s-s12-s16+s345)/2,p3*p6->(s12-s123-s345+s45)/2,p4*p6->(p5s+s123-s45-s56)/2};
DoSectors[{1},{PR[k1,m1,n1]*PR[k1+p1,m2,n2]*PR[k1+p1+p2,m3,n3]*PR[k1+p1+p2+p3,m4,n4]*PR[k1+p1+p2+p3+p4,m5,n5]*PR[k1+p1+p2+p3+p4+p5,m6,n6]},{k1}][-4,0]

(* AMBRE *)

0.0227763`

(* AutoSectors *)

0.035439991508944245`

n1=n2=n3=n4=n5=n6=1;
m1=Sqrt[49/256];m2=Sqrt[49/256];m3=Sqrt[49/256];m4=Sqrt[81/1600];m5=Sqrt[81/1600];m6=Sqrt[49/256];
s12=4;s23=-1/10;s34=1/5;s45=3/10;s56=2/5;s16=-1/5;s123=3/10;s234=-5/2;s345=1.753247474;
p1s=0;p2s=0;p3s=49/256;p4s=81/1600;p5s=49/256;p6s=9/100;
invariants={p1^2->p1s,p2^2->p2s,p3^2->p3s,p4^2->p4s,p5^2->p5s,p6^2->p6s,p1*p2->(-p1s-p2s+s12)/2,p2*p3->(-p2s-p3s+s23)/2,p3*p4->(-p3s-p4s+s34)/2,p4*p5->(-p4s-p5s+s45)/2,p5*p6->(-p5s-p6s+s56)/2,p1*p6->(-p1s-p6s+s16)/2,p1*p3->(p2s-s12+s123-s23)/2,p2*p4->(p3s-s23+s234-s34)/2,p3*p5->(p4s-s34+s345-s45)/2,p1*p4->(-s123+s23-s234+s56)/2,p1*p5->(p6s-s16+s234-s56)/2,p2*p5->(s16-s234+s34-s345)/2,p2*p6->(p1s-s12-s16+s345)/2,p3*p6->(s12-s123-s345+s45)/2,p4*p6->(p5s+s123-s45-s56)/2};
DoSectors[{1},{PR[k1,m1,n1]*PR[k1+p1,m2,n2]*PR[k1+p1+p2,m3,n3]*PR[k1+p1+p2+p3,m4,n4]*PR[k1+p1+p2+p3+p4,m5,n5]*PR[k1+p1+p2+p3+p4+p5,m6,n6]},{k1}][-4,0]

(* hexagon *)

-653.989+3.23965 I

n1=n2=n3=n4=n5=n6=1;
p1s=p2s=p3s=p4s=p5s=p6s=-1;
s12=s23=s34=s45=s56=s16=s123=s234=-1;
s345=-5/2;
m1=m2=m3=m4=m5=m6=1;
invariants={p1^2->p1s,p2^2->p2s,p3^2->p3s,p4^2->p4s,p5^2->p5s,p6^2->p6s,p1*p2->(-p1s-p2s+s12)/2,p2*p3->(-p2s-p3s+s23)/2,p3*p4->(-p3s-p4s+s34)/2,p4*p5->(-p4s-p5s+s45)/2,p5*p6->(-p5s-p6s+s56)/2,p1*p6->(-p1s-p6s+s16)/2,p1*p3->(p2s-s12+s123-s23)/2,p2*p4->(p3s-s23+s234-s34)/2,p3*p5->(p4s-s34+s345-s45)/2,p1*p4->(-s123+s23-s234+s56)/2,p1*p5->(p6s-s16+s234-s56)/2,p2*p5->(s16-s234+s34-s345)/2,p2*p6->(p1s-s12-s16+s345)/2,p3*p6->(s12-s123-s345+s45)/2,p4*p6->(p5s+s123-s45-s56)/2};
DoSectors[{1},{PR[k1,m1,n1]*PR[k1+p1,m2,n2]*PR[k1+p1+p2,m3,n3]*PR[k1+p1+p2+p3,m4,n4]*PR[k1+p1+p2+p3+p4,m5,n5]*PR[k1+p1+p2+p3+p4+p5,m6,n6]},{k1}][-4,1]

(* hexagon OK *)

Vector

n1=n2=n3=n4=n5=n6=1;
p1s=p2s=p3s=p4s=p5s=p6s=-1;
s12=s23=s34=s45=s56=s16=s123=s234=-1;
s345=-5/2;
m1=m2=m3=m4=m5=m6=1;
invariants={p1^2->p1s,p2^2->p2s,p3^2->p3s,p4^2->p4s,p5^2->p5s,p6^2->p6s,p1*p2->(-p1s-p2s+s12)/2,p2*p3->(-p2s-p3s+s23)/2,p3*p4->(-p3s-p4s+s34)/2,p4*p5->(-p4s-p5s+s45)/2,p5*p6->(-p5s-p6s+s56)/2,p1*p6->(-p1s-p6s+s16)/2,p1*p3->(p2s-s12+s123-s23)/2,p2*p4->(p3s-s23+s234-s34)/2,p3*p5->(p4s-s34+s345-s45)/2,p1*p4->(-s123+s23-s234+s56)/2,p1*p5->(p6s-s16+s234-s56)/2,p2*p5->(s16-s234+s34-s345)/2,p2*p6->(p1s-s12-s16+s345)/2,p3*p6->(s12-s123-s345+s45)/2,p4*p6->(p5s+s123-s45-s56)/2};
DoSectors[{k1*p4},{PR[k1,m1,n1]*PR[k1+p1,m2,n2]*PR[k1+p1+p2,m3,n3]*PR[k1+p1+p2+p3,m4,n4]*PR[k1+p1+p2+p3+p4,m5,n5]*PR[k1+p1+p2+p3+p4+p5,m6,n6]},{k1}][-4,1]

