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drell_yan_integrands.cpp
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1502 lines (1325 loc) · 101 KB
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#include <iostream>
#include <tgmath.h>
using namespace std;
#include "cuba.h"
class flows {
private:
double p1[4];
double p2[4];
public:
flows(){};
flows(double* np1, double* np2){for(int i=0; i<4; i++){p1[i]=np1[i]; p2[i]=np2[i];}};
double norm(double vx, double vy, double vz){return pow(pow(vx,2.)+pow(vy,2.)+pow(vz,2.),0.5);};
double sp(double vx, double vy, double vz, double wx, double wy, double wz){return vx*wx+vy*wy+vz*wz;}
double flow1(double kx, double ky, double kz, double lx, double ly, double lz, bool var){
if(var==0){
return (p1[0]+p2[0])/(norm(kx,ky,kz)+norm(kx-p1[1]-p2[1],ky-p1[2]-p2[2],kz-p1[3]-p2[3]));
};
if(var==1){
return (p1[0]+p2[0])/(norm(lx,ly,lz)+norm(lx-p1[1]-p2[1],ly-p1[2]-p2[2],lz-p1[3]-p2[3]));
};
return 0;
}
double flow2(double kx, double ky, double kz, double lx, double ly, double lz, bool var){
if(var==0){
return (p1[0]+p2[0])/(norm(kx,ky,kz)+norm(kx-lx,ky-ly,kz-lz)+norm(lx+p1[1]+p2[1],ly+p1[2]+p2[2],lz+p1[3]+p2[3]));
}
if(var==1){
return (p1[0]+p2[0])/(norm(lx,ly,lz)+norm(kx-lx,ky-ly,kz-lz)+norm(kx+p1[1]+p2[1],ky+p1[2]+p2[2],kz+p1[3]+p2[3]));
}
return 0;
}
double flow3(double kx, double ky, double kz, double lx, double ly, double lz){
return -(p1[0]+p2[0])/(-norm(lx,ly,lz)+norm(kx+lx,ky+ly,kz+lz)+norm(kx+p1[1]+p2[1],ky+p1[2]+p2[2],kz+p1[3]+p2[3]));
}
double flow4(double kx, double ky, double kz, double lx, double ly, double lz){
return -(p1[0]+p2[0])/(norm(kx+lx,ky+ly,kz+lz)+norm(kx+lx+p1[1]+p2[1],ky+ly+p1[2]+p2[2],kz+lz+p1[3]+p2[3]));
}
double flow5(double kx, double ky, double kz, double lx, double ly, double lz){
return -(p1[0]+p2[0])/(norm(kx,ky,kz)+norm(lx,ly,lz)+norm(kx+lx+p1[1]+p2[1],ky+ly+p1[2]+p2[2],kz+lz+p1[3]+p2[3]));
}
double flow6(double kx, double ky, double kz, double lx, double ly, double lz){
return -(p1[0]+p2[0])/(norm(lx,ly,lz)+norm(kx-lx+p1[1]+p2[1],ky-ly+p1[2]+p2[2],kz-lz+p1[3]+p2[3]));
}
double flow7(double kx, double ky, double kz, double lx, double ly, double lz){
return (p1[0]+p2[0])/(norm(lx,ly,lz)+norm(kx-lx+p1[1]+p2[1],ky-ly+p1[2]+p2[2],kz-lz+p1[3]+p2[3])-norm(kx,ky,kz));
}
double jacques1(double kx, double ky, double kz, double lx, double ly, double lz, bool var){
if(var==0){
return 2*norm(kx,ky,kz);
}
if(var==1){
return 2*norm(lx,ly,lz);
}
return 0;
}
double jacques2(double kx, double ky, double kz, double lx, double ly, double lz, bool var){
if(var==0){
return norm(kx,ky,kz)+norm(kx-lx,ky-ly,kz-lz)+norm(lx,ly,lz);
}
if(var==1){
return norm(lx,ly,lz)+norm(kx-lx,ky-ly,kz-lz)+norm(kx,ky,kz);
}
return 0;
}
double jacques3(double kx, double ky, double kz, double lx, double ly, double lz){
return abs(-norm(lx,ly,lz)+norm(kx+lx,ky+ly,kz+lz)+norm(kx,ky,kz));
}
double jacques4(double kx, double ky, double kz, double lx, double ly, double lz){
return norm(kx+lx,ky+ly,kz+lz)+norm(kx+lx,ky+ly,kz+lz);
}
double jacques5(double kx, double ky, double kz, double lx, double ly, double lz){
return norm(kx,ky,kz)+norm(lx,ly,lz)+norm(kx+lx,ky+ly,kz+lz);
}
double jacques6(double kx, double ky, double kz, double lx, double ly, double lz){
return norm(lx,ly,lz)+norm(kx-lx,ky-ly,kz-lz);
}
double jacques7(double kx, double ky, double kz, double lx, double ly, double lz){
return abs(norm(lx,ly,lz)+norm(kx-lx,ky-ly,kz-lz)-norm(kx,ky,kz));
}
};
class integrands{
private:
double p1[4];
double p2[4];
double p10;
double p1x;
double p1y;
double p1z;
double p20;
double p2x;
double p2y;
double p2z;
double MUV;
flows f;
double sigma;
double constant;
public:
integrands(double* np1, double* np2, double nMUV, flows nf, double nsigma){for(int i=0; i<4; i++){p1[i]=np1[i]; p2[i]=np2[i];}; f=nf;
p10=p1[0];
p1x=p1[1];
p1y=p1[2];
p1z=p1[3];
p20=p2[0];
p2x=p2[1];
p2y=p2[2];
p2z=p2[3];
MUV=nMUV;
sigma=nsigma;
constant=0.389379*pow(10,9.)*pow(4*2*acos(0.0)/132.507,2.)*(4*2*acos(0.0)*0.118/9)/(pow(2*2*acos(0.0),5.)*4*8*pow(p10*p20-p1x*p2x-p1y*p2y-p1z*p2z,3.));
};
double Power(double x, double c){return pow(x,c);}
double Sqrt(double x){return pow(x,0.5);}
double Abs(double x){return abs(x);}
double dt_num (double k0, double kx, double ky, double kz, double l0, double lx, double ly, double lz){
return 512*(Power(l0,2) - Power(lx,2) - Power(ly,2) - Power(lz,2))*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*
(k0*p20 - kx*p2x - ky*p2y - kz*p2z) - 512*(k0*l0 - kx*lx - ky*ly - kz*lz)*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*
(k0*p20 - kx*p2x - ky*p2y - kz*p2z) - 256*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*
(k0*p20 - kx*p2x - ky*p2y - kz*p2z) + 256*Power(l0*p10 - lx*p1x - ly*p1y - lz*p1z,2)*
(k0*p20 - kx*p2x - ky*p2y - kz*p2z) + 256*(k0*l0 - kx*lx - ky*ly - kz*lz)*
(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*(k0*p20 - kx*p2x - ky*p2y - kz*p2z) -
256*(Power(l0,2) - Power(lx,2) - Power(ly,2) - Power(lz,2))*(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*
(k0*p20 - kx*p2x - ky*p2y - kz*p2z) + 256*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*
Power(k0*p20 - kx*p2x - ky*p2y - kz*p2z,2) - 512*(k0*l0 - kx*lx - ky*ly - kz*lz)*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*
(l0*p20 - lx*p2x - ly*p2y - lz*p2z) + 256*Power(k0*p10 - kx*p1x - ky*p1y - kz*p1z,2)*
(l0*p20 - lx*p2x - ly*p2y - lz*p2z) + 512*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*
(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*(l0*p20 - lx*p2x - ly*p2y - lz*p2z) -
256*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*(l0*p20 - lx*p2x - ly*p2y - lz*p2z) -
256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*
(l0*p20 - lx*p2x - ly*p2y - lz*p2z) + 256*(k0*l0 - kx*lx - ky*ly - kz*lz)*
(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*(l0*p20 - lx*p2x - ly*p2y - lz*p2z) -
256*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(k0*p20 - kx*p2x - ky*p2y - kz*p2z)*(l0*p20 - lx*p2x - ly*p2y - lz*p2z) -
256*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*(k0*p20 - kx*p2x - ky*p2y - kz*p2z)*(l0*p20 - lx*p2x - ly*p2y - lz*p2z) +
512*(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*(k0*p20 - kx*p2x - ky*p2y - kz*p2z)*
(l0*p20 - lx*p2x - ly*p2y - lz*p2z) + 256*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*
Power(l0*p20 - lx*p2x - ly*p2y - lz*p2z,2) + 512*Power(k0*l0 - kx*lx - ky*ly - kz*lz,2)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) - 256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*
(Power(l0,2) - Power(lx,2) - Power(ly,2) - Power(lz,2))*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) -
256*(k0*l0 - kx*lx - ky*ly - kz*lz)*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) -
256*(k0*l0 - kx*lx - ky*ly - kz*lz)*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) +
512*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) -
256*(k0*l0 - kx*lx - ky*ly - kz*lz)*(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) - 256*(k0*l0 - kx*lx - ky*ly - kz*lz)*(k0*p20 - kx*p2x - ky*p2y - kz*p2z)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) - 256*(k0*l0 - kx*lx - ky*ly - kz*lz)*(l0*p20 - lx*p2x - ly*p2y - lz*p2z)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) + 512*(k0*p20 - kx*p2x - ky*p2y - kz*p2z)*(l0*p20 - lx*p2x - ly*p2y - lz*p2z)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) + 256*(k0*l0 - kx*lx - ky*ly - kz*lz)*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)) -
256*(Power(l0,2) - Power(lx,2) - Power(ly,2) - Power(lz,2))*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)) -
256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)) +
256*(k0*l0 - kx*lx - ky*ly - kz*lz)*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)) +
512*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)) -
512*(k0*l0 - kx*lx - ky*ly - kz*lz)*(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)) -
