/** * returns the modified spherical Bessel function of the second kind needed * for bound states. \param l = order of the function (orbital angular momentum) \param rho = independent variable (rho = k * r) */ double sphericalB::k(int l, double rho) { switch (l) { case 0: return k0(rho); case 1: return k1(rho); case 2: return k2(rho); case 3: return k3(rho); case 4: return k4(rho); case 5: return k5(rho); case 6: return k6(rho); case 7: return k7(rho); default: cout << "no l>6 programed in sphericalB" << endl; return 0.; } }
void RK4_step( // replaces x(t) by x(t + dt) Matrix<double,1>& x, // solution vector double dt, // fixed time step Matrix<double,1> flow(Matrix<double,1>&)) // derivative vector { int n = x.size(); Matrix<double,1> f(n), k1(n), k2(n), k3(n), k4(n), x_temp(n); f = flow(x); for (int i = 0; i < n; i++) { k1[i] = dt * f[i]; x_temp[i] = x[i] + k1[i] / 2; } f = flow(x_temp); for (int i = 0; i < n; i++) { k2[i] = dt * f[i]; x_temp[i] = x[i] + k2[i] / 2; } f = flow(x_temp); for (int i = 0; i < n; i++) { k3[i] = dt * f[i]; x_temp[i] = x[i] + k3[i]; } f = flow(x_temp); for (int i = 0; i < n; i++) k4[i] = dt * f[i]; for (int i = 0; i < n; i++) x[i] += (k1[i] + 2 * k2[i] + 2 * k3[i] + k4[i]) / 6; }
TextStream& SVGFEComposite::externalRepresentation(TextStream& ts) const { ts << "[type=COMPOSITE] "; SVGFilterEffect::externalRepresentation(ts); if (!in2().isEmpty()) ts << " [in2=\"" << in2() << "\"]"; ts << " [k1=" << k1() << " k2=" << k2() << " k3=" << k3() << " k4=" << k4() << "]"; return ts; }
FloatRect FEComposite::determineAbsolutePaintRect(const FloatRect& originalRequestedRect) { FloatRect requestedRect = originalRequestedRect; if (clipsToBounds()) requestedRect.intersect(maxEffectRect()); // We may be called multiple times if result is used more than once. Return // quickly if nothing new is required. if (absolutePaintRect().contains(enclosingIntRect(requestedRect))) return requestedRect; // No mapPaintRect required for FEComposite. FloatRect input1Rect = inputEffect(1)->determineAbsolutePaintRect(requestedRect); FloatRect affectedRect; switch (m_type) { case FECOMPOSITE_OPERATOR_IN: // 'in' has output only in the intersection of both inputs. affectedRect = intersection(input1Rect, inputEffect(0)->determineAbsolutePaintRect(input1Rect)); break; case FECOMPOSITE_OPERATOR_ATOP: // 'atop' has output only in the extents of the second input. // Make sure first input knows where it needs to produce output. inputEffect(0)->determineAbsolutePaintRect(input1Rect); affectedRect = input1Rect; break; case FECOMPOSITE_OPERATOR_ARITHMETIC: if (k4() > 0) { // Make sure first input knows where it needs to produce output. inputEffect(0)->determineAbsolutePaintRect(requestedRect); // Arithmetic with non-zero k4 may influnce the complete filter primitive // region. So we can't optimize the paint region here. affectedRect = requestedRect; break; } if (k2() <= 0) { // Input 0 does not appear where input 1 is not present. FloatRect input0Rect = inputEffect(0)->determineAbsolutePaintRect(input1Rect); if (k3() > 0) { affectedRect = input1Rect; } else { // Just k1 is positive. Use intersection. affectedRect = intersection(input1Rect, input0Rect); } break; } // else fall through to use union default: // Take the union of both input effects. affectedRect = unionRect(input1Rect, inputEffect(0)->determineAbsolutePaintRect(requestedRect)); break; } affectedRect.intersect(requestedRect); addAbsolutePaintRect(affectedRect); return affectedRect; }
PassRefPtr<FilterEffect> SVGFECompositeElement::build(SVGFilterBuilder* filterBuilder) { FilterEffect* input1 = filterBuilder->getEffectById(in1()); FilterEffect* input2 = filterBuilder->getEffectById(in2()); if (!input1 || !input2) return 0; return FEComposite::create(input1, input2, static_cast<CompositeOperationType>(_operator()), k1(), k2(), k3(), k4()); }
int main() { try { symbol k("k"),q("q"),p("p"),p1("p1"),p2("p2"),p3("p3"),ms("ms"),l("l"),s("s"),m1s("m1s"),m2s("m2s"),m3s("m3s"); symbol l1("l1"),l2("l2"),l3("l3"),l4("l4"),t("t"),p4("p4"),p5("p5"),p6("p6"),tp("tp"),v1("v1"),v2("v2"),l5("l5"); symbol k1("k1"),k2("k2"),k3("k3"),k4("k4"),k5("k5"),ms1("ms1"),ms2("ms2"),ms3("ms3"),ms4("ms4"); symbol s12("s12"),s23("s23"),s34("s34"),s45("s45"),s51("s51"),s13("s13"),s15("s15"),s56("s56"),s16("s16"),s123("s123"),s234("s234"),s345("s345"); lst inv_l; inv_l.append(p1*p1 == 0); inv_l.append( p2*p2 == 0);inv_l.append( p3*p3 == 0);inv_l.append( p4*p4 == 0);inv_l.append( p5*p5 == 0);inv_l.append( p6*p6 == 0); inv_l.append(p1* p2 == s12/2);inv_l.append( p2* p3 == s23/2);inv_l.append( p3* p4 == s34/2);inv_l.append( p4* p5 == s45/2); inv_l.append(p5* p6 == s56/2);inv_l.append( p1* p6 == s16/2);inv_l.append( p1* p3 == (-s12 + s123 - s23)/2); inv_l.append(p2* p4 == (-s23 + s234 - s34)/2); inv_l.append( p3* p5 == (-s34 + s345 - s45)/2); inv_l.append(p1* p4 == (-s123 + s23 - s234 + s56)/2); inv_l.append(p1* p5 == (-s16 + s234 - s56)/2); inv_l.append( p2* p5 == (s16 - s234 + s34 - s345)/2); inv_l.append( p2* p6 == (-s12 - s16 + s345)/2); inv_l.append( p3* p6 == (s12 - s123 - s345 + s45)/2); inv_l.append( p4* p6 == (s123 - s45 - s56)/2); RoMB_loop_by_loop hexag(lst(k1), lst(-pow(p1 + k1,2),-pow(p1 + p2 + k1,2), -pow(p1 + p2 + p3 + k1,2), -pow(p1 + p2 + p3 + p4 + k1,2), -pow(p1+p2+p3+p4+p5+k1,2),-pow(k1,2)), inv_l, lst(1,1,1,1,1,1),true); hexag.integrate_map(lst(s12 == -1, s23 == -2, s34 == -3, s45 == -4, s56 == -5, s16 == -6, s123 == -7, s234 == -8, s345 == -9)); /* FRESULT for parameters: {s12==-1,s23==-2,s34==-3,s45==-4,s56==-5,s16==-6,s123==-7,s234==-8,s345==-9} FRESULT anl : = -0.1955084880526298663-1/240*log(8)*log(6)+947/60480*log(2)^2-1/480*log(6)*log(4)+1/1080*log(3)*log(7)+131/7560*log(9)*log(2)+19/1260*log(9)^2-1/560*log(8)*log(4)+523/60480*log(3)^2-1/1080*log(7)*log(5)+41/4320*log(3)*log(5)-1/48*log(8)*log(5)-1/1080*log(7)*log(4)+22/945*log(6)*log(7)+19/3780*log(3)*log(4)+493/30240*Pi^2+43/1008*eps^(-2)+49/8640*log(5)^2-641/30240*log(2)*log(6)+1/1080*log(9)*log(5)-22/945*log(2)*log(7)+271/60480*log(4)^2-3/112*log(8)*log(3)-19/3780*log(9)*log(4)+1/1080*log(4)*log(5)-61/2520*log(9)*log(7)+61/5040*log(7)^2+1/168*log(3)*log(2)+1/168*log(8)*log(9)+13/3360*log(2)*log(4)-1/30240*(-1132.7960047725738361+576*log(8)-163*log(3)+264*log(9)+533*log(2)-479*log(6)-444*log(7)+271*log(4)-287*log(5))*eps^(-1)+47/1680*log(8)^2-17/1680*log(8)*log(2)+767/60480*log(6)^2-22/945*log(9)*log(6)-13/1890*log(3)*log(9) FRESULT num: = 1.9907333428263254975E-4+(0.032177795803854872908)*eps^(-1)+(0.04265873015873015873)*eps^(-2) eps^-2 term: 43/1008 +/- 0 eps^-1 term: 0.03746018534300839405-2/105*log(8)+163/30240*log(3)-11/1260*log(9)-533/30240*log(2)+479/30240*log(6)+37/2520*log(7)-271/30240*log(4)+41/4320*log(5) +/- 9.022403780167233619E-6 eps^0 term: -0.1955084880526298663-1/240*log(8)*log(6)+947/60480*log(2)^2-1/480*log(6)*log(4)+1/1080*log(3)*log(7)+131/7560*log(9)*log(2)+19/1260*log(9)^2-1/560*log(8)*log(4)+523/60480*log(3)^2-1/1080*log(7)*log(5)+41/4320*log(3)*log(5)-1/48*log(8)*log(5)-1/1080*log(7)*log(4)+22/945*log(6)*log(7)+19/3780*log(3)*log(4)+493/30240*Pi^2+49/8640*log(5)^2-641/30240*log(2)*log(6)+1/1080*log(9)*log(5)-22/945*log(2)*log(7)+271/60480*log(4)^2-3/112*log(8)*log(3)-19/3780*log(9)*log(4)+1/1080*log(4)*log(5)-61/2520*log(9)*log(7)+61/5040*log(7)^2+1/168*log(3)*log(2)+1/168*log(8)*log(9)+13/3360*log(2)*log(4)+47/1680*log(8)^2-17/1680*log(8)*log(2)+767/60480*log(6)^2-22/945*log(9)*log(6)-13/1890*log(3)*log(9) +/- 1.04620404922048185285E-4 */ } catch(std::exception &p) { std::cerr<<"******************************************************************"<<endl; std::cerr<<" >>>ERROR: "<<p.what()<<endl; std::cerr<<"******************************************************************"<<endl; return 1; } return 0; }
bool SVGFECompositeElement::build(SVGResourceFilter* filterResource) { FilterEffect* input1 = filterResource->builder()->getEffectById(in1()); FilterEffect* input2 = filterResource->builder()->getEffectById(in2()); if(!input1 || !input2) return false; RefPtr<FilterEffect> effect = FEComposite::create(input1, input2, static_cast<CompositeOperationType>(_operator()), k1(), k2(), k3(), k4()); filterResource->addFilterEffect(this, effect.release()); return true; }