(* hexagon OK???*)

n1=n2=n3=n4=n5=n6=1;
p1s=p2s=p3s=p4s=p5s=p6s=-1;
s12=s23=s34=s45=s56=s16=s123=s234=-1;
s345=-5/2;
m1=m2=m3=m4=m5=m6=1;
invariants={p1^2->p1s,p2^2->p2s,p3^2->p3s,p4^2->p4s,p5^2->p5s,p6^2->p6s,p1*p2->(-p1s-p2s+s12)/2,p2*p3->(-p2s-p3s+s23)/2,p3*p4->(-p3s-p4s+s34)/2,p4*p5->(-p4s-p5s+s45)/2,p5*p6->(-p5s-p6s+s56)/2,p1*p6->(-p1s-p6s+s16)/2,p1*p3->(p2s-s12+s123-s23)/2,p2*p4->(p3s-s23+s234-s34)/2,p3*p5->(p4s-s34+s345-s45)/2,p1*p4->(-s123+s23-s234+s56)/2,p1*p5->(p6s-s16+s234-s56)/2,p2*p5->(s16-s234+s34-s345)/2,p2*p6->(p1s-s12-s16+s345)/2,p3*p6->(s12-s123-s345+s45)/2,p4*p6->(p5s+s123-s45-s56)/2};
DoSectors[{k1*p2},{PR[k1,m1,n1]*PR[k1+p1,m2,n2]*PR[k1+p1+p2,m3,n3]*PR[k1+p1+p2+p3,m4,n4]*PR[k1+p1+p2+p3+p4,m5,n5]*PR[k1+p1+p2+p3+p4+p5,m6,n6]},{k1}][-4,0]

(* hexagon OK *)

Tensor rank 2

n1=n2=n3=n4=n5=n6=1;
p1s=p2s=p3s=p4s=p5s=p6s=-1;
s12=s23=s34=s45=s56=s16=s123=s234=-1;
s345=-5/2;
m1=m2=m3=m4=m5=m6=1;
invariants={p1^2->p1s,p2^2->p2s,p3^2->p3s,p4^2->p4s,p5^2->p5s,p6^2->p6s,p1*p2->(-p1s-p2s+s12)/2,p2*p3->(-p2s-p3s+s23)/2,p3*p4->(-p3s-p4s+s34)/2,p4*p5->(-p4s-p5s+s45)/2,p5*p6->(-p5s-p6s+s56)/2,p1*p6->(-p1s-p6s+s16)/2,p1*p3->(p2s-s12+s123-s23)/2,p2*p4->(p3s-s23+s234-s34)/2,p3*p5->(p4s-s34+s345-s45)/2,p1*p4->(-s123+s23-s234+s56)/2,p1*p5->(p6s-s16+s234-s56)/2,p2*p5->(s16-s234+s34-s345)/2,p2*p6->(p1s-s12-s16+s345)/2,p3*p6->(s12-s123-s345+s45)/2,p4*p6->(p5s+s123-s45-s56)/2};
DoSectors[{k1*p2,k1*p3},{PR[k1,m1,n1]*PR[k1+p1,m2,n2]*PR[k1+p1+p2,m3,n3]*PR[k1+p1+p2+p3,m4,n4]*PR[k1+p1+p2+p3+p4,m5,n5]*PR[k1+p1+p2+p3+p4+p5,m6,n6]},{k1}][-4,0]

(* hexagon OK *)

Tensor rank 3

n1=n2=n3=n4=n5=n6=1;
p1s=p2s=p3s=p4s=p5s=p6s=-1;
s12=s23=s34=s45=s56=s16=s123=s234=-1;
s345=-5/2;
m1=m2=m3=m4=m5=m6=1;
invariants={p1^2->p1s,p2^2->p2s,p3^2->p3s,p4^2->p4s,p5^2->p5s,p6^2->p6s,p1*p2->(-p1s-p2s+s12)/2,p2*p3->(-p2s-p3s+s23)/2,p3*p4->(-p3s-p4s+s34)/2,p4*p5->(-p4s-p5s+s45)/2,p5*p6->(-p5s-p6s+s56)/2,p1*p6->(-p1s-p6s+s16)/2,p1*p3->(p2s-s12+s123-s23)/2,p2*p4->(p3s-s23+s234-s34)/2,p3*p5->(p4s-s34+s345-s45)/2,p1*p4->(-s123+s23-s234+s56)/2,p1*p5->(p6s-s16+s234-s56)/2,p2*p5->(s16-s234+s34-s345)/2,p2*p6->(p1s-s12-s16+s345)/2,p3*p6->(s12-s123-s345+s45)/2,p4*p6->(p5s+s123-s45-s56)/2};
DoSectors[{k1*p2,k1*p3,k1*p5},{PR[k1,m1,n1]*PR[k1+p1,m2,n2]*PR[k1+p1+p2,m3,n3]*PR[k1+p1+p2+p3,m4,n4]*PR[k1+p1+p2+p3+p4,m5,n5]*PR[k1+p1+p2+p3+p4+p5,m6,n6]},{k1}][-4,0]

(* hexagon OK *)