256*(k0*l0 - kx*lx - ky*ly - kz*lz)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z)*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2));
}
double dt_num_UV_left(double k0, double kx, double ky, double kz, double l0, double lx, double ly, double lz){
return (32*(Power(l0,2) - Power(lx,2) - Power(ly,2) - Power(lz,2))*p10*p20)/
Power(Power(kx,2) + Power(ky,2) + Power(kz,2) + Power(MUV,2),1.5) -
(32*l0*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*p20)/Power(Power(kx,2) + Power(ky,2) + Power(kz,2) + Power(MUV,2),1.5) -
(16*p10*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*p20)/Power(Power(kx,2) + Power(ky,2) + Power(kz,2) + Power(MUV,2),1.5) +
(16*l0*(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*p20)/
Power(Power(kx,2) + Power(ky,2) + Power(kz,2) + Power(MUV,2),1.5) +
(16*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*Power(p20,2))/Power(Power(kx,2) + Power(ky,2) + Power(kz,2) + Power(MUV,2),1.5) -
(96*(Power(l0,2) - Power(lx,2) - Power(ly,2) - Power(lz,2))*(-(kx*p1x) - ky*p1y - kz*p1z)*(-(kx*p2x) - ky*p2y - kz*p2z))/
Power(Power(kx,2) + Power(ky,2) + Power(kz,2) + Power(MUV,2),2.5) +
(96*(-(kx*lx) - ky*ly - kz*lz)*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*(-(kx*p2x) - ky*p2y - kz*p2z))/
Power(Power(kx,2) + Power(ky,2) + Power(kz,2) + Power(MUV,2),2.5) +
(48*(-(kx*p1x) - ky*p1y - kz*p1z)*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*(-(kx*p2x) - ky*p2y - kz*p2z))/
Power(Power(kx,2) + Power(ky,2) + Power(kz,2) + Power(MUV,2),2.5) -
(48*(-(kx*lx) - ky*ly - kz*lz)*(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*(-(kx*p2x) - ky*p2y - kz*p2z))/
Power(Power(kx,2) + Power(ky,2) + Power(kz,2) + Power(MUV,2),2.5) -
(48*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*Power(-(kx*p2x) - ky*p2y - kz*p2z,2))/
Power(Power(kx,2) + Power(ky,2) + Power(kz,2) + Power(MUV,2),2.5) -
(32*l0*p10*(l0*p20 - lx*p2x - ly*p2y - lz*p2z))/Power(Power(kx,2) + Power(ky,2) + Power(kz,2) + Power(MUV,2),1.5) +
(16*Power(p10,2)*(l0*p20 - lx*p2x - ly*p2y - lz*p2z))/Power(Power(kx,2) + Power(ky,2) + Power(kz,2) + Power(MUV,2),1.5) +
(96*(-(kx*lx) - ky*ly - kz*lz)*(-(kx*p1x) - ky*p1y - kz*p1z)*(l0*p20 - lx*p2x - ly*p2y - lz*p2z))/
Power(Power(kx,2) + Power(ky,2) + Power(kz,2) + Power(MUV,2),2.5) -
(48*Power(-(kx*p1x) - ky*p1y - kz*p1z,2)*(l0*p20 - lx*p2x - ly*p2y - lz*p2z))/
Power(Power(kx,2) + Power(ky,2) + Power(kz,2) + Power(MUV,2),2.5) +
(96*Power(MUV,2)*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*(l0*p20 - lx*p2x - ly*p2y - lz*p2z))/
Power(Power(kx,2) + Power(ky,2) + Power(kz,2) + Power(MUV,2),2.5) +
(128*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*(l0*p20 - lx*p2x - ly*p2y - lz*p2z))/
Power(Power(kx,2) + Power(ky,2) + Power(kz,2) + Power(MUV,2),1.5) -
(48*Power(MUV,2)*(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*(l0*p20 - lx*p2x - ly*p2y - lz*p2z))/
Power(Power(kx,2) + Power(ky,2) + Power(kz,2) + Power(MUV,2),2.5) -
(64*(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*(l0*p20 - lx*p2x - ly*p2y - lz*p2z))/
Power(Power(kx,2) + Power(ky,2) + Power(kz,2) + Power(MUV,2),1.5) -
(16*p10*p20*(l0*p20 - lx*p2x - ly*p2y - lz*p2z))/Power(Power(kx,2) + Power(ky,2) + Power(kz,2) + Power(MUV,2),1.5) +
(48*(-(kx*p1x) - ky*p1y - kz*p1z)*(-(kx*p2x) - ky*p2y - kz*p2z)*(l0*p20 - lx*p2x - ly*p2y - lz*p2z))/
Power(Power(kx,2) + Power(ky,2) + Power(kz,2) + Power(MUV,2),2.5) -
(96*Power(-(kx*lx) - ky*ly - kz*lz,2)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z))/
Power(Power(kx,2) + Power(ky,2) + Power(kz,2) + Power(MUV,2),2.5) +
(48*(-Power(kx,2) - Power(ky,2) - Power(kz,2))*(Power(l0,2) - Power(lx,2) - Power(ly,2) - Power(lz,2))*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z))/Power(Power(kx,2) + Power(ky,2) + Power(kz,2) + Power(MUV,2),2.5) +
(32*Power(l0,2)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z))/
Power(Power(kx,2) + Power(ky,2) + Power(kz,2) + Power(MUV,2),1.5) -
(16*(Power(l0,2) - Power(lx,2) - Power(ly,2) - Power(lz,2))*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z))/
Power(Power(kx,2) + Power(ky,2) + Power(kz,2) + Power(MUV,2),1.5) -
(16*l0*p10*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z))/Power(Power(kx,2) + Power(ky,2) + Power(kz,2) + Power(MUV,2),1.5) +
(48*(-(kx*lx) - ky*ly - kz*lz)*(-(kx*p1x) - ky*p1y - kz*p1z)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z))/
Power(Power(kx,2) + Power(ky,2) + Power(kz,2) + Power(MUV,2),2.5) -
(48*(-Power(kx,2) - Power(ky,2) - Power(kz,2))*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z))/Power(Power(kx,2) + Power(ky,2) + Power(kz,2) + Power(MUV,2),2.5) -
(48*Power(MUV,2)*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z))/
Power(Power(kx,2) + Power(ky,2) + Power(kz,2) + Power(MUV,2),2.5) -
(48*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z))/
Power(Power(kx,2) + Power(ky,2) + Power(kz,2) + Power(MUV,2),1.5) -
(16*l0*p20*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z))/Power(Power(kx,2) + Power(ky,2) + Power(kz,2) + Power(MUV,2),1.5) +
(48*(-(kx*lx) - ky*ly - kz*lz)*(-(kx*p2x) - ky*p2y - kz*p2z)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z))/
Power(Power(kx,2) + Power(ky,2) + Power(kz,2) + Power(MUV,2),2.5) -
(48*(-Power(kx,2) - Power(ky,2) - Power(kz,2))*(l0*p20 - lx*p2x - ly*p2y - lz*p2z)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z))/Power(Power(kx,2) + Power(ky,2) + Power(kz,2) + Power(MUV,2),2.5) -
(48*Power(MUV,2)*(l0*p20 - lx*p2x - ly*p2y - lz*p2z)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z))/
Power(Power(kx,2) + Power(ky,2) + Power(kz,2) + Power(MUV,2),2.5) -
(48*(l0*p20 - lx*p2x - ly*p2y - lz*p2z)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z))/
Power(Power(kx,2) + Power(ky,2) + Power(kz,2) + Power(MUV,2),1.5) +
(16*l0*p10*(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)))/
Power(Power(kx,2) + Power(ky,2) + Power(kz,2) + Power(MUV,2),1.5) -
(48*(-(kx*lx) - ky*ly - kz*lz)*(-(kx*p1x) - ky*p1y - kz*p1z)*(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)))/
Power(Power(kx,2) + Power(ky,2) + Power(kz,2) + Power(MUV,2),2.5) -
(48*Power(MUV,2)*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)))/
Power(Power(kx,2) + Power(ky,2) + Power(kz,2) + Power(MUV,2),2.5) -
(64*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)))/
Power(Power(kx,2) + Power(ky,2) + Power(kz,2) + Power(MUV,2),1.5);
}
double dt_num_UV_right(double k0, double kx, double ky, double kz, double l0, double lx, double ly, double lz){
return (32*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*p10*p20)/
Power(Power(lx,2) + Power(ly,2) + Power(lz,2) + Power(MUV,2),1.5) -
(32*k0*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*p20)/Power(Power(lx,2) + Power(ly,2) + Power(lz,2) + Power(MUV,2),1.5) -
(16*p10*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*p20)/Power(Power(lx,2) + Power(ly,2) + Power(lz,2) + Power(MUV,2),1.5) +
(16*k0*(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*p20)/
Power(Power(lx,2) + Power(ly,2) + Power(lz,2) + Power(MUV,2),1.5) +
(16*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*Power(p20,2))/Power(Power(lx,2) + Power(ly,2) + Power(lz,2) + Power(MUV,2),1.5) -
(32*k0*p10*(k0*p20 - kx*p2x - ky*p2y - kz*p2z))/Power(Power(lx,2) + Power(ly,2) + Power(lz,2) + Power(MUV,2),1.5) +
(16*Power(p10,2)*(k0*p20 - kx*p2x - ky*p2y - kz*p2z))/Power(Power(lx,2) + Power(ly,2) + Power(lz,2) + Power(MUV,2),1.5) +
(96*Power(MUV,2)*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(k0*p20 - kx*p2x - ky*p2y - kz*p2z))/
Power(Power(lx,2) + Power(ly,2) + Power(lz,2) + Power(MUV,2),2.5) +
(128*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(k0*p20 - kx*p2x - ky*p2y - kz*p2z))/
Power(Power(lx,2) + Power(ly,2) + Power(lz,2) + Power(MUV,2),1.5) +
(96*(-(kx*lx) - ky*ly - kz*lz)*(-(lx*p1x) - ly*p1y - lz*p1z)*(k0*p20 - kx*p2x - ky*p2y - kz*p2z))/
Power(Power(lx,2) + Power(ly,2) + Power(lz,2) + Power(MUV,2),2.5) -