bool SVGFECompositeElement::build(FilterBuilder* builder) { FilterEffect* input1 = builder->getEffectById(in1()); FilterEffect* input2 = builder->getEffectById(in2()); if(!input1 || !input2) return false; RefPtr<FilterEffect> addedEffect = FEComposite::create(input1, input2, static_cast<CompositeOperationType> (_operator()), k1(), k2(), k3(), k4()); builder->add(result(), addedEffect.release()); return true; }
void RK4::integrate(std::valarray<double> &X, std::valarray<double> &V, double dt, SolarSystem mysystem, double G, double eps) { std::valarray<double> k1(1,6*mysystem.numberOfBodies()); std::valarray<double> k2(1,6*mysystem.numberOfBodies()); std::valarray<double> k3(1,6*mysystem.numberOfBodies()); std::valarray<double> k4(1,6*mysystem.numberOfBodies()); // RK4 integration using vector X from solarysystem class. k1 = mysystem.calculateRK4(X, V, G, eps) * dt; k2 = mysystem.calculateRK4(X + 0.5 * k1, V, G, eps) * dt; k3 = mysystem.calculateRK4(X + 0.5 * k2, V, G, eps) * dt; k4 = mysystem.calculateRK4(X + k3, V, G, eps) * dt; X += (1.0/6) * (k1 + 2 * (k2 + k3) + k4); }
void DynamicalSystem::integrateStepRungeKutta(double dt, const Ref<const VectorXd> x, Ref<VectorXd> x_updated, Ref<VectorXd> xd_updated) const { // 4th order Runge-Kutta for a 1st order system // http://en.wikipedia.org/wiki/Runge-Kutta_method#The_Runge.E2.80.93Kutta_method int l = x.size(); VectorXd k1(l), k2(l), k3(l), k4(l); differentialEquation(x,k1); VectorXd input_k2 = x + dt*0.5*k1; differentialEquation(input_k2,k2); VectorXd input_k3 = x + dt*0.5*k2; differentialEquation(input_k3,k3); VectorXd input_k4 = x + dt*k3; differentialEquation(input_k4,k4); x_updated = x + dt*(k1 + 2.0*(k2+k3) + k4)/6.0; differentialEquation(x_updated,xd_updated); }
void ctBdG::RK_Propagator(int i, int eta){ VectorXcd wvVec(4), k1(4), k2(4), k3(4), k4(4); double normwv; wvVec(0) = _bdg_u(i,eta); wvVec(1) = _bdg_a(i,eta); wvVec(2) = _bdg_b(i,eta); wvVec(3) = _bdg_v(i,eta); k1 = -myI * (_bdg * wvVec); k2 = -myI * (_bdg * (wvVec+_dt*k1*0.5)); k3 = -myI * (_bdg * (wvVec+_dt*k2*0.5)); k4 = -myI * (_bdg * (wvVec+_dt*k3)); wvVec += _dt*(k1+2.0*k2+2.0*k3+k4)/6.0; normwv = wvVec.norm(); wvVec /= normwv; // cout << normwv << endl; _bdg_u(i,eta) = wvVec(0); _bdg_a(i,eta) = wvVec(1); _bdg_b(i,eta) = wvVec(2); _bdg_v(i,eta) = wvVec(3); }
void rk (ODEFunc ode, float *xn, float *xn1, int dim, float time, float tdelt, float *scratch) { float *kv1, *kv2, *kv3, *kv4, *a, *s; kv1 = &scratch[dim * 0]; kv2 = &scratch[dim * 1]; kv3 = &scratch[dim * 2]; kv4 = &scratch[dim * 3]; a = &scratch[dim * 4]; s = &scratch[dim * 5]; k1 (ode, xn, kv1, time, tdelt); k2 (ode, xn, kv2, kv1, time, tdelt, dim, s); k3 (ode, xn, kv3, kv2, time, tdelt, dim, s); k4 (ode, xn, kv4, kv3, time, tdelt, dim, s); vector_scale (kv2, 2, kv2, dim); vector_scale (kv3, 2, kv3, dim); vector_add (kv1, kv2, a, dim); vector_add (a, kv3, a, dim); vector_add (a, kv4, a, dim); vector_scale (a, tdelt / 6.0, a, dim); vector_add (xn, a, xn1, dim); }
int main() { try { symbol k("k"),q("q"),p("p"),p1("p1"),p2("p2"),p3("p3"),ms("ms"),l("l"),s("s"),m1s("m1s"),m2s("m2s"),m3s("m3s"); symbol l1("l1"),l2("l2"),l3("l3"),l4("l4"),t("t"),p4("p4"),p5("p5"),tp("tp"),v1("v1"),v2("v2"),l5("l5"); symbol k1("k1"),k2("k2"),k3("k3"),k4("k4"),k5("k5"),ms1("ms1"),ms2("ms2"),ms3("ms3"),ms4("ms4"); // oneloop box // UFXmap l45 = UF(lst(k),lst(pow(k,2),pow(k+p1,2),pow(k+p1+p2,2),pow(k+p1+p2+p3,2)),lst(pow(p1,2)==0,pow(p2,2)==0)); // MBintegral root_int(l45,lst(1,1,1,1),1); //two loop box bubble // UFXmap l45 = UF(lst(k,l),lst(pow(k,2),pow(k+p1,2),pow(k+p1+p2,2),pow(l+p1+p2,2),pow(l+p1+p2+p3,2),pow(l,2),pow(k-l,2)),lst(pow(p1,2)==0,pow(p2,2)==0,pow(p3,2)==0)); //MBintegral root_int(l45,lst(1,1,1,1,1,1,1),2); // B0 // UFXmap l45 = UF(lst(k),lst(ms-pow(k,2),ms-pow(-k,2)),lst(ms==1)); // MBintegral root_int(l45,lst(1,1),1); // 2 loop sunrise //UFXmap l45 = UF(lst(k,q),lst(ms-pow(k,2),ms-pow(-q-k,2),ms-pow(q,2)),lst(ms==1)); //MBintegral root_int(l45,lst(1,1,1),2); //RoMB_planar box2loop(lst(k,l),lst(pow(k,2),pow(k+p1,2),pow(k+p1+p2,2),pow(l+p1+p2,2),pow(l+p1+p2+p3,2),pow(l,2),pow(k-l,2)),lst(pow(p1,2)==0,pow(p2,2)==0,pow(p3,2)==0),lst(1,1,1,1,1,1,1),2); // RoMB_planar box1loop(lst(k),lst(pow(k,2),pow(k+p1,2)-ms,pow(k+p1+p2,2),pow(k+p1+p2+p3,2)),lst(pow(p1,2)==0,pow(p2,2)==0,pow(p3,2)==0,p1==0,p2==0,p3==0,ms==1),lst(1,1,1,1),1); // RoMB_planar B0_1loop(lst(k),lst(pow(k,2)-ms,pow(p+k,2)-ms),lst(ms==0,pow(p,2)==1),lst(1,1),1); // RoMB_planar C0_1loop(lst(k),lst(pow(k,2)-ms,pow(p1+k,2)-ms,pow(p1+p2+k,2)),lst(ms==1,pow(p1,2)==0,pow(p2,2)==0,p1*p2==50),lst(1,1,1),1); //cout<<" new point "<<endl<<root_int.new_point()<<endl; // cout<<" saved point "<<endl<<root_int.get_point()<<endl; // MBcontinue(root_int); //cout<<MB_lst(l45,lst(1,1,1,1),1).expand()<<endl; // RoMB_loop_by_loop box2loop(lst(k,l),lst(pow(k,2),pow(k+p1,2),pow(k+p1+p2,2),pow(l+p1+p2,2),pow(l+p1+p2+p3,2),pow(l,2),pow(k-l,2)),lst(pow(p1,2)==0,pow(p2,2)==0,pow(p3,2)==0),lst(1,1,1,1,1,1,1)); // RoMB_loop_by_loop t2(lst(k,l), lst(pow(k,2),pow(p+k,2),pow(p+k+l,2),pow(l,2),pow(k+l,2)),lst(pow(p,2)==1),lst(1,1,1,1,1)); // works!!! // RoMB_loop_by_loop sunset(lst(k,l), lst(pow(k,2)-1,pow(p-k-l,2)-4,pow(l,2)-5),lst(pow(p,2)==s),lst(1,1,1)); // RoMB_loop_by_loop sunset(lst(k,l), lst(pow(k,2)-m1s,pow(-k-l,2)-m2s,pow(l,2)-m3s),lst(pow(p,2)==s),lst(1,1,1)); // sunset.integrate(lst(m1s==1,m2s==1,m3s==1,s==0),0); // bubble sunset 2=loop // RoMB_loop_by_loop sunset_bub(lst(k,l), lst(-pow(k,2)+ms,-pow(-k-l,2)+ms,-pow(l,2)+ms),lst(pow(p,2)==0),lst(1,1,1)); // sunset_bub.integrate_map(lst(ms==1,m2s==1,m3s==1,s==0),1); // bubble sunset 3=loop //#define TOPO 1 //#if TOPO==1 /****************************************************************** * FRESULT for parameters: {ms==1,m2s==1,m3s==1,s==0} * * FRESULT anl : = 21.308685443306456902+23/3*eps^(-2)+2*eps^(-3)+35/2*eps^(-1) * FRESULT num: = 21.308685443306456902+(7.6666666666666666665)*eps^(-2)+(2.0)*eps^(-3)+(17.5)*eps^(-1) * eps^-3 term: 2 +/- 0 * eps^-2 term: 23/3 +/- 0 * eps^-1 term: 35/2 +/- 0 * eps^0 term: 21.308685443306456902 +/- 0.01814768000077260732 ***************************************************************/ // RoMB_loop_by_loop sunset_bub(lst(p,k,l), lst(-pow(p,2)+ms,-pow(k,2)+ms,-pow(l,2)+ms,-pow(-p-k-l,2)+ms),lst(pow(l3,2)==s),lst(1,1,1,1)); // sunset_bub.integrate_map(lst(ms==1,m2s==1,m3s==1,s==0),1); //#elif TOPO==2 // RoMB_loop_by_loop sunset_bub_d(lst(l1,l2,l3), lst(-pow(l1,2)+ms,-pow(l2,2)+ms,-pow(l3,2)+ms,-pow(l1+l2,2)+ms,-pow(l1+l2+l3,2)+ms),lst(pow(p,2)==s),lst(1,1,1,1,1)); // sunset_bub_d.integrate_map(lst(ms==1,m2s==1,m3s==1,s==0),1); //#elif TOPO==3 // RoMB_loop_by_loop sunset_bub_e(lst(l1,l2,l3), lst(-pow(l1,2)+ms,-pow(l2,2)+ms,-pow(l3,2)+ms,-pow(l1-l2,2)+ms,-pow(l2-l3,2)+ms,-pow(l3-l1,2)+ms),lst(pow(p,2)==s),lst(1,1,1,1,1,1)); // sunset_bub_e.integrate_map(lst(ms==1,m2s==1,m3s==1,s==0),1); //#endif //bubble 4-loop // RoMB_loop_by_loop sunset_bub(lst(k,l1,l2,l3), lst(-pow(k,2)+ms,-pow(l2,2)+ms,-pow(l1,2)+ms,-pow(l3,2)+ms,-pow(k+l1+l2+l3,2)+ms),lst(pow(p,2)==s),lst(1,1,1,1,1)); // sunset_bub.integrate(lst(ms==1,m2s==1,m3s==1,s==0),0); #define TOPO 5 #if TOPO==1 //bubble 5-loop /* FRESULT for parameters: {ms==1,m2s==1,m3s==1,s==0} FRESULT anl : = 274.5475357301444122+1247/24*eps^(-3)+6/5*Pi^4+(125.67152533053854918)*eps^(-2)+3*eps^(-5)+33/2*eps^(-4)+(259.98755698571087874)*eps^(-1)-110/3*zeta(3) FRESULT num: = 347.3630251884288798+(51.958333333333333332)*eps^(-3)+(125.67152533053854918)*eps^(-2)+(3.0)*eps^(-5)+(16.5)*eps^(-4)+(259.98755698571087874)*eps^(-1) eps^-5 term: 3 +/- 0 eps^-4 term: 33/2 +/- 0 eps^-3 term: 1247/24 +/- 0 eps^-2 term: 125.67152533053854918 +/- 5.2760713655226570643E-5 eps^-1 term: 259.98755698571087874 +/- 9.888628922902401464E-6 eps^0 term: 274.5475357301444122+6/5*Pi^4-110/3*zeta(3) +/- 0.043609817405085687474 */ RoMB_loop_by_loop sunset_bub5(lst(l3,k,l1,l2,l4), lst(-pow(l3,2)+ms,-pow(k,2)+ms,-pow(l1,2)+ms,-pow(l2,2)+ms,-pow(l4,2)+ms,-pow(k+l1+l2+l3+l4,2)+ms),lst(pow(p,2)==s),lst(1,1,1,1,1,1)); sunset_bub5.integrate_map(lst(ms==1,m2s==1,m3s==1,s==0),1); #elif TOPO==2 RoMB_loop_by_loop