Tensor rank 4

n1=n2=n3=n4=n5=n6=1;
p1s=p2s=p3s=p4s=p5s=p6s=-1;
s12=s23=s34=s45=s56=s16=s123=s234=-1;
s345=-5/2;
m1=m2=m3=m4=m5=m6=1;
invariants={p1^2->p1s,p2^2->p2s,p3^2->p3s,p4^2->p4s,p5^2->p5s,p6^2->p6s,p1*p2->(-p1s-p2s+s12)/2,p2*p3->(-p2s-p3s+s23)/2,p3*p4->(-p3s-p4s+s34)/2,p4*p5->(-p4s-p5s+s45)/2,p5*p6->(-p5s-p6s+s56)/2,p1*p6->(-p1s-p6s+s16)/2,p1*p3->(p2s-s12+s123-s23)/2,p2*p4->(p3s-s23+s234-s34)/2,p3*p5->(p4s-s34+s345-s45)/2,p1*p4->(-s123+s23-s234+s56)/2,p1*p5->(p6s-s16+s234-s56)/2,p2*p5->(s16-s234+s34-s345)/2,p2*p6->(p1s-s12-s16+s345)/2,p3*p6->(s12-s123-s345+s45)/2,p4*p6->(p5s+s123-s45-s56)/2};
DoSectors[{k1*p2,k1*p3,k1*p5,k1*p1},{PR[k1,m1,n1]*PR[k1+p1,m2,n2]*PR[k1+p1+p2,m3,n3]*PR[k1+p1+p2+p3,m4,n4]*PR[k1+p1+p2+p3+p4,m5,n5]*PR[k1+p1+p2+p3+p4+p5,m6,n6]},{k1}][-2,0]

(* hexagon OK *)

Two loop

Self Energy

Scalar

n1=1;n2=1;n3=1;
m=1;
invariants={p1^2->-11};
DoSectors[{k1*p1,k1*p1,k1*p1},{PR[p1-k1-k2,m,n1]*PR[k1,m,n2]*PR[k2,0,n3]},{k1,k2},OutputForm->InputForm][-4,1]

FORMAT[x2 x3+x1 (x2+x3)/2]/.FORMAT->StandardForm

x2*x3 + x1*(x2 + x3)

Vector

invariants={p1^2->-11};
DoSectors[{k1*p1},{PR[p1-k1-k2,1,1]*PR[k1,1,1]*PR[k2,0,1]},{k1,k2}][-4,1]

(* IdSolver OK *)

(* AMBRE OK *)

invariants={p1^2->-11};
DoSectors[{k2*p1},{PR[p1-k1-k2,1,1]*PR[k1,1,1]*PR[k2,0,1]},{k1,k2}][-4,1]

(* AMBRE OK *)

Tensor rank 2

n1=1;n2=1;n3=1;n4=1;n5=1;
m=1;s=-11;
invariants={p1^2->s};
DoSectors[{k2*p1,k1*p1},{PR[k1,0,n1]*PR[k2,0,n2]*PR[k2-k1,0,n3]*PR[k1+p1,0,n4]*PR[k2+p1,0,n5]},{k1,k2}][-4,1]

(* AMBRE OK *)

n1=1;n2=1;n3=1;
m=1;
invariants={p1^2->-11};
DoSectors[{k1*p1,k2*p1},{PR[p1-k1-k2,m,n1]*PR[k1,m,n2]*PR[k2,0,n3]},{k1,k2}][-4,2]

(* AMBRE OK *)

invariants={p1^2->-11};
DoSectors[{k1*k2},{PR[p1-k1-k2,1,1]*PR[k1,1,1]*PR[k2,0,1]},{k1,k2}][-4,1]

(* AMBRE OK *)

invariants={p1^2->-11};
DoSectors[{k2*k1},{PR[p1-k1-k2,1,2]*PR[k1,1,1]*PR[k2,0,1]},{k1,k2}][-4,1]

invariants={p1^2->-11};
DoSectors[{k1*k1},{PR[p1-k1-k2,1,2]*PR[k1,1,1]*PR[k2,0,1]},{k1,k2}][-4,1]

(* IdSolver OK *)

invariants={p1^2->-11};
DoSectors[{k2*k2},{PR[p1-k1-k2,1,2]*PR[k1,1,1]*PR[k2,0,1]},{k1,k2}][-4,1]

invariants={p1^2->-11};
DoSectors[{k1*p1,k2*p1},{PR[p1-k1-k2,1,2]*PR[k1,1,1]*PR[k2,0,1]},{k1,k2}][-2,1]

(* IdSolver OK *)

Tensor rank 3

n1=1;n2=1;n3=1;n4=1;n5=1;
m=1;s=-11;
invariants={p1^2->s};
DoSectors[{k2*p1,k2*p1,k1*p1},{PR[k1,0,n1]*PR[k2,0,n2]*PR[k2-k1,0,n3]*PR[k1+p1,0,n4]*PR[k2+p1,0,n5]},{k1,k2},SetStrategy->X][-2,0]

(* AMBRE OK *)

n1=1;n2=1;n3=1;
m=1;
invariants={p1^2->-11};
DoSectors[{k2*p1,k2*p1,k1*p1},{PR[p1+k1,m,n1]*PR[k1-k2,m,n2]*PR[k2,0,n3]},{k1,k2}][-4,1]

(* AMBRE OK *)

n1=1;n2=1;n3=1;
m=1;
invariants={p1^2->-11};
DoSectors[{k2*p1,k2*p1,k1*p1},{PR[p1+k1,m,n1]*PR[k1-k2,m,n2]*PR[k2,0,n3]},{k1,k2}][-4,1]

n1=1;n2=1;n3=1;
m=1;
invariants={p1^2->-11};
DoSectors[{z1*p1,z1*p1,z1*p1},{PR[p1+z1+z2,m,n1]*PR[z1,m,n2]*PR[z2,0,n3]},{z2,z1}][-4,1]