(48*Power(-(lx*p1x) - ly*p1y - lz*p1z,2)*(k0*p20 - kx*p2x - ky*p2y - kz*p2z))/
Power(Power(lx,2) + Power(ly,2) + Power(lz,2) + Power(MUV,2),2.5) -
(48*Power(MUV,2)*(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*(k0*p20 - kx*p2x - ky*p2y - kz*p2z))/
Power(Power(lx,2) + Power(ly,2) + Power(lz,2) + Power(MUV,2),2.5) -
(64*(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*(k0*p20 - kx*p2x - ky*p2y - kz*p2z))/
Power(Power(lx,2) + Power(ly,2) + Power(lz,2) + Power(MUV,2),1.5) -
(16*p10*p20*(k0*p20 - kx*p2x - ky*p2y - kz*p2z))/Power(Power(lx,2) + Power(ly,2) + Power(lz,2) + Power(MUV,2),1.5) +
(96*(-(kx*lx) - ky*ly - kz*lz)*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(-(lx*p2x) - ly*p2y - lz*p2z))/
Power(Power(lx,2) + Power(ly,2) + Power(lz,2) + Power(MUV,2),2.5) -
(96*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*(-(lx*p1x) - ly*p1y - lz*p1z)*(-(lx*p2x) - ly*p2y - lz*p2z))/
Power(Power(lx,2) + Power(ly,2) + Power(lz,2) + Power(MUV,2),2.5) +
(48*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(-(lx*p1x) - ly*p1y - lz*p1z)*(-(lx*p2x) - ly*p2y - lz*p2z))/
Power(Power(lx,2) + Power(ly,2) + Power(lz,2) + Power(MUV,2),2.5) -
(48*(-(kx*lx) - ky*ly - kz*lz)*(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*(-(lx*p2x) - ly*p2y - lz*p2z))/
Power(Power(lx,2) + Power(ly,2) + Power(lz,2) + Power(MUV,2),2.5) +
(48*(-(lx*p1x) - ly*p1y - lz*p1z)*(k0*p20 - kx*p2x - ky*p2y - kz*p2z)*(-(lx*p2x) - ly*p2y - lz*p2z))/
Power(Power(lx,2) + Power(ly,2) + Power(lz,2) + Power(MUV,2),2.5) -
(48*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*Power(-(lx*p2x) - ly*p2y - lz*p2z,2))/
Power(Power(lx,2) + Power(ly,2) + Power(lz,2) + Power(MUV,2),2.5) -
(96*Power(-(kx*lx) - ky*ly - kz*lz,2)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z))/
Power(Power(lx,2) + Power(ly,2) + Power(lz,2) + Power(MUV,2),2.5) +
(48*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*(-Power(lx,2) - Power(ly,2) - Power(lz,2))*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z))/Power(Power(lx,2) + Power(ly,2) + Power(lz,2) + Power(MUV,2),2.5) +
(32*Power(k0,2)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z))/
Power(Power(lx,2) + Power(ly,2) + Power(lz,2) + Power(MUV,2),1.5) -
(16*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z))/
Power(Power(lx,2) + Power(ly,2) + Power(lz,2) + Power(MUV,2),1.5) -
(16*k0*p10*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z))/Power(Power(lx,2) + Power(ly,2) + Power(lz,2) + Power(MUV,2),1.5) -
(48*(-Power(lx,2) - Power(ly,2) - Power(lz,2))*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z))/Power(Power(lx,2) + Power(ly,2) + Power(lz,2) + Power(MUV,2),2.5) -
(48*Power(MUV,2)*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z))/
Power(Power(lx,2) + Power(ly,2) + Power(lz,2) + Power(MUV,2),2.5) -
(48*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z))/
Power(Power(lx,2) + Power(ly,2) + Power(lz,2) + Power(MUV,2),1.5) +
(48*(-(kx*lx) - ky*ly - kz*lz)*(-(lx*p1x) - ly*p1y - lz*p1z)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z))/
Power(Power(lx,2) + Power(ly,2) + Power(lz,2) + Power(MUV,2),2.5) -
(16*k0*p20*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z))/Power(Power(lx,2) + Power(ly,2) + Power(lz,2) + Power(MUV,2),1.5) -
(48*(-Power(lx,2) - Power(ly,2) - Power(lz,2))*(k0*p20 - kx*p2x - ky*p2y - kz*p2z)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z))/Power(Power(lx,2) + Power(ly,2) + Power(lz,2) + Power(MUV,2),2.5) -
(48*Power(MUV,2)*(k0*p20 - kx*p2x - ky*p2y - kz*p2z)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z))/
Power(Power(lx,2) + Power(ly,2) + Power(lz,2) + Power(MUV,2),2.5) -
(48*(k0*p20 - kx*p2x - ky*p2y - kz*p2z)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z))/
Power(Power(lx,2) + Power(ly,2) + Power(lz,2) + Power(MUV,2),1.5) +
(48*(-(kx*lx) - ky*ly - kz*lz)*(-(lx*p2x) - ly*p2y - lz*p2z)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z))/
Power(Power(lx,2) + Power(ly,2) + Power(lz,2) + Power(MUV,2),2.5) +
(16*k0*p10*(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)))/
Power(Power(lx,2) + Power(ly,2) + Power(lz,2) + Power(MUV,2),1.5) -
(48*Power(MUV,2)*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)))/
Power(Power(lx,2) + Power(ly,2) + Power(lz,2) + Power(MUV,2),2.5) -
(64*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)))/
Power(Power(lx,2) + Power(ly,2) + Power(lz,2) + Power(MUV,2),1.5) -
(48*(-(kx*lx) - ky*ly - kz*lz)*(-(lx*p1x) - ly*p1y - lz*p1z)*(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)))/
Power(Power(lx,2) + Power(ly,2) + Power(lz,2) + Power(MUV,2),2.5);
}
double t_channel_num(double k0, double kx, double ky, double kz, double l0, double lx, double ly, double lz){
return -512*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*
(k0*p20 - kx*p2x - ky*p2y - kz*p2z) - 1024*(k0*l0 - kx*lx - ky*ly - kz*lz)*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*
(k0*p20 - kx*p2x - ky*p2y - kz*p2z) + 256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*
(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*(k0*p20 - kx*p2x - ky*p2y - kz*p2z) -
256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*
(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*(k0*p20 - kx*p2x - ky*p2y - kz*p2z) -
512*(k0*l0 - kx*lx - ky*ly - kz*lz)*(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*
(k0*p20 - kx*p2x - ky*p2y - kz*p2z) + 256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*
(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(l0*p20 - lx*p2x - ly*p2y - lz*p2z) +
256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*
(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*(l0*p20 - lx*p2x - ly*p2y - lz*p2z) -
256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) - 512*(k0*l0 - kx*lx - ky*ly - kz*lz)*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) + 256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*
(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) -
256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*(k0*p20 - kx*p2x - ky*p2y - kz*p2z)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) - 512*(k0*l0 - kx*lx - ky*ly - kz*lz)*(k0*p20 - kx*p2x - ky*p2y - kz*p2z)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) + 256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*
(l0*p20 - lx*p2x - ly*p2y - lz*p2z)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) -
256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)) -
512*(k0*l0 - kx*lx - ky*ly - kz*lz)*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)) +
256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2));
}
double t_channel_num_derivative(double k0, double kx, double ky, double kz, double l0, double lx, double ly, double lz){
return (-256*(k0*l0 - kx*lx - ky*ly - kz*lz)*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*p20 -
256*(k0*l0 - kx*lx - ky*ly - kz*lz)*(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*p20 -
256*(k0*l0 - kx*lx - ky*ly - kz*lz)*p10*(k0*p20 - kx*p2x - ky*p2y - kz*p2z) -
1024*k0*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(k0*p20 - kx*p2x - ky*p2y - kz*p2z) -
512*l0*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(k0*p20 - kx*p2x - ky*p2y - kz*p2z) +
256*k0*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*(k0*p20 - kx*p2x - ky*p2y - kz*p2z) -
512*k0*(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*(k0*p20 - kx*p2x - ky*p2y - kz*p2z) -
256*l0*(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*(k0*p20 - kx*p2x - ky*p2y - kz*p2z) +
256*k0*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(l0*p20 - lx*p2x - ly*p2y - lz*p2z) +
256*k0*(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*(l0*p20 - lx*p2x - ly*p2y - lz*p2z) -
256*(k0*l0 - kx*lx - ky*ly - kz*lz)*p10*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) -
512*k0*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) -