sunset_bubC2(lst(l1,l2,l3,l4,l5), lst(-pow(l3,2)+ms,-pow(l5,2)+ms,-pow(l1,2)+ms,-pow(l2,2)+ms,-pow(l4,2)+ms,-pow(l5+l1+l2,2)+ms,-pow(l5+l3+l4,2)+ms),lst(pow(p,2)==s),lst(1,1,1,1,1,1,1)); sunset_bubC2.integrate_map(lst(ms==1,m2s==1,m3s==1,s==0),0); // RoMB_loop_by_loop sunset_bubC2(lst(l1,l2,l3,l4,l5), lst(-pow(l3,2)+ms,-pow(l5,2)+ms,-pow(l1,2)+ms,-pow(l2,2)+ms,-pow(l4,2)+ms,-pow(l3+l4+l5,2)+ms,-pow(l1+l2+l5+l3+l4,2)+ms),lst(pow(p,2)==s),lst(1,1,1,1,1,1,1)); // sunset_bubC2.integrate_map(lst(ms==1,m2s==1,m3s==1,s==0),0); // RoMB_loop_by_loop sunset_bubC1(lst(l1,l2,l3,l4,l5), lst(-pow(l3,2)+ms,-pow(l5,2)+ms,-pow(l1,2)+ms,-pow(l2,2)+ms,-pow(l4,2)+ms,-pow(l2+l3+l4+l5,2)+ms,-pow(l1+l2+l5+l3+l4,2)+ms),lst(pow(p,2)==s),lst(1,1,1,1,1,1,1),true); // sunset_bubC1.integrate_map(lst(ms==1,m2s==1,m3s==1,s==0),0); /* MEGA 5-LOOP BUBBLE with 12 propagators */ //RoMB_loop_by_loop l5p12(lst(k5,k2,k1,k4,k3),lst(-pow(k1,2)+ms,-pow(k2,2)+ms,-pow(k3,2)+ms,-pow(k4,2)+ms,-pow(k5,2)+ms, //-pow(k1-k3,2)+ms,-pow(k1-k4,2)+ms,-pow(k3-k2,2)+ms,-pow(k2-k4,2)+ms,-pow(k5+k3-k1,2)+ms,-pow(k5+k3-k2,2)+ms,-pow(k5+k3-k4,2)+ms),lst(pow(p,2)==0),lst(1,1,1,1,1,1,1,1,1,1,1,1)); //l5p12.integrate(lst(ms==0),0); #elif TOPO==3 /* FRESULT for parameters: {ms==1} FRESULT anl : = 1/5400*eps^(-2)*(-1540485.6006392892897+233937*zeta(3)-1505*Pi^4+6656*Pi^2)-1/10*(233.57451266786976057+Pi^2)*eps^(-4)-1/4*eps^(-6)+1/216000*eps^(-1)*(-7.391571256935002719E7+37697940*zeta(3)-40800*zeta(3)*Pi^2-727494*Pi^4+12801600*zeta(5)-1399535*Pi^2)-(3.7800000113486752996)*eps^(-5)+1/1200*(-100893.525326654920406+5280*zeta(3)-349*Pi^2)*eps^(-3) FRESULT num: = -(465.22101564968708165)*eps^(-1)-(0.25)*eps^(-6)-(24.344411706895911919)*eps^(-4)-(3.7800000113486752996)*eps^(-5)-(81.65929734496037395)*eps^(-3)-(248.18307592543818119)*eps^(-2) eps^-6 term: -1/4 +/- 0 eps^-5 term: -3.7800000113486752996 +/- 3.2541102943124789963E-10 eps^-4 term: -23.357451266786976057-1/10*Pi^2 +/- 2.7206664064692618508E-5 eps^-3 term: -84.07793777221243367+22/5*zeta(3)-349/1200*Pi^2 +/- 1.5019954980075151021E-4 eps^-2 term: -285.2751112294980166+25993/600*zeta(3)-301/1080*Pi^4+832/675*Pi^2 +/- 0.00206337770109377918 eps^-1 term: -342.20237300625012586+69811/400*zeta(3)-17/90*zeta(3)*Pi^2-121249/36000*Pi^4+889/15*zeta(5)-279907/43200*Pi^2 +/- 6.187359464224749039 */ RoMB_loop_by_loop l5c1(lst(k2,k5,k3,k4,k1),lst(-pow(k3,2)+ms,-pow(k2,2)+ms,-pow(k1,2)+ms,-pow(k4,2)+ms,-pow(k5,2)+ms, -pow(k1+k3+k4,2)+ms,-pow(k2+k5-k3-k4,2)+ms),lst(pow(p,2)==0),lst(1,1,1,1,1,1,1)); l5c1.integrate_map(lst(ms==1),0); #elif TOPO==4 // point in 2 RoMB_loop_by_loop l5c1(lst(k2,k5,k3,k4,k1),lst(-pow(k3,2)+ms,-pow(k2,2)+ms,-pow(k1,2)+ms,-pow(k4,2)+ms,-pow(k5,2)+ms, -pow(k1+k3+k4,2)+ms,-pow(k2+k5-k3-k4,2)+ms),lst(pow(p,2)==0),lst(1,2,1,1,1,1,1)); l5c1.integrate_map(lst(ms==1),0); #elif TOPO==5 // point in 1 RoMB_loop_by_loop l5c1(lst(k2,k5,k3,k4,k1),lst(-pow(k3,2)+ms,-pow(k2,2)+ms,-pow(k1,2)+ms,-pow(k4,2)+ms,-pow(k5,2)+ms, -pow(k1+k3+k4,2)+ms,-pow(k2+k5-k3-k4,2)+ms),lst(pow(p,2)==0),lst(2,1,1,1,1,1,1)); l5c1.integrate_map(lst(ms==1),0); #endif // RoMB_loop_by_loop t2loop(lst(l,k), lst(-pow(k,2)+ms,-pow(p+k,2)+ms,-pow(p+k+l,2)+ms,-pow(k+l,2)+ms,-pow(l,2)+ms),lst(pow(p,2)==s,ms==0),lst(1,1,1,1,1)); //t2loop.integrate_map(lst(s==-1,ms == 0),3); /* RoMB_loop_by_loop bubble_five_loop(lst(k,l1,l2,l3,l4), lst(pow(k,2)-ms,pow(l1,2)-ms,pow(l2,2)-ms,pow(l3,2)-ms,pow(l4,2)-ms,pow(k+l1,2)-ms,pow(k+l1+l2,2)-ms,pow(k+l1+l2+l3,2)-ms,pow(k+l1+l2+l3+l4,2)-ms,pow(k+l1+l2+l3,2)-ms,pow(k+l1+l2,2)-ms,pow(k+l1,2)-ms), lst(ms==1), lst(1,1,1,1,1,1,1,1,1,1,1,1)); */ // works!!! // RoMB_loop_by_loop B0_1loop_lbl(lst(k),lst(pow(k,2)-2-ms,pow(p+k,2)-ms),lst(ms==0,pow(p,2)==1),lst(2,1)); // RoMB_loop_by_loop B0_1loop_lbl(lst(k),lst(pow(k,2)-m1s,pow(p+k,2)-m2s),lst(pow(p,2)==s),lst(1,1)); // B0_1loop_lbl.integrate(lst(s==-1,m1s==1,m2s==1)); //MB works??? // RoMB_loop_by_loop C0_1loop_lbl(lst(k),lst(pow(k,2),pow(k+p1,2)-m1s,pow(k-p2,2)-m2s),lst(ms==1,pow(p1,2)==m1s,pow(p2,2)==m2s,p1*p2==(s-m1s-m2s)/2),lst(1,1,1)); // C0_1loop_lbl.integrate(lst(m1s==1,m2s==1,s==-100)); //MB works??? /* RoMB_loop_by_loop box1loopm0(lst(k),lst(-pow(k,2),-pow(k+p1,2),-pow(k+p1+p2,2),-pow(k+p1+p2+p4,2)), lst(pow(p1,2)==0,pow(p2,2)==0,pow(p4,2)==0, p1*p2==-s/2,// p1*p4==s/2+t/2,// p2*p4==-t/2 // ), lst(1,1,1,1),false); box1loopm0.integrate_map(lst(s==3,t==1)); box1loopm0.integrate(lst(s==5,t==2)); */ //MASIVE BOX LBL /* RoMB_loop_by_loop box1loopm(lst(k),lst(-pow(k,2)+ms,-pow(k+p1,2)+ms,-pow(k+p1+p2,2)+ms,-pow(k+p1+p2+p4,2)+ms), lst(pow(p1,2)==0,pow(p2,2)==0,pow(p4,2)==0, p1*p2==-s/2,// p1*p4==(s/2+t/2),// p2*p4==-t/2 // ), lst(1,1,1,1),false); box1loopm.integrate_map(lst(ms1==1,ms2==1,ms3==1,ms4==1,ms==1,s==30,t==5)); */ //triple box /* RoMB_loop_by_loop tribox1loopm(lst(k1,k2,k3),lst(-pow(k1,2)+ms,-pow(k1+p1,2),-pow(k1+p1+p2,2)+ms, -pow(k1-k2,2),-pow(k2,2)+ms,-pow(k2+p1+p2,2)+ms, -pow(k2-k3,2),-pow(k3,2)+ms,-pow(k3+p1+p2,2)+ms, -pow(k3-p3,2)), lst(pow(p1,2)==ms,pow(p2,2)==ms,pow(p3,2)==ms,pow(p4,2)==ms, p1*p2==s/2-ms,// p1*p3==t/2-ms,// p2*p3==ms-(s+t)/2 // ), lst(1,1,1,1,1,1,1,1,1,1),true); tribox1loopm.integrate_map(lst(ms1==1,ms2==1,ms3==1,ms4==1,ms==1,s==-1/2,t==-3)); */ //double box /* RoMB_loop_by_loop dobox1loopm(lst(k1,k2),lst(-pow(k1,2),-pow(k1+p1,2),-pow(k1+p1+p2,2), -pow(k1-k2,2),-pow(k2,2),-pow(k2+p1+p2,2), -pow(k2-p3,2)), lst(pow(p1,2)==0,pow(p2,2)==0,pow(p3,2)==0,pow(p4,2)==0, p1*p2==s/2,// p1*p3==t/2,// p2*p3==-(s+t)/2 // ), lst(1,1,1,1,1,1,1),true); dobox1loopm.integrate_map(lst(ms1==1,ms2==1,ms3==1,ms4==1,ms==1,s==-1/2,t==-3)); */ /* 4-loop tadpole */ /* RoMB_loop_by_loop tad4(lst(l1, l2, l3, l4),lst(-pow(l1,2)+ ms,-pow(l2,2)+ ms,-pow(l3 ,2)+ ms,-pow(l4,2),-pow(l1+l2+l3+l4,2)),lst(),lst(1,1,1,1,1)); tad4.integrate_map(lst(ms == 1),1); */ /* Pentagon */ /* RoMB_loop_by_loop pent(lst(k1),lst(-pow(p1 + k1,2)+ ms,-pow(p1 + p5 + k1,2), -pow(p1 + p5 + p4 + k1,2)+ ms,-pow(p1 + p5 + p4 + p3 + k1,2)+ ms, -pow(k1,2)), lst( p1*p1 == ms, p2*p2 == ms, p3*p3 == 0, p4*p4 == ms, p5*p5 == ms, p1*p2 == 1/2* (tp - 2* ms), p1*p3 == 1/2* (t - tp - v1), p1*p4 == ms - 1/2* (s + t - v1), p1*p5 == 1/2* (s - 2* ms), p2* p3 == 1/2* v1, p2* p4 == 1/2* (s - 2* ms - v1 - v2), p2* p5 == ms - 1/2* (s + tp - v2), p3* p4 == 1/2* v2, p3* p5 == 1/2* (tp - t - v2), p4* p5 == 1/2* (t - 2* ms)), lst(1,1,1,1,1)); pent.integrate_map(lst(s==-2,t==-3,v2==-4,tp==-5,v1==-6,ms==1)); */ /* RoMB_loop_by_loop pent(lst(k1),lst(-pow(p1 + k1,2)+ ms,-pow(p1 + p5 + k1,2), -pow(p1 + p5 + p4 + k1,2)+ ms,-pow(p1 + p5 + p4 + p3 + k1,2)+ ms, -pow(k1,2)), lst( p1*p1 == ms, p2*p2 == ms, p3*p3 == 0, p4*p4 == ms, p5*p5 == ms, p1*p2 == 1/2* (tp - 2* ms), wild(1)*p1*p3 == wild(1)*1/2* (t - tp - v1), wild(2)*p1*p4 == wild(2)*(ms - 1/2* (s + t - v1)), wild(3)* p1*p5 == wild(3)*1/2* (s - 2* ms), wild(4)*p2* p3 == wild(4)*1/2* v1, wild(5)*p2* p4 == wild(5)*1/2* (s - 2* ms - v1 - v2), wild(6)*p2* p5 ==wild(6)*( ms - 1/2* (s + tp - v2)), wild(7)*p3* p4 == wild(7)*1/2* v2, wild(8)*p3* p5 == wild(8)*1/2* (tp - t - v2), wild()*p4* p5 == wild()*1/2* (t - 2* ms)), lst(1,1,1,1,1)); pent.integrate_map(lst(s==-2,t==-3,v2==-4,tp==-5,v1==-6,ms==1)); */ } catch(std::exception &p) { std::cerr<<"******************************************************************"<<endl; std::cerr<<" >>>ERROR: "<<p.what()<<endl; std::cerr<<"******************************************************************"<<endl; return 1; } return 0; }