(* AMBRE OK *)

n1=1;n2=1;n3=1;n4=1;n5=1;
m=1;
invariants={p1^2->-11};
DoSectors[{k2*p1,k2*p1,k2*p1},{PR[p1+k1,m,n1]*PR[p1+k1+k2,m,n2]*PR[k1+k2,0,n3]*PR[k2,0,n4]*PR[k1,0,n5]},{k1,k2},SetStrategy->X,TempFileDelete->False][-4,-1]

n1=1;n2=1;n3=1;
m=1;
invariants={p1^2->-11};
DoSectors[{k1*p1,k1*p1,k1*p1},{PR[p1-k1-k2,m,n1]*PR[k1,m,n2]*PR[k2,0,n3]},{k1,k2}][-4,1]

(* AMBRE OK *)

n1=1;n2=1;n3=1;
m=1;
invariants={p1^2->-11};
DoSectors[{k1*p1,k1*k2},{PR[p1-k1-k2,m,n1]*PR[k1,m,n2]*PR[k2,0,n3]},{k1,k2}][-4,1]

(* AMBRE OK *)

n1=1;n2=1;n3=1;
m=1;
invariants={p1^2->-11};
DoSectors[{k1*p1,k1*p1,k2*p1},{PR[p1-k1-k2,m,n1]*PR[k1,m,n2]*PR[k2,0,n3]},{k1,k2}][-4,1]

(* AMBRE OK *)

n1=1;n2=1;n3=1;
m=1;
invariants={p1^2->-11};
DoSectors[{k2*p1,k2*p1,k1*p1},{PR[p1+k1,m,n1]*PR[k1-k2,m,n2]*PR[k2,0,n3]},{k1,k2}][-4,1]

invariants={p1^2->-11};
DoSectors[{k1*p1,k2*p1,k2*p1},{PR[p1-k1-k2,1,2]*PR[k1,1,1]*PR[k2,0,2]},{k1,k2}][-4,1]

(* IdSolver OK *)

(* AMBRE OK *)

invariants={p1^2->-11};
DoSectors[{k1*p1,k2*p1,k2*p1},{PR[p1-k1-k2,1,2]*PR[k1,1,1]*PR[k2,0,1]},{k1,k2}][-4,1]

(* IdSolver OK *)

(* AMBRE OK *)

invariants={p1^2->-1/11};
DoSectors[{k1*p1,k2*p1,k2*p1},{PR[p1-k1-k2,1,2]*PR[k1,1,1]*PR[k2,0,1]},{k1,k2}][-4,1]

(* IdSolver OK *)

(* AMBRE OK *)

invariants={p1^2->-11};
DoSectors[{k2*p1,k2*p1,k2*p1},{PR[p1-k1-k2,1,2]*PR[k1,1,1]*PR[k2,0,1]},{k1,k2}][-4,1]

(* IdSolver OK *)

(* AMBRE OK *)

invariants={p1^2->-1/11};
DoSectors[{k2*p1,k2*p1,k2*p1},{PR[p1-k1-k2,1,2]*PR[k1,1,1]*PR[k2,0,1]},{k1,k2}][-4,1]

(* IdSolver OK *)

(* AMBRE OK *)

invariants={p1^2->-11};
DoSectors[{k2*p1,k2*p1,k2*p1},{PR[p1-k1-k2,1,1]*PR[k1,1,1]*PR[k2,0,1]},{k1,k2}][-4,1]

(* IdSolver OK *)

(* AMBRE OK *)

invariants={p1^2->-1/11};
DoSectors[{k2*p1,k2*p1,k2*p1},{PR[p1-k1-k2,1,1]*PR[k1,1,1]*PR[k2,0,1]},{k1,k2}][-4,1]

(* IdSolver OK *)

(* AMBRE OK *)

invariants={p1^2->-11};
DoSectors[{k1*p1,k2*p1,k2*p1},{PR[p1-k1-k2,1,1]*PR[k1,1,1]*PR[k2,0,1]},{k1,k2}][-4,1]

(* IdSolver OK *)

(* AMBRE OK *)

invariants={p1^2->-1/11};
DoSectors[{k1*p1,k2*p1,k2*p1},{PR[p1-k1-k2,1,1]*PR[k1,1,1]*PR[k2,0,1]},{k1,k2}][-4,1]

(* IdSolver OK *)

(* AMBRE OK *)

invariants={p1^2->-11};
DoSectors[{k1*p1,k1*p1,k2*p1},{PR[p1-k1-k2,1,1]*PR[k1,1,1]*PR[k2,0,1]},{k1,k2}][-4,1]

(* IdSolver OK *)

(* AMBRE OK *)

invariants={p1^2->-1/11};
DoSectors[{k1*p1,k1*p1,k2*p1},{PR[p1-k1-k2,1,1]*PR[k1,1,1]*PR[k2,0,1]},{k1,k2}][-4,1]

(* IdSolver OK *)

(* AMBRE OK *)

invariants={p1^2->-11};
DoSectors[{k1*p1,k1*p1,k1*p1},{PR[p1-k1-k2,1,1]*PR[k1,1,1]*PR[k2,0,1]},{k1,k2}][-4,1]

(* IdSolver OK *)

(* AMBRE OK *)

invariants={p1^2->-1/11};
DoSectors[{k1*p1,k1*p1,k1*p1},{PR[p1-k1-k2,1,1]*PR[k1,1,1]*PR[k2,0,1]},{k1,k2}][-4,1]

(* IdSolver OK *)

(* AMBRE OK *)

Tensor rank 4

n1=1;n2=1;n3=1;
m=1;
invariants={p1^2->-11};
DoSectors[{k1*p1,k1*p1,k2*p1,k2*p1},{PR[p1-k1-k2,0,n1]*PR[k1,0,n2]*PR[k2,0,n3]},{k1,k2}][-4,1]

(* AMBRE OK *)

n1=1;n2=1;n3=1;
m=1;
invariants={p1^2->-1};
DoSectors[{k1*p1,k1*p1,k2*p1,k2*p1},{PR[p1-k1-k2,0,n1]*PR[k1,0,n2]*PR[k2,0,n3]},{k1,k2}][-4,1]