256*l0*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) +
256*k0*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) -
256*(k0*l0 - kx*lx - ky*ly - kz*lz)*p20*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) -
512*k0*(k0*p20 - kx*p2x - ky*p2y - kz*p2z)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) -
256*l0*(k0*p20 - kx*p2x - ky*p2y - kz*p2z)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) +
256*k0*(l0*p20 - lx*p2x - ly*p2y - lz*p2z)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) -
256*(k0*l0 - kx*lx - ky*ly - kz*lz)*p10*(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)) -
512*k0*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)) -
256*l0*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)) +
256*k0*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)))/
(Power(k0 + l0,2) - Power(kx + lx,2) - Power(ky + ly,2) - Power(kz + lz,2)) -
(2*(k0 + l0)*(-512*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*
(k0*p20 - kx*p2x - ky*p2y - kz*p2z) - 1024*(k0*l0 - kx*lx - ky*ly - kz*lz)*
(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(k0*p20 - kx*p2x - ky*p2y - kz*p2z) +
256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*
(k0*p20 - kx*p2x - ky*p2y - kz*p2z) - 256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*
(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*(k0*p20 - kx*p2x - ky*p2y - kz*p2z) -
512*(k0*l0 - kx*lx - ky*ly - kz*lz)*(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*
(k0*p20 - kx*p2x - ky*p2y - kz*p2z) + 256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*
(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(l0*p20 - lx*p2x - ly*p2y - lz*p2z) +
256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*
(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*(l0*p20 - lx*p2x - ly*p2y - lz*p2z) -
256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) -
512*(k0*l0 - kx*lx - ky*ly - kz*lz)*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) +
256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) -
256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*(k0*p20 - kx*p2x - ky*p2y - kz*p2z)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) -
512*(k0*l0 - kx*lx - ky*ly - kz*lz)*(k0*p20 - kx*p2x - ky*p2y - kz*p2z)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) +
256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*(l0*p20 - lx*p2x - ly*p2y - lz*p2z)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) -
256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)) -
512*(k0*l0 - kx*lx - ky*ly - kz*lz)*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)) +
256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2))))/
Power(Power(k0 + l0,2) - Power(kx + lx,2) - Power(ky + ly,2) - Power(kz + lz,2),2);
}
double u_channel_num(double k0, double kx, double ky, double kz, double l0, double lx, double ly, double lz){
return 128*(Power(l0,2) - Power(lx,2) - Power(ly,2) - Power(lz,2))*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*
(k0*p20 - kx*p2x - ky*p2y - kz*p2z) - 128*(k0*l0 - kx*lx - ky*ly - kz*lz)*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*
(k0*p20 - kx*p2x - ky*p2y - kz*p2z) - 64*Power(l0*p10 - lx*p1x - ly*p1y - lz*p1z,2)*
(k0*p20 - kx*p2x - ky*p2y - kz*p2z) + 64*(Power(l0,2) - Power(lx,2) - Power(ly,2) - Power(lz,2))*
(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*(k0*p20 - kx*p2x - ky*p2y - kz*p2z) +
128*(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*Power(k0*p20 - kx*p2x - ky*p2y - kz*p2z,2) -
128*(k0*l0 - kx*lx - ky*ly - kz*lz)*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(l0*p20 - lx*p2x - ly*p2y - lz*p2z) +
128*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*
(l0*p20 - lx*p2x - ly*p2y - lz*p2z) + 64*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*
(l0*p20 - lx*p2x - ly*p2y - lz*p2z) - 64*(k0*l0 - kx*lx - ky*ly - kz*lz)*
(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*(l0*p20 - lx*p2x - ly*p2y - lz*p2z) +
64*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*(k0*p20 - kx*p2x - ky*p2y - kz*p2z)*(l0*p20 - lx*p2x - ly*p2y - lz*p2z) +
128*(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*(k0*p20 - kx*p2x - ky*p2y - kz*p2z)*
(l0*p20 - lx*p2x - ly*p2y - lz*p2z) - 64*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*
Power(l0*p20 - lx*p2x - ly*p2y - lz*p2z,2) +
64*Power(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2),2)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) +
128*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*(k0*l0 - kx*lx - ky*ly - kz*lz)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) + 128*Power(k0*l0 - kx*lx - ky*ly - kz*lz,2)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) - 64*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*
(Power(l0,2) - Power(lx,2) - Power(ly,2) - Power(lz,2))*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) +
128*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) + 128*(k0*l0 - kx*lx - ky*ly - kz*lz)*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) + 128*Power(k0*p10 - kx*p1x - ky*p1y - kz*p1z,2)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) + 64*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*
(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) +
64*(k0*l0 - kx*lx - ky*ly - kz*lz)*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) +
128*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) - 64*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*
(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) -
64*(k0*l0 - kx*lx - ky*ly - kz*lz)*(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) + 128*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*
(k0*p20 - kx*p2x - ky*p2y - kz*p2z)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) +
128*(k0*l0 - kx*lx - ky*ly - kz*lz)*(k0*p20 - kx*p2x - ky*p2y - kz*p2z)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) +
128*Power(k0*p20 - kx*p2x - ky*p2y - kz*p2z,2)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) +
64*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*(l0*p20 - lx*p2x - ly*p2y - lz*p2z)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) + 64*(k0*l0 - kx*lx - ky*ly - kz*lz)*(l0*p20 - lx*p2x - ly*p2y - lz*p2z)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) + 128*(k0*p20 - kx*p2x - ky*p2y - kz*p2z)*
(l0*p20 - lx*p2x - ly*p2y - lz*p2z)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) +
64*(Power(l0,2) - Power(lx,2) - Power(ly,2) - Power(lz,2))*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)) +
128*Power(k0*p10 - kx*p1x - ky*p1y - kz*p1z,2)*(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)) -
64*(k0*l0 - kx*lx - ky*ly - kz*lz)*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)) +
128*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)) -
128*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*
(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)) -
128*(k0*l0 - kx*lx - ky*ly - kz*lz)*(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)) -
64*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z)*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)) -
64*(k0*l0 - kx*lx - ky*ly - kz*lz)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z)*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2));
}
double s_channel_num(double k0, double kx, double ky, double kz, double l0, double lx, double ly, double lz){
return -512*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*
(k0*p20 - kx*p2x - ky*p2y - kz*p2z) + 1024*(k0*l0 - kx*lx - ky*ly - kz*lz)*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*
(k0*p20 - kx*p2x - ky*p2y - kz*p2z) - 1024*Power(k0*p10 - kx*p1x - ky*p1y - kz*p1z,2)*
(k0*p20 - kx*p2x - ky*p2y - kz*p2z) - 256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*
(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*(k0*p20 - kx*p2x - ky*p2y - kz*p2z) +
512*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*(k0*p20 - kx*p2x - ky*p2y - kz*p2z) -