void display(void) { glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT); glLoadIdentity(); gluLookAt(r*cos(c*du), h, r*sin(c*du), 0, 0, 0, 0, 3, 0); //head position;eye direction(0.0,0.0,0.0),original point;(0.0,1.0,0.0),head above direction¡£ //cylinder a(1, 15, 0, 90, 0, 0, 5, 0); //r,h,xangle yangle zangle, module position(xx yy zz) //sphere b(3, 100, 100, 0, 0, 0, 0, 2.5, 0); //r,xangle yangle zangle, module position(xx yy zz) //cube c(5, 10, 0, 0, 1, 1, 1); //length xangle yangle zangle, module position(xx yy zz) //rectangularpyramid d(4, 0, 0, 0, 0, 2, 0); //length xangle yangle zangle, module position(xx yy zz) //triangularpyramid f(2, 0, 0, 0, 8, 8, 8);//length xangle yangle zangle, module position(xx yy zz) //f.draw(); sphere sp(3, 100, 100, 0, 0, -2, 0, 8, 0); cylinder cy(3, 5, 0, 90, 0, -3, 9, -10); cube cu(3, 0, 0, 0, 0, 8, 10); triangularpyramid tr(2, 0, 0, 0, 0, -6, 8); rectangularpyramid rec(2, 0, 0, 0, 0, -6, -8); cylinder k1(0.3, 2, 90, 0, 0, 0, 0, 0); cylinder k2(0.3, 2, -90, 0, 0, 0, 0, 0); cylinder k3(0.3, 2, -45, 0, 0, 0, 0, 0); cylinder k4(0.3, 2.5, 45, 0, 0, 0, 0, 0); cylinder u1(0.3, 2, 90, 0, 0, 0, 0, 3); cylinder u2(0.3, 1.5, -90, 0, 0, 0, 0, 3); cylinder u3(0.3, 2, 0, 0, 0, 0, -1.8, 3); cylinder u4(0.3, 2, 90, 0, 0, 0, 0, 5); cylinder u5(0.3, 1.5, -90, 0, 0, 0, 0, 5); cylinder g1(0.3, 2, -90, 0, 0, 0, -0.5, 6.4); cylinder g2(0.3, 1.5, -90, 0, 0, 0, -0.5, 6.4); cylinder g3(0.3, 2, 0, 0, 0, 0, -0.3, 6.4); cylinder g4(0.3, 2, 0, 0, 0, 0, 1.3, 6.4); cylinder g5(0.3, 2, 90, 0, 0, 0, 0, 8.4); cylinder g6(0.3, 1.5, -90, 0, 0, 0, 0, 8.4); cylinder g7(0.3, 2, 0, 0, 0, 0, -1.8, 6.4); cylinder e1(0.3, 1.8, -90, 0, 0, 0, -0.2, 10); cylinder e2(0.3, 1.8, 90, 0, 0, 0, -0.2, 10); cylinder e3(0.3, 2, 0, 0, 0, 0, -0.3, 10); cylinder e4(0.3, 2, 0, 0, 0, 0, 1.3, 10); cylinder e5(0.3, 2, 0, 0, 0, 0, -1.8, 10); cylinder r1(0.3, 1.8, -90, 0, 0, 0, -0.2, 13.5); cylinder r2(0.3, 1.8, 90, 0, 0, 0, -0.2, 13.5); cylinder r3(0.3, 2, 0, 0, 0, 0, -0.3, 13.5); cylinder r4(0.3, 1.2, 0, 0, 0, 0, 1.3, 13.5); cylinder r5(0.3, 1.7, 60, 0, 0, 0, 1.3, 14.5); cylinder r6(0.3, 2.5, 45, 0, 0, 0, 0, 13.5); cylinder c1(0.3, 2, 90, 0, 0, 0, 0, -15); cylinder c2(0.3, 2, -90, 0, 0, 0, 0, -15); cylinder c3(0.3, 3, 0, 0, 0, 0, -1.8, -15); cylinder c4(0.3, 3, 0, 0, 0, 0, 1.8, -15); cylinder plus1(0.3,3.5, 0, 0, 0, 0, 0, -11); cylinder plus2(0.3, 4, 90, 0, 0, 0, 2, -9.2); cylinder plus3(0.3, 3.5, 0, 0, 0, 0, 0, -6); cylinder plus4(0.3, 4, 90, 0, 0, 0, 2, -4.2); cy.draw(); sp.draw(); cu.draw(); tr.draw(); rec.draw(); k1.draw(); k2.draw(); k3.draw(); k4.draw(); u1.draw(); u2.draw(); u3.draw(); u4.draw(); u5.draw(); g1.draw(); g2.draw(); g3.draw(); g4.draw(); g5.draw(); g6.draw(); g7.draw(); e1.draw(); e2.draw(); e3.draw(); e4.draw(); e5.draw(); r1.draw(); r2.draw(); r3.draw(); r4.draw(); r5.draw(); r6.draw(); c1.draw(); c2.draw(); c3.draw(); c4.draw(); plus1.draw(); plus2.draw(); plus3.draw(); plus4.draw(); glFlush(); }
int main() { try { symbol k("k"),q("q"),p("p"),p1("p1"),p2("p2"),p3("p3"),ms("ms"),l("l"),s("s"),m1s("m1s"),m2s("m2s"),m3s("m3s"); symbol l1("l1"),l2("l2"),l3("l3"),l4("l4"),t("t"),p4("p4"),p5("p5"),tp("tp"),v1("v1"),v2("v2"),l5("l5"); symbol k1("k1"),k2("k2"),k3("k3"),k4("k4"),k5("k5"),ms1("ms1"),ms2("ms2"),ms3("ms3"),ms4("ms4"); // oneloop box // UFXmap l45 = UF(lst(k),lst(pow(k,2),pow(k+p1,2),pow(k+p1+p2,2),pow(k+p1+p2+p3,2)),lst(pow(p1,2)==0,pow(p2,2)==0)); // MBintegral root_int(l45,lst(1,1,1,1),1); //two loop box bubble // UFXmap l45 = UF(lst(k,l),lst(pow(k,2),pow(k+p1,2),pow(k+p1+p2,2),pow(l+p1+p2,2),pow(l+p1+p2+p3,2),pow(l,2),pow(k-l,2)),lst(pow(p1,2)==0,pow(p2,2)==0,pow(p3,2)==0)); //MBintegral root_int(l45,lst(1,1,1,1,1,1,1),2); // B0 // UFXmap l45 = UF(lst(k),lst(ms-pow(k,2),ms-pow(-k,2)),lst(ms==1)); // MBintegral root_int(l45,lst(1,1),1); // 2 loop sunrise //UFXmap l45 = UF(lst(k,q),lst(ms-pow(k,2),ms-pow(-q-k,2),ms-pow(q,2)),lst(ms==1)); //MBintegral root_int(l45,lst(1,1,1),2); //RoMB_planar box2loop(lst(k,l),lst(pow(k,2),pow(k+p1,2),pow(k+p1+p2,2),pow(l+p1+p2,2),pow(l+p1+p2+p3,2),pow(l,2),pow(k-l,2)),lst(pow(p1,2)==0,pow(p2,2)==0,pow(p3,2)==0),lst(1,1,1,1,1,1,1),2); // RoMB_planar box1loop(lst(k),lst(pow(k,2),pow(k+p1,2)-ms,pow(k+p1+p2,2),pow(k+p1+p2+p3,2)),lst(pow(p1,2)==0,pow(p2,2)==0,pow(p3,2)==0,p1==0,p2==0,p3==0,ms==1),lst(1,1,1,1),1); // RoMB_planar B0_1loop(lst(k),lst(pow(k,2)-ms,pow(p+k,2)-ms),lst(ms==0,pow(p,2)==1),lst(1,1),1); // RoMB_planar C0_1loop(lst(k),lst(pow(k,2)-ms,pow(p1+k,2)-ms,pow(p1+p2+k,2)),lst(ms==1,pow(p1,2)==0,pow(p2,2)==0,p1*p2==50),lst(1,1,1),1); //cout<<" new point "<<endl<<root_int.new_point()<<endl; // cout<<" saved point "<<endl<<root_int.get_point()<<endl; // MBcontinue(root_int); //cout<<MB_lst(l45,lst(1,1,1,1),1).expand()<<endl; // RoMB_loop_by_loop box2loop(lst(k,l),lst(pow(k,2),pow(k+p1,2),pow(k+p1+p2,2),pow(l+p1+p2,2),pow(l+p1+p2+p3,2),pow(l,2),pow(k-l,2)),lst(pow(p1,2)==0,pow(p2,2)==0,pow(p3,2)==0),lst(1,1,1,1,1,1,1)); // RoMB_loop_by_loop t2(lst(k,l), lst(pow(k,2),pow(p+k,2),pow(p+k+l,2),pow(l,2),pow(k+l,2)),lst(pow(p,2)==1),lst(1,1,1,1,1)); // works!!! // RoMB_loop_by_loop sunset(lst(k,l), lst(pow(k,2)-1,pow(p-k-l,2)-4,pow(l,2)-5),lst(pow(p,2)==s),lst(1,1,1)); // RoMB_loop_by_loop sunset(lst(k,l), lst(pow(k,2)-m1s,pow(-k-l,2)-m2s,pow(l,2)-m3s),lst(pow(p,2)==s),lst(1,1,1)); // sunset.integrate(lst(m1s==1,m2s==1,m3s==1,s==0),0); // bubble sunset 2=loop // RoMB_loop_by_loop sunset_bub(lst(k,l), lst(-pow(k,2)+ms,-pow(-k-l,2)+ms,-pow(l,2)+ms),lst(pow(p,2)==0),lst(1,1,1)); // sunset_bub.integrate(lst(ms==1,m2s==1,m3s==1,s==0),1); // bubble sunset 3=loop // RoMB_loop_by_loop sunset_bub(lst(p,k,l), lst(-pow(p,2)+ms,-pow(k,2)+ms,-pow(l,2)+ms,-pow(-p-k-l,2)+ms),lst(pow(l3,2)==s),lst(1,1,1,1)); // sunset_bub.integrate(lst(ms==1,m2s==1,m3s==1,s==0),0); // RoMB_loop_by_loop sunset_bub_d(lst(l1,l2,l3), lst(-pow(l1,2)+ms,-pow(l2,2)+ms,-pow(l3,2)+ms,-pow(l1+l2,2)+ms,-pow(l1+l2+l3,2)+ms),lst(pow(p,2)==s),lst(1,1,1,1,1)); // sunset_bub_d.integrate(lst(ms==1,m2s==1,m3s==1,s==0),-1); // RoMB_loop_by_loop sunset_bub_e(lst(l1,l2,l3), lst(-pow(l1,2)+ms,-pow(l2,2)+ms,-pow(l3,2)+ms,-pow(l1-l2,2)+ms,-pow(l2-l3,2)+ms,-pow(l3-l1,2)+ms),lst(pow(p,2)==s),lst(1,1,1,1,1,1)); // sunset_bub_e.integrate_map(lst(ms==1,m2s==1,m3s==1,s==0),1); //bubble 4-loop // RoMB_loop_by_loop sunset_bub(lst(k,l1,l2,l3), lst(-pow(k,2)+ms,-pow(l2,2)+ms,-pow(l1,2)+ms,-pow(l3,2)+ms,-pow(k+l1+l2+l3,2)+ms),lst(pow(p,2)==s),lst(1,1,1,1,1)); // sunset_bub.integrate(lst(ms==1,m2s==1,m3s==1,s==0),0); //bubble 5-loop // RoMB_loop_by_loop sunset_bub5(lst(l3,k,l1,l2,l4), lst(-pow(l3,2)+ms,-pow(k,2)+ms,-pow(l1,2)+ms,-pow(l2,2)+ms,-pow(l4,2)+ms,-pow(k+l1+l2+l3+l4,2)+ms),lst(pow(p,2)==s),lst(1,1,1,1,1,1)); // sunset_bub5.integrate_map(lst(ms==1,m2s==1,m3s==1,s==0),3); // RoMB_loop_by_loop sunset_bubC2(lst(l1,l2,l3,l4,l5), lst(-pow(l3,2)+ms,-pow(l5,2)+ms,-pow(l1,2)+ms,-pow(l2,2)+ms,-pow(l4,2)+ms,-pow(l5+l1+l2,2)+ms,-pow(l5+l3+l4,2)+ms),lst(pow(p,2)==s),lst(1,1,1,1,1,1,1)); // sunset_bubC2.integrate_map(lst(ms==1,m2s==1,m3s==1,s==0),0); // RoMB_loop_by_loop sunset_bubC2(lst(l1,l2,l3,l4,l5), lst(-pow(l3,2)+ms,-pow(l5,2)+ms,-pow(l1,2)+ms,-pow(l2,2)+ms,-pow(l4,2)+ms,-pow(l3+l4+l5,2)+ms,-pow(l1+l2+l5+l3+l4,2)+ms),lst(pow(p,2)==s),lst(1,1,1,1,1,1,1)); // sunset_bubC2.integrate_map(lst(ms==1,m2s==1,m3s==1,s==0),0); // RoMB_loop_by_loop sunset_bubC1(lst(l1,l2,l3,l4,l5), lst(-pow(l3,2)+ms,-pow(l5,2)+ms,-pow(l1,2)+ms,-pow(l2,2)+ms,-pow(l4,2)+ms,-pow(l2+l3+l4+l5,2)+ms,-pow(l1+l2+l5+l3+l4,2)+ms),lst(pow(p,2)==s),lst(1,1,1,1,1,1,1)); // sunset_bubC1.integrate_map(lst(ms==1,m2s==1,m3s==1,s==0),0); /* MEGA 5-LOOP BUBBLE with 12 propagators */ //RoMB_loop_by_loop l5p12(lst(k5,k2,k1,k4,k3),lst(-pow(k1,2)+ms,-pow(k2,2)+ms,-pow(k3,2)+ms,-pow(k4,2)+ms,-pow(k5,2)+ms, //-pow(k1-k3,2)+ms,-pow(k1-k4,2)+ms,-pow(k3-k2,2)+ms,-pow(k2-k4,2)+ms,-pow(k5+k3-k1,2)+ms,-pow(k5+k3-k2,2)+ms,-pow(k5+k3-k4,2)+ms),lst(pow(p,2)==0),lst(1,1,1,1,1,1,1,1,1,1,1,1)); //l5p12.integrate(lst(ms==0),0); //RoMB_loop_by_loop l5c1(lst(k2,k5,k3,k4,k1),lst(-pow(k3,2)+ms,-pow(k2,2)+ms,-pow(k1,2)+ms,-pow(k4,2)+ms,-pow(k5,2)+ms, //-pow(k1+k3+k4,2)+ms,-pow(k2+k5-k3-k4,2)+ms),lst(pow(p,2)==0),lst(1,1,1,1,1,1,1)); //l5c1.integrate_map(lst(ms==1),0); // RoMB_loop_by_loop t2loop(lst(k,l), lst(-pow(k,2)+ms,-pow(p+k,2)+ms,-pow(p+k+l,2)+ms,-pow(k+l,2)+ms,-pow(l,2)+ms),lst(pow(p,2)==s),lst(1,1,1,1,1)); // t2loop.integrate(lst(s==1,ms == 0),1); /* RoMB_loop_by_loop bubble_five_loop(lst(k,l1,l2,l3,l4), lst(pow(k,2)-ms,pow(l1,2)-ms,pow(l2,2)-ms,pow(l3,2)-ms,pow(l4,2)-ms,pow(k+l1,2)-ms,pow(k+l1+l2,2)-ms,pow(k+l1+l2+l3,2)-ms,pow(k+l1+l2+l3+l4,2)-ms,pow(k+l1+l2+l3,2)-ms,pow(k+l1+l2,2)-ms,pow(k+l1,2)-ms), lst(ms==1), lst(1,1,1,1,1,1,1,1,1,1,1,1)); */ // works!!! // RoMB_loop_by_loop B0_1loop_lbl(lst(k),lst(pow(k,2)-2-ms,pow(p+k,2)-ms),lst(ms==0,pow(p,2)==1),lst(2,1)); // RoMB_loop_by_loop B0_1loop_lbl(lst(k),lst(pow(k,2)-m1s,pow(p+k,2)-m2s),lst(pow(p,2)==s),lst(1,1)); // B0_1loop_lbl.integrate(lst(s==-1,m1s==1,m2s==1)); //MB