(* AMBRE OK *)

n1=1;n2=1;n3=1;
m=1;
invariants={p1^2->-1/3};
DoSectors[{k1*p1,k1*p1,k1*p1,k1*p1},{PR[p1-k1-k2,0,n1]*PR[k1,0,n2]*PR[k2,0,n3]},{k1,k2}][-4,1]

(* AMBRE OK *)

n1=1;n2=1;n3=1;
m=1;
invariants={p1^2->-1/3};
DoSectors[{k1*k2,k1*k2},{PR[p1-k1-k2,0,n1]*PR[k1,0,n2]*PR[k2,0,n3]},{k1,k2}][-4,1]

(* AMBRE OK *)

n1=1;n2=1;n3=1;
m=1;
invariants={p1^2->-33};
DoSectors[{k1*k1,k2*k2},{PR[p1-k1-k2,0,n1]*PR[k1,0,n2]*PR[k2,0,n3]},{k1,k2}][-4,1]

(* AMBRE WRONG *)

n1=1;n2=1;n3=1;
m=1;
invariants={p1^2->-1};
DoSectors[{k1*p1,k2*k2,k1*p1},{PR[p1-k1-k2,0,n1]*PR[k1,0,n2]*PR[k2,0,n3]},{k1,k2}][-4,1]

(* AMBRE ??? *)

n1=1;n2=1;n3=1;
m=1;
invariants={p1^2->-342};
DoSectors[{k1*p1,k2*k2,k1*p1},{PR[p1-k1-k2,0,n1]*PR[k1,0,n2]*PR[k2,0,n3]},{k1,k2}][-4,1]

(* AMBRE WORONG *)

n1=1;n2=1;n3=1;
m=1;
invariants={p1^2->-342};
DoSectors[{k1*k2,k1*k2},{PR[p1-k1-k2,0,n1]*PR[k1,0,n2]*PR[k2,0,n3]},{k1,k2}][-4,1]

(* AMBRE OK *)

n1=1;n2=1;n3=1;
m=1;
invariants={p1^2->-342};
DoSectors[{k1*k1,k2*k2},{PR[p1-k1-k2,0,n1]*PR[k1,0,n2]*PR[k2,0,n3]},{k1,k2}][-4,1]

(* AMBRE ??? *)

n1=1;n2=1;n3=1;
m=1;
invariants={p1^2->-11};
DoSectors[{k1*k1,k2*k2},{PR[p1+k1,0,n1]*PR[k1-k2,0,n2]*PR[k2,0,n3]},{k1,k2}][-4,1]

???

0.`+((1.1641532182693481`*^-10)/eps)+1.862645149230957`*^-9 eps

n1=1;n2=1;n3=1;n4=1;n5=1;
m=1;s=-11;
invariants={p1^2->s};
DoSectors[{k2*p1,k2*p1,k1*p1,k1*p1},{PR[k1,0,n1]*PR[k2,0,n2]*PR[k2-k1,0,n3]*PR[k1+p1,0,n4]*PR[k2+p1,0,n5]},{k1,k2},SetStrategy->X][-4,1]

(* AMBRE OK *)

invariants={p1^2->-1/11};
+DoSectors[{k1*k2,k1*k1},PR[p1-k1-k2,1,1]*PR[k1,1,1]*PR[k2,0,1],{k1,k2},invariants][-4,1]

(* AMBRE OK *)

n1=1;n2=1;n3=1;
s=-1/11;m=1;
invariants={p1^2->s};
DoSectors[{k1*p1,k2*p1,k1*p1,k1*p1},PR[p1-k1-k2,m,n1]*PR[k1,m,n2]*PR[k2,0,n3],{k1,k2},invariants][-4,1]

(* AMBRE OK *)

Tensor rank 5

invariants={p1^2->-1/11};
DoSectors[{k1*p1,k1*p1,k1*p1,k1*k2},{PR[p1-k1-k2,1,1]*PR[k1,1,1]*PR[k2,0,1]},{k1,k2}][-4,1]

(* AMBRE OK *)

invariants={p1^2->-1/11};
DoSectors[{k1*k2,k1*k2,k2*p1},{PR[p1-k1-k2,1,1]*PR[k1,1,1]*PR[k2,0,1]},{k1,k2}][-4,1]

(* AMBRE OK *)

invariants={p1^2->-11};
DoSectors[{k1*p1,k1*p1,k1*p1,k1*k2},PR[p1-k1-k2,1,1]*PR[k1,1,1]*PR[k2,0,1],{k1,k2},invariants][-4,1]

(* AMBRE OK *)

Vertex

Scalar

s=-11;m=1;
invariants={p1^2->m^2,p2^2->m^2,p1*p2->1/2s-m^2};
DoSectors[{1},PR[p1-k1+k2,1,1]*PR[k1,0,1]*PR[k2,0,1]*PR[p2-k2,1,1],{k1,k2},invariants][-4,1]

(* AMBRE OK *)

Vector

s=-11;m=1;
invariants={p1^2->m^2,p2^2->m^2,p1*p2->1/2s-m^2};
DoSectors[{k1*p2},PR[p1-k1+k2,1,1]*PR[k1,0,1]*PR[k2,0,1]*PR[p2-k2,1,1],{k1,k2},invariants,ShowErrors->False][-4,1]

(* IdSolver OK *)

(* AMBRE OK *)

Tensor rank 2

s=-11;m=1;
invariants={p1^2->m^2,p2^2->m^2,p1*p2->1/2s-m^2};DoSectors[{k1*p2,k1*p1},{PR[p1-k1+k2,1,2]*PR[k1,0,1]*PR[k2,0,1]*PR[p2-k2,1,1]},{k1,k2}][-2,1]