256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*
(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*(k0*p20 - kx*p2x - ky*p2y - kz*p2z) +
512*(k0*l0 - kx*lx - ky*ly - kz*lz)*(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*
(k0*p20 - kx*p2x - ky*p2y - kz*p2z) - 1024*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*
(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*(k0*p20 - kx*p2x - ky*p2y - kz*p2z) +
256*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*
(k0*p20 - kx*p2x - ky*p2y - kz*p2z) - 256*Power(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2),2)*
(k0*p20 - kx*p2x - ky*p2y - kz*p2z) - 1024*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*
Power(k0*p20 - kx*p2x - ky*p2y - kz*p2z,2) -
512*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*Power(k0*p20 - kx*p2x - ky*p2y - kz*p2z,2) -
512*(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*Power(k0*p20 - kx*p2x - ky*p2y - kz*p2z,2) -
256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*
(l0*p20 - lx*p2x - ly*p2y - lz*p2z) - 512*Power(k0*p10 - kx*p1x - ky*p1y - kz*p1z,2)*
(l0*p20 - lx*p2x - ly*p2y - lz*p2z) - 256*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*
(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*(l0*p20 - lx*p2x - ly*p2y - lz*p2z) +
512*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(k0*p20 - kx*p2x - ky*p2y - kz*p2z)*(l0*p20 - lx*p2x - ly*p2y - lz*p2z) +
512*(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*(k0*p20 - kx*p2x - ky*p2y - kz*p2z)*
(l0*p20 - lx*p2x - ly*p2y - lz*p2z) - 256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*
(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) +
512*(k0*l0 - kx*lx - ky*ly - kz*lz)*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) -
512*Power(k0*p10 - kx*p1x - ky*p1y - kz*p1z,2)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) +
512*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) - 256*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*
(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) -
256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*(k0*p20 - kx*p2x - ky*p2y - kz*p2z)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) + 512*(k0*l0 - kx*lx - ky*ly - kz*lz)*(k0*p20 - kx*p2x - ky*p2y - kz*p2z)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) - 2048*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*
(k0*p20 - kx*p2x - ky*p2y - kz*p2z)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) -
768*(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*(k0*p20 - kx*p2x - ky*p2y - kz*p2z)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) - 512*Power(k0*p20 - kx*p2x - ky*p2y - kz*p2z,2)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) + 512*(k0*p20 - kx*p2x - ky*p2y - kz*p2z)*
(l0*p20 - lx*p2x - ly*p2y - lz*p2z)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) -
512*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*Power(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z,2) -
512*(k0*p20 - kx*p2x - ky*p2y - kz*p2z)*Power(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z,2) -
256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)) +
512*(k0*l0 - kx*lx - ky*ly - kz*lz)*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)) -
512*Power(k0*p10 - kx*p1x - ky*p1y - kz*p1z,2)*(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)) +
512*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)) -
256*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)) -
1024*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(k0*p20 - kx*p2x - ky*p2y - kz*p2z)*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)) -
256*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*(k0*p20 - kx*p2x - ky*p2y - kz*p2z)*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)) -
256*(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*(k0*p20 - kx*p2x - ky*p2y - kz*p2z)*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)) +
256*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(l0*p20 - lx*p2x - ly*p2y - lz*p2z)*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)) -
768*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z)*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)) -
256*(k0*p20 - kx*p2x - ky*p2y - kz*p2z)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z)*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)) -
256*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*Power(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2),2);
}
double st_channel_num(double k0, double kx, double ky, double kz, double l0, double lx, double ly, double lz){
return 512*(Power(l0,2) - Power(lx,2) - Power(ly,2) - Power(lz,2))*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*
(k0*p20 - kx*p2x - ky*p2y - kz*p2z) - 512*(k0*l0 - kx*lx - ky*ly - kz*lz)*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*
(k0*p20 - kx*p2x - ky*p2y - kz*p2z) + 256*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*
(k0*p20 - kx*p2x - ky*p2y - kz*p2z) - 256*Power(l0*p10 - lx*p1x - ly*p1y - lz*p1z,2)*
(k0*p20 - kx*p2x - ky*p2y - kz*p2z) - 256*(k0*l0 - kx*lx - ky*ly - kz*lz)*
(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*(k0*p20 - kx*p2x - ky*p2y - kz*p2z) +
256*(Power(l0,2) - Power(lx,2) - Power(ly,2) - Power(lz,2))*
(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*(k0*p20 - kx*p2x - ky*p2y - kz*p2z) -
256*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*Power(k0*p20 - kx*p2x - ky*p2y - kz*p2z,2) -
512*(k0*l0 - kx*lx - ky*ly - kz*lz)*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(l0*p20 - lx*p2x - ly*p2y - lz*p2z) -
256*Power(k0*p10 - kx*p1x - ky*p1y - kz*p1z,2)*(l0*p20 - lx*p2x - ly*p2y - lz*p2z) +
512*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*
(l0*p20 - lx*p2x - ly*p2y - lz*p2z) + 256*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*
(l0*p20 - lx*p2x - ly*p2y - lz*p2z) + 256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*
(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*(l0*p20 - lx*p2x - ly*p2y - lz*p2z) -
256*(k0*l0 - kx*lx - ky*ly - kz*lz)*(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*
(l0*p20 - lx*p2x - ly*p2y - lz*p2z) + 256*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(k0*p20 - kx*p2x - ky*p2y - kz*p2z)*
(l0*p20 - lx*p2x - ly*p2y - lz*p2z) + 256*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*(k0*p20 - kx*p2x - ky*p2y - kz*p2z)*
(l0*p20 - lx*p2x - ly*p2y - lz*p2z) - 256*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*
Power(l0*p20 - lx*p2x - ly*p2y - lz*p2z,2) +
512*Power(k0*l0 - kx*lx - ky*ly - kz*lz,2)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) -
256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*
(Power(l0,2) - Power(lx,2) - Power(ly,2) - Power(lz,2))*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) +
256*(k0*l0 - kx*lx - ky*ly - kz*lz)*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) +
256*(k0*l0 - kx*lx - ky*ly - kz*lz)*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) +
256*(k0*l0 - kx*lx - ky*ly - kz*lz)*(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) + 256*(k0*l0 - kx*lx - ky*ly - kz*lz)*(k0*p20 - kx*p2x - ky*p2y - kz*p2z)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) + 256*(k0*l0 - kx*lx - ky*ly - kz*lz)*(l0*p20 - lx*p2x - ly*p2y - lz*p2z)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) + 512*(k0*l0 - kx*lx - ky*ly - kz*lz)*
Power(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z,2) -
256*(k0*l0 - kx*lx - ky*ly - kz*lz)*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)) +
256*(Power(l0,2) - Power(lx,2) - Power(ly,2) - Power(lz,2))*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)) +
256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)) -
256*(k0*l0 - kx*lx - ky*ly - kz*lz)*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)) +