works??? // RoMB_loop_by_loop C0_1loop_lbl(lst(k),lst(pow(k,2),pow(k+p1,2)-m1s,pow(k-p2,2)-m2s),lst(ms==1,pow(p1,2)==m1s,pow(p2,2)==m2s,p1*p2==(s-m1s-m2s)/2),lst(1,1,1)); // C0_1loop_lbl.integrate(lst(m1s==1,m2s==1,s==-100)); //MB works??? /* RoMB_loop_by_loop box1loopm0(lst(k),lst(-pow(k,2),-pow(k+p1,2),-pow(k+p1+p2,2),-pow(k+p1+p2+p4,2)), lst(pow(p1,2)==0,pow(p2,2)==0,pow(p4,2)==0, p1*p2==-s/2,// p1*p4==s/2+t/2,// p2*p4==-t/2 // ), lst(1,1,1,1),false); box1loopm0.integrate_map(lst(s==3,t==1)); box1loopm0.integrate(lst(s==5,t==2)); */ //MASIVE BOX LBL RoMB_loop_by_loop box1loopm(lst(k),lst(-pow(k,2)+ms,-pow(k+p1,2)+ms,-pow(k+p1+p2,2)+ms,-pow(k+p1+p2+p4,2)+ms), lst(pow(p1,2)==0,pow(p2,2)==0,pow(p4,2)==0, p1*p2==s/2,// p1*p4==-(s/2+t/2),// p2*p4==t/2 // ), lst(1,1,1,1),false); box1loopm.integrate_map(lst(ms1==1,ms2==1,ms3==1,ms4==1,ms==1,s==-3,t==-1),3); //triple box /* RoMB_loop_by_loop tribox1loopm(lst(k1,k2,k3),lst(-pow(k1,2)+ms,-pow(k1+p1,2),-pow(k1+p1+p2,2)+ms, -pow(k1-k2,2),-pow(k2,2)+ms,-pow(k2+p1+p2,2)+ms, -pow(k2-k3,2),-pow(k3,2)+ms,-pow(k3+p1+p2,2)+ms, -pow(k3-p3,2)), lst(pow(p1,2)==ms,pow(p2,2)==ms,pow(p3,2)==ms,pow(p4,2)==ms, p1*p2==s/2-ms,// p1*p3==t/2-ms,// p2*p3==ms-(s+t)/2 // ), lst(1,1,1,1,1,1,1,1,1,1),true); tribox1loopm.integrate_map(lst(ms1==1,ms2==1,ms3==1,ms4==1,ms==1,s==-1/2,t==-3)); */ //double box /* RoMB_loop_by_loop dobox1loopm(lst(k1,k2),lst(-pow(k1,2),-pow(k1+p1,2),-pow(k1+p1+p2,2), -pow(k1-k2,2),-pow(k2,2),-pow(k2+p1+p2,2), -pow(k2-p3,2)), lst(pow(p1,2)==0,pow(p2,2)==0,pow(p3,2)==0,pow(p4,2)==0, p1*p2==s/2-ms,// p1*p3==t/2-ms,// p2*p3==ms-(s+t)/2 // ), lst(1,1,1,1,1,1,1),false); dobox1loopm.integrate_map(lst(ms1==1,ms2==1,ms3==1,ms4==1,ms==1,s==-1/2,t==-3)); */ /* 4-loop tadpole */ // RoMB_loop_by_loop tad4(lst(l1, l2, l3, l4),lst(pow(l1,2)- ms,pow(l2,2)- ms,pow(l3 ,2)- ms,pow(l4,2),pow(l1+l2+l3+l4,2)),lst(),lst(1,1,1,1,1)); // tad4.integrate(lst(ms == 1),-2); /* Pentagon */ /* RoMB_loop_by_loop pent(lst(k1),lst(-pow(p1 + k1,2)+ ms,-pow(p1 + p5 + k1,2), -pow(p1 + p5 + p4 + k1,2)+ ms,-pow(p1 + p5 + p4 + p3 + k1,2)+ ms, -pow(k1,2)), lst( p1*p1 == ms, p2*p2 == ms, p3*p3 == 0, p4*p4 == ms, p5*p5 == ms, p1*p2 == 1/2* (tp - 2* ms), p1*p3 == 1/2* (t - tp - v1), p1*p4 == ms - 1/2* (s + t - v1), p1*p5 == 1/2* (s - 2* ms), p2* p3 == 1/2* v1, p2* p4 == 1/2* (s - 2* ms - v1 - v2), p2* p5 == ms - 1/2* (s + tp - v2), p3* p4 == 1/2* v2, p3* p5 == 1/2* (tp - t - v2), p4* p5 == 1/2* (t - 2* ms)), lst(1,1,1,1,1)); pent.integrate_map(lst(s==-2,t==-3,v2==-4,tp==-5,v1==-6,ms==1)); */ /* RoMB_loop_by_loop pent(lst(k1),lst(-pow(p1 + k1,2)+ ms,-pow(p1 + p5 + k1,2), -pow(p1 + p5 + p4 + k1,2)+ ms,-pow(p1 + p5 + p4 + p3 + k1,2)+ ms, -pow(k1,2)), lst( p1*p1 == ms, p2*p2 == ms, p3*p3 == 0, p4*p4 == ms, p5*p5 == ms, p1*p2 == 1/2* (tp - 2* ms), wild(1)*p1*p3 == wild(1)*1/2* (t - tp - v1), wild(2)*p1*p4 == wild(2)*(ms - 1/2* (s + t - v1)), wild(3)* p1*p5 == wild(3)*1/2* (s - 2* ms), wild(4)*p2* p3 == wild(4)*1/2* v1, wild(5)*p2* p4 == wild(5)*1/2* (s - 2* ms - v1 - v2), wild(6)*p2* p5 ==wild(6)*( ms - 1/2* (s + tp - v2)), wild(7)*p3* p4 == wild(7)*1/2* v2, wild(8)*p3* p5 == wild(8)*1/2* (tp - t - v2), wild()*p4* p5 == wild()*1/2* (t - 2* ms)), lst(1,1,1,1,1)); pent.integrate_map(lst(s==-2,t==-3,v2==-4,tp==-5,v1==-6,ms==1)); */ } catch(std::exception &p) { std::cerr<<"******************************************************************"<<endl; std::cerr<<" >>>ERROR: "<<p.what()<<endl; std::cerr<<"******************************************************************"<<endl; return 1; } return 0; }
// YOU NEED THIS: http://doc.qt.io/qt-5/qtest.html void TestKey::test(){ Key k1(1024); qDebug()<<"K1:"<<k1.id(); Key k2(k1); qDebug()<<"K2:"<<k2.id(); qDebug()<<"K1:"<<k1.id(); Key k3(1024); qDebug()<<"K3:"<<k3.id(); k3=k1; qDebug()<<"K3:"<<k3.id(); /* QVERIFY(k1.id()==k2.id()); QVERIFY(k1.id()==k3.id()); QVERIFY(k1.kid()==k2.kid()); QVERIFY(k1.kid()==k3.kid()); QVERIFY(k1.kct()==k2.kct()); QVERIFY(k1.kct()==k3.kct()); */ qDebug()<<"K1:"<<k3.kid()<< " of " <<k3.kct(); qDebug()<<"K2:"<<k3.kid()<< " of " <<k3.kct(); qDebug()<<"K3:"<<k3.kid()<< " of " <<k3.kct(); Key k4(1024); qDebug()<<"K4:"<<k4.kid()<< " of " <<k4.kct()<< " VAR: "<<k4.toVariantMap(false); QByteArray orig=QString("THIS IS THE ORIGINAL TEXT").toUtf8(); QByteArray signature = k1.sign(orig); qDebug()<<"ORIG: "<<orig; qDebug()<<"SIGN: "<<signature; //const auto priPath = QString("/home/lennart/keypairs/private_key.pem"); const auto pubPath = QString("/home/lennart/keypairs/public_key.pem"); utility::fileToByteArray(pubPath); int ret=0; qpolarssl::Pki pkiPrivate; qpolarssl::Pki pkiPublic; pkiPrivate.generateKeyPair(OCTOMY_KEY_BITS); pkiPublic.parsePublicKey(pkiPrivate.getPEMPubkey()); const QByteArray sourceData = QString("OctoMY™ test data in cleartext").toUtf8(); const QByteArray signature2 = pkiPrivate.sign(sourceData, OCTOMY_KEY_HASH_POLAR); const int siglen=signature2.length(); if((siglen <= 64) ){ qWarning()<< "Signature size "<<QString::number(siglen)<<" was less than 64"; } else{ qDebug()<<"Signature size "<<QString::number(siglen)<<" was OK"; } QVERIFY((siglen > 64) ); ret = pkiPublic.verify(sourceData, signature2, OCTOMY_KEY_HASH_POLAR); if(ret!=0){ qWarning()<<"Signature verification failed with code -"<<QString::number(-ret,16); } else{ qDebug()<<"Signature verification was OK"; } QVERIFY(ret==0); QVERIFY(k1.verify(orig, signature)); QVERIFY(!k4.verify(orig, signature)); }
void RK4_solve(cube &data_vector,double step_size,int time_steps, int n_planets,vec masses,double G,double epsilon){ //Define all the different variables used for the method mat k1(n_planets,6); mat k2(n_planets,6); mat k3(n_planets,6); mat k4(n_planets,6); mat start_data(n_planets,6); mat accel(n_planets,3); k1.fill(0); k2.fill(0); k3.fill(0); k4.fill(0); start_data.fill(0); accel.fill(0); //Evolve through time clock_t start,finish; start = clock(); for(int t=0;t< time_steps-1;t++){ //Calculate inital acceleration accel_calculate(data_vector,masses,n_planets,accel,t,G,epsilon); for(int i=0;i< n_planets;i++){ //Set start data for(int j=0;j<6;j++){ start_data(i,j) = data_vector(i,j,t); //Calculate k1 for each dim for(int j=0;j<3;j++){ k1(i,j)= step_size*data_vector(i,3+j,t); k1(i,3+j)= step_size*accel(i,j); } } //Save temp vel for(int j=0;j<6;j++){ data_vector(i,j,t)= start_data(i,j) +k1(i,j)/2.; } } //end k1 step //Calculate new acceleration at this temporary position accel_calculate(data_vector,masses,n_planets,accel,t,G,epsilon); for(int i=0;i<n_planets;i++){ //Calculate k2 for each dim k2(i,0)= step_size*data_vector(i,3,t); k2(i,1)= step_size*data_vector(i,4,t); k2(i,2)= step_size*data_vector(i,5,t); k2(i,3)= step_size*accel(i,0); k2(i,4)= step_size*accel(i,1); k2(i,5)= step_size*accel(i,2); //Save temp pos & temp vel data_vector(i,0,t)= start_data(i,0) +k2(i,0)/2.; data_vector(i,1,t)= start_data(i,1) +k2(i,1)/2.; data_vector(i,2,t)= start_data(i,2) +k2(i,2)/2.; data_vector(i,3,t)= start_data(i,3) +k2(i,3)/2.; data_vector(i,4,t)= start_data(i,4) +k2(i,4)/2.; data_vector(i,5,t)= start_data(i,5) +k2(i,5)/2.; } //Calculate new acceleration again accel_calculate(data_vector,masses,n_planets,accel,t,G,epsilon); for(int i=0;i<n_planets;i++){ //Calculate k3 for each dim k3(i,0)= step_size*data_vector(i,3,t); k3(i,1)= step_size*data_vector(i,4,t); k3(i,2)= step_size*data_vector(i,5,t); k3(i,3)= step_size*accel(i,0); k3(i,4)= step_size*accel(i,1); k3(i,5)= step_size*accel(i,2); //Save temp vel and pos data_vector(i,0,t)= start_data(i,0) +k3(i,0); data_vector(i,1,t)= start_data(i,1) +k3(i,1); data_vector(i,2,t)= start_data(i,2) +k3(i,2); data_vector(i,3,t)= start_data(i,3) +k3(i,3); data_vector(i,4,t)= start_data(i,4) +k3(i,4); data_vector(i,5,t)= start_data(i,5) +k3(i,5); } //Calculate new acceleration again accel_calculate(data_vector,masses,n_planets,accel,t,G,epsilon); for(int i=0;i<n_planets;i++){ //Calculate k4 for each dim k4(i,0)= step_size*data_vector(i,3,t); k4(i,1)= step_size*data_vector(i,4,t); k4(i,2)= step_size*data_vector(i,5,t); k4(i,3)= step_size*accel(i,0); k4(i,4)= step_size*accel(i,1); k4(i,5)= step_size*accel(i,2); //Return start position to data_vector data_vector(i,0,t)= start_data(i,0); data_vector(i,1,t)= start_data(i,1); data_vector(i,2,t)= start_data(i,2); data_vector(i,3,t)= start_data(i,3); data_vector(i,4,t)= start_data(i,4); data_vector(i,5,t)= start_data(i,5); } for(int i=0;i<n_planets;i++){ //Update new position for(int j=0;j<6;j++){ data_vector(i,j,t+1) = data_vector(i,j,t) + 1/6.*(k1(i,j) + 2.*k2(i,j) + 2.*k3(i,j) + k4(i,j)); } } } finish = clock(); cout << "Total RK4 time = "<< ((float)(finish-start)/CLOCKS_PER_SEC)<<" sec" << endl; cout << "RK4 time/step = "<< ((float)(finish-start)/CLOCKS_PER_SEC)/time_steps<<" sec" << endl; }