(* IdSolver OK *)

(* AMBRE OK *)

s=-11;m=1;
invariants={p1^2->m^2,p2^2->m^2,p1*p2->1/2s-m^2};
DoSectors[{k1*p2,k2*p1},PR[p1-k1+k2,1,2]*PR[k1,0,1]*PR[k2,0,1]*PR[p2-k2,1,1],{k1,k2},invariants][-4,1]

(* IdSolver OK *)

Tensor rank 3

s=-11;m=1;
invariants={p1^2->m^2,p2^2->m^2,p1*p2->1/2s-m^2};
DoSectors[{k1*p2,k1*p1,k2*p1},PR[p1-k1+k2,1,2]*PR[k1,0,1]*PR[k2,0,1]*PR[p2-k2,1,1],{k1,k2},invariants][-4,1]

(* IdSolver OK *)

(* AMBRE OK *)

s=-1/11;m=1;
invariants={p1^2->m^2,p2^2->m^2,p1*p2->1/2s-m^2};
DoSectors[{k1*k2,k1*p1},{PR[p1-k1+k2,1,1]*PR[k1,0,1]*PR[k2,0,1]*PR[p2-k2,1,1]},{k1,k2}][-4,1]

(* AMBRE OK *)

n1=1;n2=1;n3=1;n4=1;n5=1;
s=-11;m=1;
invariants={p1^2->m^2,p2^2->m^2,p1*p2->1/2s-m^2};
DoSectors[{k1*p1,k1*p1,k2*p1},{PR[k1,0,n1]PR[k1+p1,m,n2]PR[k2,0,n3]PR[k1-k2+p1,m,n4]PR[k1-k2+p1+p2,0,n5]},{k1,k2}][-4,0]

(* AMBRE OK *)

s=-11;m=1;
invariants={p1^2->m^2,p2^2->m^2,p1*p2->1/2s-m^2};
DoSectors[{k1*p2,k2*p1,k2*p1},PR[p1-k1+k2,1,2]*PR[k1,0,1]*PR[k2,0,1]*PR[p2-k2,1,1],{k1,k2},invariants][-4,1]

(* IdSolver OK *)

(* AMBRE OK *)

s=-1/11;m=1;
invariants={p1^2->m^2,p2^2->m^2,p1*p2->1/2s-m^2};
DoSectors[{k1*p2,k2*p1,k2*p1},PR[p1-k1+k2,1,2]*PR[k1,0,1]*PR[k2,0,1]*PR[p2-k2,1,1],{k1,k2},invariants][-4,1]

(* IdSolver OK *)

(* AMBRE OK *)

Tensor rank 4

s=-1/3;m=1;
invariants={p1^2->m^2,p2^2->m^2,p1*p2->1/2s-m^2};
DoSectors[{k1*k1,k1*k1},PR[p1-k1+k2,1,2]*PR[k1,0,1]*PR[k2,0,1]*PR[p2-k2,1,1],{k1,k2},invariants][-4,1]

(* IdSolver OK *)

(* AMBRE OK *)

s=-1/11;m=1;
invariants={p1^2->m^2,p2^2->m^2,p1*p2->1/2s-m^2};
DoSectors[{k1*k1,k1*k1},PR[p1-k1+k2,1,2]*PR[k1,0,1]*PR[k2,0,1]*PR[p2-k2,1,1],{k1,k2},invariants][-4,1]

s=-3;m=1;
invariants={p1^2->m^2,p2^2->m^2,p1*p2->1/2s-m^2};
DoSectors[{k1*k2,k1*k2},PR[p1-k1+k2,1,2]*PR[k1,0,1]*PR[k2,0,1]*PR[p2-k2,1,1],{k1,k2},invariants][-4,1]

(* IdSolver OK *)

s=-31;m=1;
invariants={p1^2->m^2,p2^2->m^2,p1*p2->1/2s-m^2};
DoSectors[{k1*p1,k1*p1,k1*p1,k1*p1},PR[p1-k1+k2,1,2]*PR[k1,0,1]*PR[k2,0,1]*PR[p2-k2,1,1],{k1,k2},invariants][-4,1]

(* IdSolver OK *)

s=-7;m=1;
invariants={p1^2->m^2,p2^2->m^2,p1*p2->1/2s-m^2};
DoSectors[{k1*p1,k1*p2,k2*p2,k2*p1},PR[p1-k1+k2,1,2]*PR[k1,0,1]*PR[k2,0,1]*PR[p2-k2,1,1],{k1,k2},invariants][-4,1]

(* IdSolver OK *)

Tensor rank 5

s=-13;m=1;
invariants={p1^2->m^2,p2^2->m^2,p1*p2->1/2s-m^2};
DoSectors[{k1*p1,k1*k1,k1*k1},PR[p1-k1+k2,1,2]*PR[k1,0,1]*PR[k2,0,1]*PR[p2-k2,1,1],{k1,k2},invariants][-4,1]

(* IdSolver OK *)

s=-1/5;m=1;
invariants={p1^2->m^2,p2^2->m^2,p1*p2->1/2s-m^2};
DoSectors[{k1*p1,k1*k2,k2*k2},PR[p1-k1+k2,1,2]*PR[k1,0,1]*PR[k2,0,1]*PR[p2-k2,1,1],{k1,k2},invariants][-4,1]

(* IdSolver OK *)

