<< MB.m

<< AMBRE.m

Fullintegral[{1}, {PR[k1, 0, n5] PR[k1 - k2, 0, n2] 
            PR[k1 + p1 + p2, 0, n8] PR[k1 - p4 - p5, 0, n7] 
            PR[k1 - p5, 0, n6] PR[k2, 0, n1] PR[k2 + p1, 0, n4] 
            PR[k2 + p1 + p2, 0, n3]}, {k2, k1}];

invariants = {p1^2 -> 0, p2^2 -> 0, p3^2 -> 0, 
          p4^2 -> 0, p5^2 -> 0, p1*p2 -> s12/2, 
          p2*p3 -> s23/2, p3*p4 -> s34/2, p4*p5 -> s45/2, 
          p1*p5 -> s15/2, p1*p3 -> (-s12 - s23 + s45)/2, 
          p1*p4 -> (-s15 + s23 - s45)/2, 
          p2*p4 -> (s15 - s23 - s34)/2, 
          p2*p5 -> (-s12 - s15 + s34)/2, 
          p3*p5 -> (s12 - s34 - s45)/2};

IntPart[1]

SubLoop[integral]

IntPart[2]

repr = SubLoop[integral];

BarnesLemma[repr, 1]

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

rules = MBoptimizedRules[repr, eps -> 0, {}, {eps}]

integrals = 
        MBcontinue[repr, eps -> 0, rules, 
          Verbose -> False];

ser = 
        MBexpand[{integrals}, 
          Exp[2 eps EulerGamma], {eps, 0, -1}];

AbsoluteTiming[
      MBintegrate[
        ser, {s12 -> -2, s15 -> -1/2, s23 -> -4, 
          s34 -> -5, s45 -> -6}, 
        Verbose -> False]]

Fullintegral[{1}, {PR[k1, 0, n5] PR[k1 - k2, 0, n2] 
            PR[k1 + p1 + p2, 0, n8] PR[k1 - p4 - p5, 0, n7] 
            PR[k1 - p5, 0, n6] PR[k2, 0, n1] PR[k2 + p1, 0, n4] 
            PR[k2 + p1 + p2, 0, n3]}, {k1, k2}];

invariants = {p1^2 -> 0, p2^2 -> 0, p3^2 -> 0, 
          p4^2 -> 0, p5^2 -> 0, p1*p2 -> s12/2, 
          p2*p3 -> s23/2, p3*p4 -> s34/2, p4*p5 -> s45/2, 
          p1*p5 -> s15/2, p1*p3 -> (-s12 - s23 + s45)/2, 
          p1*p4 -> (-s15 + s23 - s45)/2, 
          p2*p4 -> (s15 - s23 - s34)/2, 
          p2*p5 -> (-s12 - s15 + s34)/2, 
          p3*p5 -> (s12 - s34 - s45)/2};

IntPart[1]

SubLoop[integral]

IntPart[2]

repr = SubLoop[integral];

BarnesLemma[repr, 1]

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

rules = MBoptimizedRules[repr, eps -> 0, {}, {eps}]

integrals = 
        MBcontinue[repr, eps -> 0, rules, 
          Verbose -> False];

ser = 
        MBexpand[{integrals}, 
          Exp[2 eps EulerGamma], {eps, 0, -1}];

MBintegrate[
        ser, {s12 -> -2, s15 -> -1/2, s23 -> -4, 
          s34 -> -5, s45 -> -6}, Verbose -> False] // 
      AbsoluteTiming

\({30.792086`7.9399841045363075\ Second, {0.159375`\/eps\^4 + 
          0.3193080330282121`\/eps\^3 + 0.42274543880473414`\/eps\^2 + 
          0.264480823446921`\/eps, {0.00006874560279338051`\/eps, 
          0}}}\)

Fullintegral[{1}, {PR[k1, 0, n1] PR[k1 + p1, 0, n2] 
            PR[k1 + p1 + p2, 0, n3] PR[k2, 0, n4] PR[k1 - k2, 0, n5] 
            PR[k2 + p1 + p2, 0, n6] PR[k2 - p3 - p4, 0, n7] 
            PR[k2 - p3, 0, n8]}, {k2, k1}];

invariants = {p1^2 -> 0, p2^2 -> 0, p3^2 -> 0, 
          p4^2 -> 0, p5^2 -> 0, p1*p2 -> s12/2, 
          p2*p3 -> s23/2, p3*p4 -> s34/2, p4*p5 -> s45/2, 
          p1*p5 -> s15/2, p1*p3 -> (-s12 - s23 + s45)/2, 
          p1*p4 -> (-s15 + s23 - s45)/2, 
          p2*p4 -> (s15 - s23 - s34)/2, 
          p2*p5 -> (-s12 - s15 + s34)/2, 
          p3*p5 -> (s12 - s34 - s45)/2};

IntPart[1]

SubLoop[integral]

IntPart[2]

repr = SubLoop[integral];

BarnesLemma[repr, 1]

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

rules = MBoptimizedRules[repr, eps -> 0, {}, {eps}]

integrals = 
        MBcontinue[repr, eps -> 0, rules, 
          Verbose -> False];

ser = 
        MBexpand[{integrals}, 
          Exp[2 eps EulerGamma], {eps, 0, -3}];

MBintegrate[
        ser, {s12 -> -2, s15 -> -1/2, s23 -> -4, 
          s34 -> -5, s45 -> -6}, Verbose -> False] // 
      AbsoluteTiming