std::deque<Vector> FlowMath::computeStreamlineRungeKutta(const Flow& flow, const Vector& r0, const float length, const float stepwidth, int* const startIndex, const tgt::vec2& thresholds) { // N: number of partitions // const float h = fabsf(stepwidth); float fn = ceilf(fabsf(length) / h); const unsigned int N = (length != 0.0f) ? static_cast<unsigned int>(fn) : 0; Vector r(r0), r_(r0); Vector k1(0.0f), k2(0.0f), k3(0.0f), k4(0.0f); Vector k1_(0.0f), k2_(0.0f), k3_(0.0f), k4_(0.0f); std::deque<Vector> points; // points on streamline in positive direction points.push_back(r0); // avoid that one of the deque is empty int indexR0 = 0; // position of r0 within deque bool lookupPos = true; // integrate along the streamline in positive direction? bool lookupNeg = true; // integrate along the streamline in negative direction? bool useThresholds = (thresholds != tgt::vec2::zero); for (unsigned int i = 0; ((N == 0) || (i < N)); ++i) { if (lookupPos == true) { const Vector& v = flow.lookupFlow(r); if (useThresholds == true) { float magnitude = tgt::length(v); if ((magnitude < thresholds.x) || (magnitude > thresholds.y)) { lookupPos = false; break; } } if (v != Vector::zero) { k1 = normalize(v) * h; k2 = normalize( flow.lookupFlow(r + (k1 / 2.0f)) ) * h; k3 = normalize( flow.lookupFlow(r + (k2 / 2.0f)) ) * h; k4 = normalize( flow.lookupFlow(r + k3) ) * h; r += ((k1 / 6.0f) + (k2 / 3.0f) + (k3 / 3.0f) + (k4 / 6.0f)); lookupPos = flow.isInsideBoundings(r); if (r == points.back()) // in case of no progress on streamline in this direction... lookupPos = false; else if (lookupPos == true) points.push_back(r); } else lookupPos = false; } if (lookupNeg == true) { const Vector& v = flow.lookupFlow(r_); if (useThresholds == true) { float magnitude = tgt::length(v); if ((magnitude < thresholds.x) || (magnitude > thresholds.y)) { lookupNeg = false; break; } } if (v != Vector::zero) { k1_ = normalize(v) * h; k2_ = normalize( flow.lookupFlow(r_ - (k1_ / 2.0f)) ) * h; k3_ = normalize( flow.lookupFlow(r_ - (k2_ / 2.0f)) ) * h; k4_ = normalize( flow.lookupFlow(r_ - k3_) ) * h; r_ -= ((k1_ / 6.0f) + (k2_ / 3.0f) + (k3_ / 3.0f) + (k4_ / 6.0f)); lookupNeg = flow.isInsideBoundings(r_); if (r_ == points.front()) // in case of no progress on streamline in this direction... lookupNeg = false; else if (lookupNeg == true) { points.push_front(r_); ++indexR0; } } else lookupNeg = false; } if ((lookupPos == false) && (lookupNeg == false)) break; } // for (; ; ++i) if (startIndex != 0) *startIndex = indexR0; return points; }
int main() { try { symbol k("k"),q("q"),p("p"),p1("p1"),p2("p2"),p3("p3"),ms("ms"),l("l"),s("s"),m1s("m1s"),m2s("m2s"),m3s("m3s"); symbol l1("l1"),l2("l2"),l3("l3"),l4("l4"),t("t"),p4("p4"),p5("p5"),tp("tp"),v1("v1"),v2("v2"),l5("l5"); symbol k1("k1"),k2("k2"),k3("k3"),k4("k4"),k5("k5"),ms1("ms1"),ms2("ms2"),ms3("ms3"),ms4("ms4"); symbol s12("s12"),s23("s23"),s34("s34"),s45("s45"),s51("s51"),s13("s13"),s15("s15"); lst inv_l = lst( p1*p1 == 0, p2*p2 == 0, p3*p3 == 0, p4*p4 == 0, p5*p5 == 0, p1*p2 == s12/2, p1*p3 == (-s12-s23+s45)/2, p1*p4 == (-s15+s23-s45)/2, p1*p5 == s15/2, p2* p3 ==s23/2, p2* p4 ==(s15-s23-s34)/2, p2* p5 ==(-s12-s15+s34)/2, p3*p4 == s34/2, p3*p5 == (s12-s34-s45)/2, p4*p5 == s45/2); #define topo 2 #if topo==1 /* 1+eps normalization FRESULT for parameters: {s12==-2,s23==-3,s34==-4,s45==-5,s15==-6,ms==1} FRESULT anl : = -0.010071141398715986043 FRESULT num: = -0.010071141398715986043 eps^0 term: -0.010071141398715986043 +/- 7.5387750593540493467E-5 */ /* Euler renormalization FRESULT for parameters: {s12==-2,s23==-3,s34==-4,s45==-5,s15==-6,ms==1} FRESULT anl : = 0.020204464861409441711 FRESULT num: = 0.020204464861409441711 eps^0 term: 0.020204464861409441711 +/- 2.9955911201888832611E-4 */ RoMB_loop_by_loop pent(lst(k1),lst(-pow(p1 + k1,2)+ms,-pow(p1 + p2 + k1,2)+ms, -pow(p1 + p2 + p3 + k1,2)+ms,-pow(p1 + p2 + p3 + p4 + k1,2)+ms, -pow(k1,2)+ms), inv_l, lst(1,1,1,1,1),false); pent.integrate_map(lst(s12==-2,s23==-3,s34==-4,s45==-5,s15==-6,ms==1)); #elif topo==2 // M=0 with factor tgamma(1-eps)^2/tgamma(1-2eps) /* PJfry * 1/eps^-2 :(-0.111111,0) * 1/eps^-1 :(0.0856421,0) * 1/eps^0 :(0.0513422,0) -3.28987 */ RoMB_loop_by_loop pent(lst(k2,k1),lst(-pow(k1,2),-pow(k1 - k2 ,2), -pow(k1+p1 + p2,2),-pow(k1 - p4 - p5,2), -pow(k1-p5,2),-pow(k2,2),-pow(k2+p1,2),-pow(k2+p1+p2,2)), inv_l, lst(1,1,1,1,1,1,1,1),true); pent.integrate_map(lst(s12==-2,s23==-4,s34==-5,s45==-6,s15==-0.5,ms==1),0); /* FRESULT for parameters: {s12==-2,s23==-4,s34==-5,s45==-6,s15==-0.5,ms==1} FRESULT anl : = 400.22174334151294225-(0.24583333333333333332)*log(4)^2*log(5)*log(2)-(3.3881317890172013563E-21)*Euler*log(5)^2+(7.284483346386982916E-20)*Euler*log(5)*log(6)*log(2)-(0.11210570324758033243)*log(4)*log(6)-(2.1006417091906648409E-19)*Euler*log(5)*log(6)-(8.470329472543003391E-21)*Euler+(1.4484263398048535798E-19)*Euler*log(5)^2*log(2)+(0.34079736377530644382)*log(4)*log(6)*log(2)-(0.17039868188765322194)*log(4)^2*log(2)+eps^(-2)*(-1.3333035413347974529-(0.12916666666666666666)*log(4)*log(6)+(1.9274705288631189937E-20)*Euler+(3.3730734255104582391E-20)*Euler*log(6)+(0.121354166666666666677)*Pi^2+(0.014440566261665527283)*log(4)+(0.054166666666666666667)*log(5)*log(6)+(3.08395284618099039E-19)*Euler^2+(0.24693368307448051649)*log(5)-(1.2046690805394493711E-20)*Euler*log(4)-(0.045833333333333333334)*log(4)*log(5)+(0.16666666666666666667)*log(2)^2-(0.0086643397569993163535)*log(6)-(0.025)*log(6)*log(2)-(1.9274705288631189937E-20)*Euler*log(5)+(0.0625)*log(6)^2-(0.27725887222397812377)*log(2)-(0.4)*log(5)*log(2)+(0.07708333333333333334)*log(4)^2+(0.178125)*log(5)^2+(0.029166666666666666667)*log(4)*log(2)+(7.709882115452475975E-20)*Euler*log(2))+(2.2022856628611808816E-20)*Euler*log(4)^3-(4.336808689942017736E-19)*Euler^2*log(2)-(0.066426604803661425496)*log(4)*log(5)^2+(0.014236111111111111113)*log(4)^4+(2.710505431213761085E-20)*Euler*log(6)-(1.1011428314305904408E-19)*Euler*log(6)*Pi^2-(0.25763888888888888888)*log(5)^3*log(2)+(0.09861111111111111112)*log(5)*log(6)^3+(0.07797905781299384727)*log(6)*log(2)^2+(2.168404344971008868E-19)*Euler*log(4)*log(5)-(3.3881317890172013563E-20)*Euler*log(4)^2+(0.058333333333333333313)*log(4)*log(5)^2*log(2)+(1.4696021634862110883E-19)*Euler*log(6)*log(2)-(1.2493735972000930001E-20)*Euler*log(5)^3-(0.32346868426130781108)*log(4)*log(5)*log(6)+(1.8223154162344101082-(1.9274705288631189937E-20)*Euler*log(5)^2-(0.17906302164465253826)*log(4)*log(6)-(3.252606517456513302E-20)*Euler+(0.275)*log(4)*log(6)*log(2)-(0.14166666666666666667)*log(4)^2*log(2)-(4.9030031577955589404E-19)*Euler^2*log(2)-(0.029166666666666666667)*log(4)*log(5)^2-(4.336808689942017736E-20)*Euler*log(6)+(0.03125)*log(6)*log(2)^2-(2.4093381610788987422E-20)*Euler*log(4)*log(5)+(2.379221434065412508E-20)*Euler*log(6)*log(2)-(0.25833333333333333333)*log(4)*log(5)*log(6)+(0.17641558449668052497)*Pi^2+(0.12916666666666666666)*log(5)*log(6)^2+(0.018016988021932553424)*log(4)-(0.35625)*log(5)^2*log(2)+(0.04043358553266347639)*log(5)*log(6)+(3.8549410577262379875E-20)*Euler*log(4)*log(6)+(3.2766998990673022894E-19)*Euler^2-(0.64791666666666666673)*zeta(3)-(0.11319444444444444446)*log(2)^3+(0.18467412722480867264)*log(5)+(0.09756944444444444444)*log(6)*Pi^2+(4.8186763221577974843E-21)*Euler*log(4)-(0.040433585532663476392)*log(4)*log(5)+(0.27725887222397812372)*log(2)^2-(0.018016988021932553429)*log(6)+(1.541976423090495195E-19)*Euler^3-(0.07509094456066074186)*log(6)*log(2)+(3.1321396094025683648E-20)*Euler*log(5)-(0.2375)*log(4)*log(6)^2+(0.08953151082232626913)*log(6)^2-(2.168404344971008868E-20)*Euler*log(2)^