Box

Scalar

n1=2;n2=1;n3=1;n4=1;n5=1;n6=1;n7=1;
s=-11;t=-33;
invariants={p1*p2->1/2*s,p3*p4->1/2*s,p1*p4->1/2*t,p2*p3->1/2*t,p1*p3->-1/2*s-1/2*t,p2*p4->-1/2*s-1/2*t,p1^2->0,p2^2->0,p3^2->0,p4^2->0};
DoSectors[{1},PR[k1+k2,0,n1]*PR[k2,0,n2]*PR[k1+k2-p1-p2,0,n3]*PR[k2-p1-p2,0,n4]*PR[k1+k2-p2,0,n5]*PR[k1,0,n6]*PR[k2+p3,0,n7],{k1,k2},invariants][-4,-1]

-((0.0000910671912761934`)/(ep^2))-((0.0000551508942301921`)/ep)

n1=1;n2=1;n3=1;n4=1;n5=1;
s=-11;t=-33;
invariants={p1*p2->1/2*s-1, p1*p3->-1/2*t+1,p1*p4->1/2*s+1/2*t-1,p2*p3->1/2*s+1/2*t-1,p2*p4->-1/2*t+1,p3*p4->1/2*s-1,p1^2->1,p2^2->1,p3^2->1,p4^2->1};
DoSectors[{1},PR[p3+k1+k2,1,n1]*PR[p1+p2-p3-k2,1,n2]*PR[p1-p3-k1-k2,0,n3]*PR[k1,0,n4]*PR[k2,0,n5],{k1,k2},invariants][-4,1]

(* AMBRE OK *)

n1=1;n2=1;n3=1;n4=1;n5=1;
s=-11;t=-33;
invariants={p1*p2->1/2*s-1, p1*p3->-1/2*t+1,p1*p4->1/2*s+1/2*t-1,p2*p3->1/2*s+1/2*t-1,p2*p4->-1/2*t+1,p3*p4->1/2*s-1,p1^2->1,p2^2->1,p3^2->1,p4^2->1};
DoSectors[{1},PR[p3+k1+k2,1,n1]*PR[p1+p2-p3-k2,1,n2]*PR[p1-p3-k1-k2,0,n3]*PR[k1,0,n4]*PR[k2,0,n5],{k1,k2},invariants][-4,1]

(* AutoSectors OK *)

(* IdSolver *)

Vector

n1=1;n2=1;n3=1;n4=1;n5=1;
s=-11;t=-33;
invariants={p1*p2->1/2*s-1, p1*p3->-1/2*t+1,p1*p4->1/2*s+1/2*t-1,p2*p3->1/2*s+1/2*t-1,p2*p4->-1/2*t+1,p3*p4->1/2*s-1,p1^2->1,p2^2->1,p3^2->1,p4^2->1};
DoSectors[{k1*p1},PR[p3+k1+k2,1,n1]*PR[p1+p2-p3-k2,1,n2]*PR[p1-p3-k1-k2,0,n3]*PR[k1,0,n4]*PR[k2,0,n5],{k1,k2},invariants][-4,1]

(* AutoSectors OK *)

n1=1;n2=1;n3=1;n4=1;n5=1;
s=-11;t=-33;
invariants={p1*p2->1/2*s-1, p1*p3->-1/2*t+1,p1*p4->1/2*s+1/2*t-1,p2*p3->1/2*s+1/2*t-1,p2*p4->-1/2*t+1,p3*p4->1/2*s-1,p1^2->1,p2^2->1,p3^2->1,p4^2->1};
DoSectors[{k2*p3},PR[p3+k1+k2,1,n1]*PR[p1+p2-p3-k2,1,n2]*PR[p1-p3-k1-k2,0,n3]*PR[k1,0,n4]*PR[k2,0,n5],{k1,k2},invariants][-4,1]

(* AutoSectors OK *)

n1=1;n2=1;n3=1;n4=1;n5=1;n6=1;n7=1;
s=-11;t=-33;
invariants={p1*p2->1/2*s,p3*p4->1/2*s,p1*p4->1/2*t,p2*p3->1/2*t,p1*p3->-1/2*s-1/2*t,p2*p4->-1/2*s-1/2*t,p1^2->0,p2^2->0,p3^2->0,p4^2->0};
DoSectors[{k1*p3},PR[k1+k2,0,n1]*PR[k2,0,n2]*PR[k1+k2-p1-p2,0,n3]*PR[k2-p1-p2,0,n4]*PR[k1+k2-p2,0,n5]*PR[k1,0,n6]*PR[k2+p3,0,n7],{k1,k2},invariants,SetStrategy->X][-5,-3]

n1=1;n2=1;n3=1;n4=1;n5=1;n6=1;n7=1;
s=-11;t=-33;
invariants={p1*p2->1/2*s,p3*p4->1/2*s,p1*p4->1/2*t,p2*p3->1/2*t,p1*p3->-1/2*s-1/2*t,p2*p4->-1/2*s-1/2*t,p1^2->0,p2^2->0,p3^2->0,p4^2->0};
DoSectors[{k1*p3},PR[k1+k2,0,n1]*PR[k2,0,n2]*PR[k1+k2-p1-p2,0,n3]*PR[k2-p1-p2,0,n4]*PR[k1+k2-p2,0,n5]*PR[k1,0,n6]*PR[k2+p3,0,n7],{k1,k2},invariants,SetStrategy->X][-4,-2]

((0.00826548`)/(eps^4))-((0.0487203`)/(eps^3))+((0.0502216`)/(eps^2))+((0.0768892`)/eps)

(* AMBRE  *)

Tensor rank2

n1=1;n2=1;n3=1;n4=1;n5=1;
s=-11;t=-33;
invariants={p1*p2->1/2*s-1,p1*p3->-1/2*t+1,p1*p4->1/2*s+1/2*t-1,p2*p3->1/2*s+1/2*t-1,p2*p4->-1/2*t+1,p3*p4->1/2*s-1,p1^2->1,p2^2->1,p3^2->1,p4^2->1};
DoSectors[{k1*p2,k1*p3},PR[p3+k1+k2,1,n1]*PR[p1+p2-p3-k2,1,n2]*PR[p1-p3-k1-k2,0,n3]*PR[k1,0,n4]*PR[k2,0,n5],{k1,k2},invariants][-4,0]