256*(k0*l0 - kx*lx - ky*ly - kz*lz)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z)*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2));
}
double bub_num(double k0, double kx, double ky, double kz, double l0, double lx, double ly, double lz){
return -1024*(k0*l0 - kx*lx - ky*ly - kz*lz)*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(k0*p20 - kx*p2x - ky*p2y - kz*p2z) +
256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*
(k0*p20 - kx*p2x - ky*p2y - kz*p2z) + 512*(k0*l0 - kx*lx - ky*ly - kz*lz)*
(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*(k0*p20 - kx*p2x - ky*p2y - kz*p2z) +
256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*
(l0*p20 - lx*p2x - ly*p2y - lz*p2z) - 256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*
(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*(l0*p20 - lx*p2x - ly*p2y - lz*p2z) +
512*(k0*l0 - kx*lx - ky*ly - kz*lz)*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) -
256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) + 512*(k0*l0 - kx*lx - ky*ly - kz*lz)*(k0*p20 - kx*p2x - ky*p2y - kz*p2z)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) - 256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*
(l0*p20 - lx*p2x - ly*p2y - lz*p2z)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) +
512*(k0*l0 - kx*lx - ky*ly - kz*lz)*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)) -
256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2));
}
double bub_num_derivative(double k0, double kx, double ky, double kz, double l0, double lx, double ly, double lz){
return -((-Sqrt(Power(lx,2) + Power(ly,2) + Power(lz,2)) + p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)))*
(512*(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*
(-(kx*lx) - ky*ly - kz*lz + Sqrt(Power(lx,2) + Power(ly,2) + Power(lz,2))*
(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))))*
(-(kx*p2x) - ky*p2y + p20*(p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))) - kz*p2z) -
1024*(-(kx*lx) - ky*ly - kz*lz + Sqrt(Power(lx,2) + Power(ly,2) + Power(lz,2))*
(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))))*
(-(kx*p1x) - ky*p1y - kz*p1z + p10*(p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))))*
(-(kx*p2x) - ky*p2y + p20*(p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))) - kz*p2z) +
256*(Sqrt(Power(lx,2) + Power(ly,2) + Power(lz,2))*p10 - lx*p1x - ly*p1y - lz*p1z)*
(-Power(kx,2) - Power(ky,2) - Power(kz,2) +
Power(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)),2))*
(-(kx*p2x) - ky*p2y + p20*(p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))) - kz*p2z) -
256*(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*
(-Power(kx,2) - Power(ky,2) - Power(kz,2) +
Power(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)),2))*
(Sqrt(Power(lx,2) + Power(ly,2) + Power(lz,2))*p20 - lx*p2x - ly*p2y - lz*p2z) +
256*(-(kx*p1x) - ky*p1y - kz*p1z + p10*
(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))))*
(-Power(kx,2) - Power(ky,2) - Power(kz,2) +
Power(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)),2))*
(Sqrt(Power(lx,2) + Power(ly,2) + Power(lz,2))*p20 - lx*p2x - ly*p2y - lz*p2z) +
512*(-(kx*lx) - ky*ly - kz*lz + Sqrt(Power(lx,2) + Power(ly,2) + Power(lz,2))*
(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))))*
(-(kx*p1x) - ky*p1y - kz*p1z + p10*(p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))))*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) -
256*(Sqrt(Power(lx,2) + Power(ly,2) + Power(lz,2))*p10 - lx*p1x - ly*p1y - lz*p1z)*
(-Power(kx,2) - Power(ky,2) - Power(kz,2) +
Power(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)),2))*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) +
512*(-(kx*lx) - ky*ly - kz*lz + Sqrt(Power(lx,2) + Power(ly,2) + Power(lz,2))*
(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))))*
(-(kx*p2x) - ky*p2y + p20*(p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))) - kz*p2z)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) -
256*(-Power(kx,2) - Power(ky,2) - Power(kz,2) +
Power(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)),2))*
(Sqrt(Power(lx,2) + Power(ly,2) + Power(lz,2))*p20 - lx*p2x - ly*p2y - lz*p2z)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) +
512*(-(kx*lx) - ky*ly - kz*lz + Sqrt(Power(lx,2) + Power(ly,2) + Power(lz,2))*
(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))))*
(-(kx*p1x) - ky*p1y - kz*p1z + p10*(p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))))*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)) -
256*(Sqrt(Power(lx,2) + Power(ly,2) + Power(lz,2))*p10 - lx*p1x - ly*p1y - lz*p1z)*
(-Power(kx,2) - Power(ky,2) - Power(kz,2) +
Power(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)),2))*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2))))/
(8.*Power(-Power(kx - lx,2) - Power(ky - ly,2) - Power(kz - lz,2) +
Power(-Sqrt(Power(lx,2) + Power(ly,2) + Power(lz,2)) + p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)),2),2)*
Abs(Sqrt(Power(lx,2) + Power(ly,2) + Power(lz,2))*
Power(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)),2)*
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)))) -
((Sqrt(Power(-kx + lx,2) + Power(-ky + ly,2) + Power(-kz + lz,2)) + p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)))*
(256*(-Power(kx,2) - Power(ky,2) - Power(kz,2) +
Power(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)),2))*
(-(lx*p1x) - ly*p1y - lz*p1z + p10*(Sqrt(Power(-kx + lx,2) + Power(-ky + ly,2) + Power(-kz + lz,2)) + p10 +
p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))))*
(-(kx*p2x) - ky*p2y + p20*(p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))) - kz*p2z) +
512*(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*
(-(kx*lx) - ky*ly - kz*lz + (p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)))*
(Sqrt(Power(-kx + lx,2) + Power(-ky + ly,2) + Power(-kz + lz,2)) + p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))))*
(-(kx*p2x) - ky*p2y + p20*(p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))) - kz*p2z) -
1024*(-(kx*p1x) - ky*p1y - kz*p1z + p10*
(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))))*
(-(kx*lx) - ky*ly - kz*lz + (p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)))*
(Sqrt(Power(-kx + lx,2) + Power(-ky + ly,2) + Power(-kz + lz,2)) + p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))))*
(-(kx*p2x) - ky*p2y + p20*(p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))) - kz*p2z) -
256*(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*
(-Power(kx,2) - Power(ky,2) - Power(kz,2) +
Power(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)),2))*
(-(lx*p2x) - ly*p2y + p20*(Sqrt(Power(-kx + lx,2) + Power(-ky + ly,2) + Power(-kz + lz,2)) + p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))) - lz*p2z) +
256*(-(kx*p1x) - ky*p1y - kz*p1z + p10*(p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))))*
(-Power(kx,2) - Power(ky,2) - Power(kz,2) +
Power(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)),2))*
(-(lx*p2x) - ly*p2y + p20*(Sqrt(Power(-kx + lx,2) + Power(-ky + ly,2) + Power(-kz + lz,2)) + p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))) - lz*p2z) -
256*(-Power(kx,2) - Power(ky,2) - Power(kz,2) +
Power(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)),2))*
(-(lx*p1x) - ly*p1y - lz*p1z + p10*(Sqrt(Power(-kx + lx,2) + Power(-ky + ly,2) + Power(-kz + lz,2)) + p10 +
p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))))*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) +
512*(-(kx*p1x) - ky*p1y - kz*p1z + p10*(p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))))*
(-(kx*lx) - ky*ly - kz*lz + (p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)))*
(Sqrt(Power(-kx + lx,2) + Power(-ky + ly,2) + Power(-kz + lz,2)) + p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))))*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) +
512*(-(kx*lx) - ky*ly - kz*lz + (p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)))*