2+(0.12083333333333333333)*log(4)^2*log(5)-(0.14375)*log(6)^2*log(2)-(0.108333333333333333334)*log(5)*log(6)*log(2)-(0.17116138620835925754)*log(2)+(2.0238440553062749435E-19)*Euler^2*log(5)-(0.025)*log(4)*log(2)^2-(0.22395833333333333336)*log(2)*Pi^2+(0.23229166666666666667)*log(5)*Pi^2+(0.029166666666666666667)*log(5)^2*log(6)-(2.4093381610788987422E-20)*Euler*log(4)*log(2)-(0.49386736614896103298)*log(5)*log(2)+(0.08541666666666666667)*log(6)^3+(0.08375528431766005821)*log(4)^2+(3.8549410577262379875E-20)*Euler*Pi^2+(0.128125)*log(5)^3+(0.108333333333333333334)*log(4)*log(5)*log(2)+(0.4)*log(5)*log(2)^2-(0.09409722222222222222)*log(4)*Pi^2+(7.709882115452475975E-20)*Euler*log(5)*log(2)+(0.26642844752772897827)*log(5)^2+(0.0750909445606607419)*log(4)*log(2)+(0.22916666666666666667)*log(4)^2*log(6)-(0.080555555555555555553)*log(4)^3+(1.1594939900192200198E-19)*Euler*log(2))*eps^(-1)-(3.1509625637859972613E-19)*Euler^2*log(5)*log(2)-(1.5246593050577406103E-20)*Euler^2*Pi^2+(0.44166666666666666666)*zeta(3)*log(6)+(0.12361655670603724154)*Pi^2+(0.062586805555555555545)*log(5)^4-(2.5410988417629010172E-20)*Euler*log(4)*log(6)^2-(0.020138888888888888871)*log(6)*log(2)^3+(0.164622455382987011)*log(5)*log(6)^2+(0.3583333333333333334)*log(5)^2*log(2)^2-(0.22152777777777777779)*log(4)*log(6)*Pi^2+(0.10729166666666666671)*log(4)^2*Pi^2-(0.031944444444444444437)*log(4)*log(5)^3+(0.0041628081498616184988)*log(4)-(9.5714723039735938315E-20)*Euler*log(4)*log(5)*log(2)+(3.9954857837891737475E-20)*Euler*log(4)^2*log(2)-(0.53574500830779106205)*log(5)^2*log(2)-(2.5199230180815435087E-19)*Euler*zeta(3)+(0.048045301391820142482)*log(5)*log(6)-(4.7433845046240818988E-20)*Euler*log(4)*log(6)-(0.06249999999999999996)*log(5)^2*log(6)*log(2)+(6.168313523040288406E-19)*Euler^2-(0.9097222222222222222)*zeta(3)*log(5)-(1.0464597017620285435)*zeta(3)-(4.539037806098981942E-19)*Euler^3*log(2)-(0.18580195256676311766)*log(2)^3-(2.710505431213761085E-20)*Euler*log(6)^3+(0.08337179655695074824)*log(5)+(0.12755833531137882431)*log(6)*Pi^2+(2.2022856628611808816E-20)*Euler*log(4)*log(5)^2-(1.3552527156068805425E-20)*Euler*log(4)+(0.012326388888888888894)*log(6)^4-(0.4125)*log(4)*zeta(3)-(0.30416666666666666667)*log(4)*log(5)*log(6)^2+(0.49166666666666666665)*log(4)*log(5)*log(6)*log(2)-(0.066666666666666666677)*log(4)*log(6)^3+(4.7433845046240818988E-20)*Euler*log(6)*log(2)^2+(0.14305555555555555555)*log(4)^3*log(2)-(0.046043413833827636543)*log(4)*log(5)-(2.168404344971008868E-19)*Euler*log(6)^2+(0.1721623299873555105)*log(2)^2-(0.0037002739109881053319)*log(6)-(2.3039296165316969223E-19)*Euler^2*log(2)^2+(1.0062751413381088028E-18)*Euler^3-(2.168404344971008868E-19)*Euler^2*log(4)*log(2)-(0.25)*log(5)*log(6)^2*log(2)+(0.20505604272398455968-(2.8912057932946784908E-20)*Euler+(0.00625)*log(4)+(0.19583333333333333331)*log(5)-(0.018750000000000000007)*log(6)-(0.16875)*log(2))*eps^(-3)-(0.030028313369887589065)*log(6)*log(2)-(0.275)*log(4)*log(6)*log(2)^2+(0.13125)*log(4)^2*log(2)^2+(4.0657581468206416275E-20)*Euler*log(5)*log(6)^2-(8.131516293641283255E-20)*Euler*log(5)-(0.2570420794576463856)*log(4)*log(6)^2-(0.47430555555555555555)*log(5)*log(2)*Pi^2+(0.2350694444444444444)*log(5)^2*Pi^2+(0.22569444444444444447)*log(2)^2*Pi^2+(0.05705379540278641918)*log(6)^2+(1.5814418841144177812E-20)*Euler*log(2)^2+(0.16173434213065390554)*log(4)^2*log(5)+(1.5585406229479126239E-19)*Euler^2*log(6)^2-(0.17328679513998632736)*log(6)^2*log(2)+(7.030373462210692814E-20)*Euler*log(4)*log(6)*log(2)-(0.086643397569993163665)*log(5)*log(6)*log(2)-(0.08580010131103669233)*log(2)+(2.2700482986415249087E-19)*Euler^2*log(5)+(0.09999999999999999998)*log(4)^2*log(6)^2-(0.07509094456066074196)*log(4)*log(2)^2-(6.7762635780344027125E-20)*Euler*log(5)*log(2)^2-(0.32876355855725183764)*log(2)*Pi^2+(8.1950437646853557805E-20)*Euler^4-(1.1858461261560204747E-20)*Euler*log(4)*Pi^2+(0.3258754453049187323)*log(5)*Pi^2+(0.06931471805599453092)*log(5)^2*log(6)+(3.642241673193491458E-20)*Euler*log(4)^2*log(6)-(1.7194768829262296883E-19)*Euler*log(4)*log(2)-(0.37135014200760985115)*log(5)*log(2)+(1.1011428314305904408E-19)*Euler*log(2)^3+(0.08375528431766005824)*log(6)^3+(1.8431436932253575378E-18)*Euler^3*log(6)+(0.056423611111111111103)*log(2)^4-(4.0826988057657276343E-19)*Euler^2*log(4)+(0.112499999999999999984)*log(6)^2*Pi^2+(0.18402777777777777775)*log(5)*log(6)*Pi^2-(0.061111111111111111102)*log(4)^3*log(6)-(0.108333333333333333294)*log(4)*log(5)*log(2)^2+(0.020833333333333333319)*log(4)*log(2)^3-(8.131516293641283255E-20)*Euler^2*log(4)^2-(6.7762635780344027125E-21)*Euler*log(4)^2*log(5)+(0.056052851623790166215)*log(4)^2-(2.6893296075324035765E-19)*Euler^2*log(5)*log(6)-(1.626303258728256651E-19)*Euler^3*log(5)+(4.2986922073155742208E-20)*Euler*Pi^2+(0.66666666666666666706)*zeta(3)*log(2)-(0.4083333333333333333)*log(4)^2*log(6)*log(2)+(0.17352747124434741951)*log(5)^3-(0.23333333333333333333)*log(4)*log(5)^2*log(6)+(0.080867171065326952724)*log(4)*log(5)*log(2)-(1.6940658945086006781E-20)*Euler*log(6)^2*log(2)-(0.13125)*log(6)^3*log(2)+(0.49675547940129413833)*log(5)*log(2)^2-(1.3552527156068805425E-20)*Euler*log(4)*log(2)^2+(0.11874999999999999999)*log(5)^2*log(6)^2+(0.140625)*eps^(-4)+(3.8963515573697815597E-20)*Euler*log(5)*Pi^2-(0.10416666666666666666)*log(4)^3*log(5)-(0.1208194043892682449)*log(4)*Pi^2-(7.284483346386982916E-20)*Euler*log(2)*Pi^2+(8.131516293641283255E-20)*Euler*log(5)*log(2)+(0.18042011616407459749)*log(5)^2+(0.40833333333333333333)*log(4)*log(6)^2*log(2)+(0.028026425811895083111)*log(4)*log(2)+(1.6940658945086006781E-19)*Euler^2*log(5)^2+(0.26570641921464570196)*log(4)^2*log(6)-(1.0164395367051604069E-20)*Euler*log(5)^2*log(6)+(1.084202172485504434E-19)*Euler^2*log(6)*log(2)+(0.31666666666666666664)*log(4)^2*log(5)*log(6)+(1.176528763736223171E-18)*Euler^3*log(4)+(3.0323779511703952139E-19)*Euler^2*log(4)*log(5)-(0.19861111111111111116)*log(6)*log(2)*Pi^2-(0.08760610198743753216)*log(4)^3+(0.19513888888888888883)*log(4)*log(2)*Pi^2-(0.17430555555555555551)*log(4)*log(5)*Pi^2+(0.11666666666666666666)*log(4)^2*log(5)^2-(1.084202172485504434E-19)*Euler^2*log(6)+(1.3044307387716225222E-19)*Euler*log(2)+(0.11249999999999999996)*log(5)*log(6)*log(2)^2-(0.26805555555555555557)*log(5)*log(2)^3+(0.13645833333333333334)*log(6)^2*log(2)^2+(0.09795428240740740744)*Pi^4+(0.033333333333333333352)*log(5)^3*log(6) FRESULT num: = 415.68016240483728552+(5.9729895535000929493)*eps^(-1)+(0.24826188972445505333)*eps^(-2)+(0.37833789689847839715)*eps^(-3)+(0.140625)*eps^(-4) eps^-4 term: 0.140625 +/- 0 eps^-3 term: 0.20505604272398455968-(2.8912057932946784908E-20)*Euler+(0.00625)*log(4)+(0.19583333333333333331)*log(5)-(0.018750000000000000007)*log(6)-(0.16875)*log(2) +/- 5.7595906625256782043E-11 eps^-2 term: -1.3333035413347974529-(0.12916666666666666666)*log(4)*log(6)+(1.9274705288631189937E-20)*Euler+(3.3730734255104582391E-20)*Euler*log(6)+(0.121354166666666666677)*Pi^2+(0.014440566261665527283)*log(4)+(0.054166666666666666667)*log(5)*log(6)+(3.08395284618099039E-19)*Euler^2+(0.24693368307448051649)*log(5)-(1.2046690805394493711E-20)*Euler*log(4)-(0.045833333333333333334)*log(4)*log(5)+(0.16666666666666666667)*log(2)^2-(0.0086643397569993163535)*log(6)-(0.025)*log(6)*log(2)-(1.9274705288631189937E-20)*Euler*log(5)+(0.0625)*log(6)^2-(0.27725887222397812377)*log(2)-(0.4)*log(5)*log(2)+(0.07708333333333333334)*log(4)^2+(0.178125)*log(5)^2+(0.029166666666666666667)*log(4)*log(2)+(7.709882115452475975E-20)*Euler*log(2) +/- 2.38034674326464079E-6 eps^-1 term: 