(* IdSolver OK *)

n1=1;n2=1;n3=1;n4=1;n5=1;
s=-11;t=-33;
invariants={p1*p2->1/2*s-1, p1*p3->-1/2*t+1,p1*p4->1/2*s+1/2*t-1,p2*p3->1/2*s+1/2*t-1,p2*p4->-1/2*t+1,p3*p4->1/2*s-1,p1^2->1,p2^2->1,p3^2->1,p4^2->1};
DoSectors[{k2*p3,k1*p4},PR[p3+k1+k2,1,n1]*PR[p1+p2-p3-k2,1,n2]*PR[p1-p3-k1-k2,0,n3]*PR[k1,0,n4]*PR[k2,0,n5],{k1,k2},invariants][-4,1]

n1=1;n2=1;n3=1;n4=1;n5=1;n6=1;n7=1;
s=-11;t=-33;
invariants={p1*p2->1/2*s,p3*p4->1/2*s,p1*p4->1/2*t,p2*p3->1/2*t,p1*p3->-1/2*s-1/2*t,p2*p4->-1/2*s-1/2*t,p1^2->0,p2^2->0,p3^2->0,p4^2->0};
DoSectors[{k1*p3,k1*p3},PR[k1+k2,0,n1]*PR[k2,0,n2]*PR[k1+k2-p1-p2,0,n3]*PR[k2-p1-p2,0,n4]*PR[k1+k2-p2,0,n5]*PR[k1,0,n6]*PR[k2+p3,0,n7],{k1,k2},invariants][-5,-4]

((4.564724999994673`*^-6)/(ep^5))-((0.28037063948376956`)/(ep^4))+((1.9323665204716483`)/(ep^3))-((1.5749390249989426`*^11)/(ep^2))+((2.2209491564276855`)/ep)

Tensor rank 3

n1=1;n2=1;n3=1;n4=1;n5=1;
s=-11;t=-33;
invariants={p1*p2->1/2*s-1, p1*p3->-1/2*t+1,p1*p4->1/2*s+1/2*t-1,p2*p3->1/2*s+1/2*t-1,p2*p4->-1/2*t+1,p3*p4->1/2*s-1,p1^2->1,p2^2->1,p3^2->1,p4^2->1};
DoSectors[{k1*p2,k1*p2,k1*p2},PR[p3+k1+k2,1,n1]*PR[p1+p2-p3-k2,1,n2]*PR[p1-p3-k1-k2,0,n3]*PR[k1,0,n4]*PR[k2,0,n5],{k1,k2},invariants][-4,1]

n1=1;n2=1;n3=1;n4=1;n5=1;
s=-11;t=-33;
invariants={p1*p2->1/2*s-1,p1*p3->-1/2*t+1,p1*p4->1/2*s+1/2*t-1,p2*p3->1/2*s+1/2*t-1,p2*p4->-1/2*t+1,p3*p4->1/2*s-1,p1^2->1,p2^2->1,p3^2->1,p4^2->1};
DoSectors[{k1*p2,k1*p3,k2*p2},PR[p3+k1+k2,1,n1]*PR[p1+p2-p3-k2,1,n2]*PR[p1-p3-k1-k2,0,n3]*PR[k1,0,n4]*PR[k2,0,n5],{k1,k2},invariants][-4,0]

(*((706.9648437499995`)/(ep^2))  ??? *)

Four loop

Tadpoles

Scalar

n1=n2=n3=n4=n5=n6=1;
m=1;
DoSectors[{1},PR[k1,m,n1]PR[k1+k2,0,n2]PR[k2,0,n3]PR[k3,0,n4]PR[k4,0,n5]PR[k1+k3+k4,m,n6],{k4,k3,k2,k1},{}][-4,-2]

(* AMBRE & hep-ph/0606232 OK *)

n1=n2=n3=n4=n5=n6=n7=1;
m=1;
DoSectors[{1},PR[k1,0,n1]PR[k1+k4,m,n2]PR[k1+k2+k4,0,n3]PR[k3,0,n4]PR[-k2-k3-k4,0,n5]PR[k4,0,n6]PR[k2,0,n7],{k3,k2,k4,k1},{}][-4,-3]//AbsoluteTiming

(* AMBRE & hep-ph/0606232 OK *)

n1=n2=n3=n4=n5=n6=n7=n8=1;
m=1;
DoSectors[{1},PR[k1,0,n1]PR[k2+k4,m,n2]PR[k2,m,n3]PR[k2-k1,m,n4]PR[k3,0,n5]PR[k2-k1+k3,0,n6]PR[k4,0,n7]PR[k2-k1+k4,0,n8],{k4,k3,k1,k2},{},SetStrategy->X][-4,0]

(* AMBRE & hep-ph/0606232  *)

40.95229441398749`+((1.803135027550452`)/(eps^2))-((1.9648722750057601`)/eps)-88.7042472662356` eps

n1=n2=n3=n4=n5=1;
m=1;
DoSectors[{1},PR[k1,m,n1]PR[k2+k1,m,n2]PR[k2+k3+k4,m,n3]PR[k4,0,n4]PR[k3,0,n5],{k3,k4,k2,k1},{}][-4,-3]

(* AMBRE & hep-ph/0606232  *)

22.955621881705927`+((0.25`)/(eps^4))+(1/(eps^3))+((2.843300366757447`)/(eps^2))+((5.781543610421034`)/eps)+80.89550616785343` eps