(Sqrt(Power(-kx + lx,2) + Power(-ky + ly,2) + Power(-kz + lz,2)) + p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))))*
(-(kx*p2x) - ky*p2y + p20*(p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))) - kz*p2z)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) -
256*(-Power(kx,2) - Power(ky,2) - Power(kz,2) +
Power(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)),2))*
(-(lx*p2x) - ly*p2y + p20*(Sqrt(Power(-kx + lx,2) + Power(-ky + ly,2) + Power(-kz + lz,2)) + p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))) - lz*p2z)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) -
256*(-Power(kx,2) - Power(ky,2) - Power(kz,2) +
Power(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)),2))*
(-(lx*p1x) - ly*p1y - lz*p1z + p10*(Sqrt(Power(-kx + lx,2) + Power(-ky + ly,2) + Power(-kz + lz,2)) + p10 +
p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))))*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)) +
512*(-(kx*p1x) - ky*p1y - kz*p1z + p10*(p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))))*
(-(kx*lx) - ky*ly - kz*lz + (p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)))*
(Sqrt(Power(-kx + lx,2) + Power(-ky + ly,2) + Power(-kz + lz,2)) + p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))))*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2))))/
(8.*Power(-Power(lx,2) - Power(ly,2) - Power(lz,2) +
Power(Sqrt(Power(-kx + lx,2) + Power(-ky + ly,2) + Power(-kz + lz,2)) + p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)),2),2)*
Abs(Sqrt(Power(-kx + lx,2) + Power(-ky + ly,2) + Power(-kz + lz,2))*
Power(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)),2)*
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)))) +
(-256*(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*p20*
(-Power(kx,2) - Power(ky,2) - Power(kz,2) +
Power(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)),2)) +
256*p20*(-(kx*p1x) - ky*p1y - kz*p1z + p10*
(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))))*
(-Power(kx,2) - Power(ky,2) - Power(kz,2) +
Power(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)),2)) +
256*p10*(-Power(kx,2) - Power(ky,2) - Power(kz,2) +
Power(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)),2))*
(-(kx*p2x) - ky*p2y + p20*(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) +
Power(kz - p1z - p2z,2))) - kz*p2z) +
512*(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*
(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)))*
(-(kx*p2x) - ky*p2y + p20*(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) +
Power(kz - p1z - p2z,2))) - kz*p2z) -
1024*(-(kx*p1x) - ky*p1y - kz*p1z + p10*(p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))))*
(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)))*
(-(kx*p2x) - ky*p2y + p20*(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) +
Power(kz - p1z - p2z,2))) - kz*p2z) -
256*p10*(-Power(kx,2) - Power(ky,2) - Power(kz,2) +
Power(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)),2))*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) -
256*p20*(-Power(kx,2) - Power(ky,2) - Power(kz,2) +
Power(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)),2))*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) +
512*(-(kx*p1x) - ky*p1y - kz*p1z + p10*(p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))))*
(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)))*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) +
512*(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)))*
(-(kx*p2x) - ky*p2y + p20*(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) +
Power(kz - p1z - p2z,2))) - kz*p2z)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) -
256*p10*(-Power(kx,2) - Power(ky,2) - Power(kz,2) +
Power(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)),2))*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)) +
512*(-(kx*p1x) - ky*p1y - kz*p1z + p10*(p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))))*
(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)))*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)))/
(16.*(-Power(lx,2) - Power(ly,2) - Power(lz,2) +
Power(Sqrt(Power(-kx + lx,2) + Power(-ky + ly,2) + Power(-kz + lz,2)) + p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)),2))*
Abs(Sqrt(Power(-kx + lx,2) + Power(-ky + ly,2) + Power(-kz + lz,2))*
Power(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)),2)*
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))));
}
double t_channel_num_2(double k0, double kx, double ky, double kz, double l0, double lx, double ly, double lz){
return -1024*(k0*l0 - kx*lx - ky*ly - kz*lz)*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(k0*p20 - kx*p2x - ky*p2y - kz*p2z) +
256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*
(k0*p20 - kx*p2x - ky*p2y - kz*p2z) - 512*(k0*l0 - kx*lx - ky*ly - kz*lz)*
(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*(k0*p20 - kx*p2x - ky*p2y - kz*p2z) +
256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*
(l0*p20 - lx*p2x - ly*p2y - lz*p2z) + 256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*
(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*(l0*p20 - lx*p2x - ly*p2y - lz*p2z) -
512*(k0*l0 - kx*lx - ky*ly - kz*lz)*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) +
256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) - 512*(k0*l0 - kx*lx - ky*ly - kz*lz)*(k0*p20 - kx*p2x - ky*p2y - kz*p2z)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) + 256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*
(l0*p20 - lx*p2x - ly*p2y - lz*p2z)*(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) -
512*(k0*l0 - kx*lx - ky*ly - kz*lz)*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)) +
256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2));
}
double t_channel_num_derivative_2(double k0, double kx, double ky, double kz, double l0, double lx, double ly, double lz){
return (-2*(k0 + l0)*(-1024*(k0*l0 - kx*lx - ky*ly - kz*lz)*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*
(k0*p20 - kx*p2x - ky*p2y - kz*p2z) + 256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*
(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*(k0*p20 - kx*p2x - ky*p2y - kz*p2z) -
512*(k0*l0 - kx*lx - ky*ly - kz*lz)*(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*
(k0*p20 - kx*p2x - ky*p2y - kz*p2z) + 256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*
(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*(l0*p20 - lx*p2x - ly*p2y - lz*p2z) +
256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*
(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*(l0*p20 - lx*p2x - ly*p2y - lz*p2z) -
512*(k0*l0 - kx*lx - ky*ly - kz*lz)*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) +
256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) -
512*(k0*l0 - kx*lx - ky*ly - kz*lz)*(k0*p20 - kx*p2x - ky*p2y - kz*p2z)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) +
256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*(l0*p20 - lx*p2x - ly*p2y - lz*p2z)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) -
512*(k0*l0 - kx*lx - ky*ly - kz*lz)*(k0*p10 - kx*p1x - ky*p1y - kz*p1z)*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)) +
256*(Power(k0,2) - Power(kx,2) - Power(ky,2) - Power(kz,2))*(l0*p10 - lx*p1x - ly*p1y - lz*p1z)*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2))))/
Power(Power(k0 + l0,2) - Power(kx + lx,2) - Power(ky + ly,2) - Power(kz + lz,2),2);
}
double bub_UV_num(double k0, double kx, double ky, double kz, double l0, double lx, double ly, double lz){
return (((3/(32.*Power(1 + Power(lx,2) + Power(ly,2) + Power(lz,2),2)) -
(3*(Sqrt(1 + Power(lx,2) + Power(ly,2) + Power(lz,2)) - p10 - p20 +
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))))/
(32.*Power(1 + Power(lx,2) + Power(ly,2) + Power(lz,2),2.5)))*
(512*(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*