1.8223154162344101082-(1.9274705288631189937E-20)*Euler*log(5)^2-(0.17906302164465253826)*log(4)*log(6)-(3.252606517456513302E-20)*Euler+(0.275)*log(4)*log(6)*log(2)-(0.14166666666666666667)*log(4)^2*log(2)-(4.9030031577955589404E-19)*Euler^2*log(2)-(0.029166666666666666667)*log(4)*log(5)^2-(4.336808689942017736E-20)*Euler*log(6)+(0.03125)*log(6)*log(2)^2-(2.4093381610788987422E-20)*Euler*log(4)*log(5)+(2.379221434065412508E-20)*Euler*log(6)*log(2)-(0.25833333333333333333)*log(4)*log(5)*log(6)+(0.17641558449668052497)*Pi^2+(0.12916666666666666666)*log(5)*log(6)^2+(0.018016988021932553424)*log(4)-(0.35625)*log(5)^2*log(2)+(0.04043358553266347639)*log(5)*log(6)+(3.8549410577262379875E-20)*Euler*log(4)*log(6)+(3.2766998990673022894E-19)*Euler^2-(0.64791666666666666673)*zeta(3)-(0.11319444444444444446)*log(2)^3+(0.18467412722480867264)*log(5)+(0.09756944444444444444)*log(6)*Pi^2+(4.8186763221577974843E-21)*Euler*log(4)-(0.040433585532663476392)*log(4)*log(5)+(0.27725887222397812372)*log(2)^2-(0.018016988021932553429)*log(6)+(1.541976423090495195E-19)*Euler^3-(0.07509094456066074186)*log(6)*log(2)+(3.1321396094025683648E-20)*Euler*log(5)-(0.2375)*log(4)*log(6)^2+(0.08953151082232626913)*log(6)^2-(2.168404344971008868E-20)*Euler*log(2)^2+(0.12083333333333333333)*log(4)^2*log(5)-(0.14375)*log(6)^2*log(2)-(0.108333333333333333334)*log(5)*log(6)*log(2)-(0.17116138620835925754)*log(2)+(2.0238440553062749435E-19)*Euler^2*log(5)-(0.025)*log(4)*log(2)^2-(0.22395833333333333336)*log(2)*Pi^2+(0.23229166666666666667)*log(5)*Pi^2+(0.029166666666666666667)*log(5)^2*log(6)-(2.4093381610788987422E-20)*Euler*log(4)*log(2)-(0.49386736614896103298)*log(5)*log(2)+(0.08541666666666666667)*log(6)^3+(0.08375528431766005821)*log(4)^2+(3.8549410577262379875E-20)*Euler*Pi^2+(0.128125)*log(5)^3+(0.108333333333333333334)*log(4)*log(5)*log(2)+(0.4)*log(5)*log(2)^2-(0.09409722222222222222)*log(4)*Pi^2+(7.709882115452475975E-20)*Euler*log(5)*log(2)+(0.26642844752772897827)*log(5)^2+(0.0750909445606607419)*log(4)*log(2)+(0.22916666666666666667)*log(4)^2*log(6)-(0.080555555555555555553)*log(4)^3+(1.1594939900192200198E-19)*Euler*log(2) +/- 4.3702165714070080051E-4 eps^0 term: 400.22174334151294225-(0.24583333333333333332)*log(4)^2*log(5)*log(2)-(3.3881317890172013563E-21)*Euler*log(5)^2+(7.284483346386982916E-20)*Euler*log(5)*log(6)*log(2)-(0.11210570324758033243)*log(4)*log(6)-(2.1006417091906648409E-19)*Euler*log(5)*log(6)-(8.470329472543003391E-21)*Euler+(1.4484263398048535798E-19)*Euler*log(5)^2*log(2)+(0.34079736377530644382)*log(4)*log(6)*log(2)-(0.17039868188765322194)*log(4)^2*log(2)+(2.2022856628611808816E-20)*Euler*log(4)^3-(4.336808689942017736E-19)*Euler^2*log(2)-(0.066426604803661425496)*log(4)*log(5)^2+(0.014236111111111111113)*log(4)^4+(2.710505431213761085E-20)*Euler*log(6)-(1.1011428314305904408E-19)*Euler*log(6)*Pi^2-(0.25763888888888888888)*log(5)^3*log(2)+(0.09861111111111111112)*log(5)*log(6)^3+(0.07797905781299384727)*log(6)*log(2)^2+(2.168404344971008868E-19)*Euler*log(4)*log(5)-(3.3881317890172013563E-20)*Euler*log(4)^2+(0.058333333333333333313)*log(4)*log(5)^2*log(2)+(1.4696021634862110883E-19)*Euler*log(6)*log(2)-(1.2493735972000930001E-20)*Euler*log(5)^3-(0.32346868426130781108)*log(4)*log(5)*log(6)-(3.1509625637859972613E-19)*Euler^2*log(5)*log(2)-(1.5246593050577406103E-20)*Euler^2*Pi^2+(0.44166666666666666666)*zeta(3)*log(6)+(0.12361655670603724154)*Pi^2+(0.062586805555555555545)*log(5)^4-(2.5410988417629010172E-20)*Euler*log(4)*log(6)^2-(0.020138888888888888871)*log(6)*log(2)^3+(0.164622455382987011)*log(5)*log(6)^2+(0.3583333333333333334)*log(5)^2*log(2)^2-(0.22152777777777777779)*log(4)*log(6)*Pi^2+(0.10729166666666666671)*log(4)^2*Pi^2-(0.031944444444444444437)*log(4)*log(5)^3+(0.0041628081498616184988)*log(4)-(9.5714723039735938315E-20)*Euler*log(4)*log(5)*log(2)+(3.9954857837891737475E-20)*Euler*log(4)^2*log(2)-(0.53574500830779106205)*log(5)^2*log(2)-(2.5199230180815435087E-19)*Euler*zeta(3)+(0.048045301391820142482)*log(5)*log(6)-(4.7433845046240818988E-20)*Euler*log(4)*log(6)-(0.06249999999999999996)*log(5)^2*log(6)*log(2)+(6.168313523040288406E-19)*Euler^2-(0.9097222222222222222)*zeta(3)*log(5)-(1.0464597017620285435)*zeta(3)-(4.539037806098981942E-19)*Euler^3*log(2)-(0.18580195256676311766)*log(2)^3-(2.710505431213761085E-20)*Euler*log(6)^3+(0.08337179655695074824)*log(5)+(0.12755833531137882431)*log(6)*Pi^2+(2.2022856628611808816E-20)*Euler*log(4)*log(5)^2-(1.3552527156068805425E-20)*Euler*log(4)+(0.012326388888888888894)*log(6)^4-(0.4125)*log(4)*zeta(3)-(0.30416666666666666667)*log(4)*log(5)*log(6)^2+(0.49166666666666666665)*log(4)*log(5)*log(6)*log(2)-(0.066666666666666666677)*log(4)*log(6)^3+(4.7433845046240818988E-20)*Euler*log(6)*log(2)^2+(0.14305555555555555555)*log(4)^3*log(2)-(0.046043413833827636543)*log(4)*log(5)-(2.168404344971008868E-19)*Euler*log(6)^2+(0.1721623299873555105)*log(2)^2-(0.0037002739109881053319)*log(6)-(2.3039296165316969223E-19)*Euler^2*log(2)^2+(1.0062751413381088028E-18)*Euler^3-(2.168404344971008868E-19)*Euler^2*log(4)*log(2)-(0.25)*log(5)*log(6)^2*log(2)-(0.030028313369887589065)*log(6)*log(2)-(0.275)*log(4)*log(6)*log(2)^2+(0.13125)*log(4)^2*log(2)^2+(4.0657581468206416275E-20)*Euler*log(5)*log(6)^2-(8.131516293641283255E-20)*Euler*log(5)-(0.2570420794576463856)*log(4)*log(6)^2-(0.47430555555555555555)*log(5)*log(2)*Pi^2+(0.2350694444444444444)*log(5)^2*Pi^2+(0.22569444444444444447)*log(2)^2*Pi^2+(0.05705379540278641918)*log(6)^2+(1.5814418841144177812E-20)*Euler*log(2)^2+(0.16173434213065390554)*log(4)^2*log(5)+(1.5585406229479126239E-19)*Euler^2*log(6)^2-(0.17328679513998632736)*log(6)^2*log(2)+(7.030373462210692814E-20)*Euler*log(4)*log(6)*log(2)-(0.086643397569993163665)*log(5)*log(6)*log(2)-(0.08580010131103669233)*log(2)+(2.2700482986415249087E-19)*Euler^2*log(5)+(0.09999999999999999998)*log(4)^2*log(6)^2-(0.07509094456066074196)*log(4)*log(2)^2-(6.7762635780344027125E-20)*Euler*log(5)*log(2)^2-(0.32876355855725183764)*log(2)*Pi^2+(8.1950437646853557805E-20)*Euler^4-(1.1858461261560204747E-20)*Euler*log(4)*Pi^2+(0.3258754453049187323)*log(5)*Pi^2+(0.06931471805599453092)*log(5)^2*log(6)+(3.642241673193491458E-20)*Euler*log(4)^2*log(6)-(1.7194768829262296883E-19)*Euler*log(4)*log(2)-(0.37135014200760985115)*log(5)*log(2)+(1.1011428314305904408E-19)*Euler*log(2)^3+(0.08375528431766005824)*log(6)^3+(1.8431436932253575378E-18)*Euler^3*log(6)+(0.056423611111111111103)*log(2)^4-(4.0826988057657276343E-19)*Euler^2*log(4)+(0.112499999999999999984)*log(6)^2*Pi^2+(0.18402777777777777775)*log(5)*log(6)*Pi^2-(0.061111111111111111102)*log(4)^3*log(6)-(0.108333333333333333294)*log(4)*log(5)*log(2)^2+(0.020833333333333333319)*log(4)*log(2)^3-(8.131516293641283255E-20)*Euler^2*log(4)^2-(6.7762635780344027125E-21)*Euler*log(4)^2*log(5)+(0.056052851623790166215)*log(4)^2-(2.6893296075324035765E-19)*Euler^2*log(5)*log(6)-(1.626303258728256651E-19)*Euler^3*log(5)+(4.2986922073155742208E-20)*Euler*Pi^2+(0.66666666666666666706)*zeta(3)*log(2)-(0.4083333333333333333)*log(4)^2*log(6)*log(2)+(0.17352747124434741951)*log(5)^3-(0.23333333333333333333)*log(4)*log(5)^2*log(6)+(0.080867171065326952724)*log(4)*log(5)*log(2)-(1.6940658945086006781E-20)*Euler*log(6)^2*log(2)-(0.13125)*log(6)^3*log(2)+(0.49675547940129413833)*log(5)*log(2)^2-(1.3552527156068805425E-20)*Euler*log(4)*log(2)^2+(0.11874999999999999999)*log(5)^2*log(6)^2+(3.8963515573697815597E-20)*Euler*log(5)*Pi^2-(0.10416666666666666666)*log(4)^3*log(5)-(0.1208194043892682449)*log(4)*Pi^2-(7.284483346386982916E-20)*Euler*log(2)*Pi^2+(8.131516293641283255E-20)*Euler*log(5)*log(2)+(0.18042011616407459749)*log(5)^2+(0.40833333333333333333)*log(4)*log(6)^2*log(2)+(0.028026425811895083111)*log(4)*log(2)+(1.6940658945086006781E-19)*Euler^2*log(5)^2+(0.26570641921464570196)*log(4)^2*log(6)-(1.0164395367051604069E-20)*Euler*log(5)^2*log(6)+(1.084202172485504434E-19)*Euler^2*log(6)*log(2)+(0.31666666666666666664)*log(4)^2*log(5)*log(6)+(1.176528763736223171E-18)*Euler^3*log(4)+(3.0323779511703952139E-19)*Euler^2*log(4)*log(5)-(0.19861111111111111116)*log(6)*log(2)*Pi^2-(0.08760610198743753216)*log(4)^3+(0.19513888888888888883)*log(4)*log(2)*Pi^2-(0.17430555555555555551)*log(4)*log(5)*Pi^2+(0.11666666666666666666)*log(4)^2*log(5)^2-(1.084202172485504434E-19)*Euler^2*log(6)+(1.3044307387716225222E-19)*Euler*log(2)+(0.11249999999999999996)*log(5)*log(6)*log(2)^2-(0.26805555555555555557)*log(5)*log(2)^3+(0.13645833333333333334)*log(6)^2*log(2)^2+(0.09795428240740740744)*Pi^4+(0.033333333333333333352)*log(5)^3*log(6) +/- 0.010448924004628639662 */ #endif } catch(std::exception &p) { std::cerr<<"******************************************************************"<<endl; std::cerr<<" >>>ERROR: "<<p.what()<<endl; std::cerr<<"******************************************************************"<<endl; return 1; } return 0; }