(-(kx*lx) - ky*ly - kz*lz + Sqrt(1 + Power(lx,2) + Power(ly,2) + Power(lz,2))*
(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))))*
(-(kx*p2x) - ky*p2y + p20*(p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))) - kz*p2z) -
1024*(-(kx*lx) - ky*ly - kz*lz + Sqrt(1 + Power(lx,2) + Power(ly,2) + Power(lz,2))*
(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))))*
(-(kx*p1x) - ky*p1y - kz*p1z + p10*(p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))))*
(-(kx*p2x) - ky*p2y + p20*(p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))) - kz*p2z) +
256*(Sqrt(1 + Power(lx,2) + Power(ly,2) + Power(lz,2))*p10 - lx*p1x - ly*p1y - lz*p1z)*
(-Power(kx,2) - Power(ky,2) - Power(kz,2) +
Power(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)),2))*
(-(kx*p2x) - ky*p2y + p20*(p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))) - kz*p2z) -
256*(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*
(-Power(kx,2) - Power(ky,2) - Power(kz,2) +
Power(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)),2))*
(Sqrt(1 + Power(lx,2) + Power(ly,2) + Power(lz,2))*p20 - lx*p2x - ly*p2y - lz*p2z) +
256*(-(kx*p1x) - ky*p1y - kz*p1z + p10*
(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))))*
(-Power(kx,2) - Power(ky,2) - Power(kz,2) +
Power(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)),2))*
(Sqrt(1 + Power(lx,2) + Power(ly,2) + Power(lz,2))*p20 - lx*p2x - ly*p2y - lz*p2z) +
512*(-(kx*lx) - ky*ly - kz*lz + Sqrt(1 + Power(lx,2) + Power(ly,2) + Power(lz,2))*
(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))))*
(-(kx*p1x) - ky*p1y - kz*p1z + p10*(p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))))*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) -
256*(Sqrt(1 + Power(lx,2) + Power(ly,2) + Power(lz,2))*p10 - lx*p1x - ly*p1y - lz*p1z)*
(-Power(kx,2) - Power(ky,2) - Power(kz,2) +
Power(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)),2))*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) +
512*(-(kx*lx) - ky*ly - kz*lz + Sqrt(1 + Power(lx,2) + Power(ly,2) + Power(lz,2))*
(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))))*
(-(kx*p2x) - ky*p2y + p20*(p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))) - kz*p2z)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) -
256*(-Power(kx,2) - Power(ky,2) - Power(kz,2) +
Power(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)),2))*
(Sqrt(1 + Power(lx,2) + Power(ly,2) + Power(lz,2))*p20 - lx*p2x - ly*p2y - lz*p2z)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) +
512*(-(kx*lx) - ky*ly - kz*lz + Sqrt(1 + Power(lx,2) + Power(ly,2) + Power(lz,2))*
(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))))*
(-(kx*p1x) - ky*p1y - kz*p1z + p10*(p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))))*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)) -
256*(Sqrt(1 + Power(lx,2) + Power(ly,2) + Power(lz,2))*p10 - lx*p1x - ly*p1y - lz*p1z)*
(-Power(kx,2) - Power(ky,2) - Power(kz,2) +
Power(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)),2))*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2))))/
Abs(Power(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)),2)*
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))) +
(2*(-1/(32.*Power(1 + Power(lx,2) + Power(ly,2) + Power(lz,2),1.5)) +
(3*(Sqrt(1 + Power(lx,2) + Power(ly,2) + Power(lz,2)) - p10 - p20 +
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))))/
(64.*Power(1 + Power(lx,2) + Power(ly,2) + Power(lz,2),2)))*
(-256*(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*p20*
(-Power(kx,2) - Power(ky,2) - Power(kz,2) +
Power(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)),2))\
+ 256*p20*(-(kx*p1x) - ky*p1y - kz*p1z +
p10*(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))))*
(-Power(kx,2) - Power(ky,2) - Power(kz,2) +
Power(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)),2))\
+ 256*p10*(-Power(kx,2) - Power(ky,2) - Power(kz,2) +
Power(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)),2))*
(-(kx*p2x) - ky*p2y + p20*(p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))) - kz*p2z) +
512*(Power(p10,2) - Power(p1x,2) - Power(p1y,2) - Power(p1z,2))*
(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)))*
(-(kx*p2x) - ky*p2y + p20*(p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))) - kz*p2z) -
1024*(-(kx*p1x) - ky*p1y - kz*p1z + p10*
(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))))*
(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)))*
(-(kx*p2x) - ky*p2y + p20*(p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))) - kz*p2z) -
256*p10*(-Power(kx,2) - Power(ky,2) - Power(kz,2) +
Power(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)),2))*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) -
256*p20*(-Power(kx,2) - Power(ky,2) - Power(kz,2) +
Power(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)),2))*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) +
512*(-(kx*p1x) - ky*p1y - kz*p1z + p10*
(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))))*
(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)))*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) +
512*(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)))*
(-(kx*p2x) - ky*p2y + p20*(p10 + p20 -
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))) - kz*p2z)*
(p10*p20 - p1x*p2x - p1y*p2y - p1z*p2z) -
256*p10*(-Power(kx,2) - Power(ky,2) - Power(kz,2) +
Power(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)),2))*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2)) +
512*(-(kx*p1x) - ky*p1y - kz*p1z + p10*
(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))))*
(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)))*
(Power(p20,2) - Power(p2x,2) - Power(p2y,2) - Power(p2z,2))))/
Abs(Power(p10 + p20 - Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2)),2)*
Sqrt(Power(kx - p1x - p2x,2) + Power(ky - p1y - p2y,2) + Power(kz - p1z - p2z,2))))/2.;
}
double dt_integrand(double kx, double ky, double kz, double lx, double ly, double lz, int tag){
double e_k=Power(Power(kx,2)+Power(ky,2)+Power(kz,2),0.5);
double e_kl=Power(Power(kx-lx,2)+Power(ky-ly,2)+Power(kz-lz,2),0.5);
double e_l=Power(Power(lx,2)+Power(ly,2)+Power(lz,2),0.5);
if(tag==1){
double dt_virtual_left=dt_num(e_k, kx, ky, kz, e_l, lx, ly, lz)/
(abs(2*e_l*2*e_k*2*(e_l-p10-p20))*
(e_k-e_l-e_kl)*(e_k-e_l+e_kl)*(e_k-p10-p20+e_k)*(-p10-p20))+
dt_num(e_l+e_kl, kx, ky, kz, e_l, lx, ly, lz)/
(abs(2*e_l*2*(e_l-p10-p20)*2*(e_kl))*
(e_l+e_kl-e_k)*(e_l+e_kl+e_k)*(e_l+e_kl-p10-p20-e_k)*(e_l+e_kl-p10-p20+e_k))+
dt_num(p10+p20+e_k, kx, ky, kz, e_l, lx, ly, lz)/
(abs(2*e_l*2*(e_l-p10-p20)*2*(e_k))*
(p10+p20)*(p10+p20+e_k+e_k)*(p10+p20+e_k-e_l-e_kl)*(p10+p20+e_k-e_l+e_kl)
);
return dt_virtual_left;
};
if(tag==2){
double dt_virtual_right=dt_num(e_k, kx, ky, kz, e_l, lx, ly, lz)/
(abs(2*e_k*2*(e_k-p10-p20)*2*e_l)*
(e_k-e_l-e_kl)*(e_k-e_l+e_kl)*(-p10-p20)*(-p10-p20+2*e_l))+
dt_num(e_k, kx, ky, kz, e_k+e_kl, lx, ly, lz)/
(abs(2*e_k*2*(e_k-p10-p20)*2*(e_kl))*
(e_k+e_kl-p10-p20-e_l)*(e_k+e_kl-p10-p20+e_l)*(e_k+e_kl-e_l)*(e_k+e_kl+e_l))+
dt_num(e_k, kx, ky, kz, e_l+p10+p20, lx, ly, lz)/
(abs(2*e_k*2*(e_k-p10-p20)*2*(e_l))*
(p10+p20)*(p10+p20+2*e_l)*(e_k-e_l-p10-p20-e_kl)*(e_k-e_l-p10-p20+e_kl)
);
return dt_virtual_right;
};
if(tag==3){
double dt_real_right=dt_num(e_k, kx, ky, kz, -e_l+p10+p20, lx, ly, lz)/
(abs(2*e_k*2*(p20+p10-e_l-e_k)*2*(e_l))*
(-p10-p20)*(-p10-p20+2*e_k)*(p10+p20)*(p10+p20-2*e_l)
);
return dt_real_right;
};
if(tag==4){
double dt_real_left=dt_num(p10+p20-e_k, kx, ky, kz, e_l, lx, ly, lz)/
(abs(2*e_l*2*(-e_l-e_k+p10+p20)*2*(e_k))*
(-p10-p20)*(-p10-p20+2*e_l)*(p10+p20)*(p10+p20-2*e_k)
);
return dt_real_left;
};
if(tag==5){
double dt_left_uv=dt_num_UV_left(0, kx, ky, kz, e_l, lx, ly, lz)/
(abs(2*e_l*2*(e_l-p10-p20))
);
return dt_left_uv;
};
if(tag==6){
double dt_right_uv=dt_num_UV_right(e_k, kx, ky, kz, 0, lx, ly, lz)/
(abs(2*e_k*2*(e_k-p10-p20))