/usr/include/Lfunction/Ldokchitser.h is in liblfunction-dev 1.23+dfsg-5.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 | #ifndef Ldokchitser_H
#define Ldokchitser_H
//finding the explicit taylor series for \phi(t) using Dokchitser algo
#define MYDIGITS 5 // estimate of precision ... will be set using the precision variable
void mult_poly_taylor(Complex *, Complex *, Complex *, int );
template <class ttype>
void L_function <ttype>::
phi_series(int precision)
{
cout << "-----------------------------------------------"<< endl << endl;
cout << "phi series for " << name << " L_function" << endl << endl;
int j,k;
// constructing the equivalence classes Lambda[k] for k = 1 to N
int pordtmp[a+1];
Complex diff;
Complex *lambda_k;
int *l;
for (j=1;j<=a;j++)
pordtmp[j]= 1;
for (j=1;j<=a;j++)
for (k=1;k<=a;k++)
if (j != k)
{
diff = 2*(lambda[j] - lambda[k]);
if((imag(diff)==0) && (fmod(real(diff),2) == 0) && (real(diff)<=0))
{
pordtmp[j]+=pordtmp[k];
pordtmp[k]=0;
}
}
Complex temp_lambda_k[a];
int temp_l[a];
j=1;
for (k=1;k<=a;k++)
if (pordtmp[k]!=0)
{
temp_lambda_k[j]= lambda[k];
temp_l[j]=pordtmp[k];
j++;
}
int N = j-1;
lambda_k = new Complex[N+1];
l = new int[N+1];
for (j=1;j<=N;j++)
{
lambda_k[j] = temp_lambda_k[j];
l[j] = temp_l[j];
}
cout << "-----------------------------------------------"<< endl << endl;
cout << "There are "<< N << " equivalence classes Lambda[j]"<<endl;
cout<< "The equivalence classes Lambda[j] for poles are represented by"<<endl;
for (j=1;j<=N;j++)
{
cout << "lambda_k["<<j<<"] = "<< lambda_k[j] << " with order l["<<j<<"] = "<<l[j]<<endl;
}
cout<<endl;
// compute the values m[j] for the respective lambda_k[j]
Complex m[N+1];
for (j=1;j<=N;j++)
m[j] = -2*lambda_k[j] + 2;
// compute sum_{k=1}^a log Gamma((s+m[j]+2*lambda[k])/2) for each j
int n,fact_n;
Complex log_Gamma[N+1][a+1][MYDIGITS+1];
Complex sum_log_Gamma[N+1][MYDIGITS+1];
for (j=1;j<=N;j++)
for (n=0;n<=MYDIGITS;n++)
sum_log_Gamma[j][n] = 0;
for (j=1;j<=N;j++)
{
for (k=1;k<=a;k++)
{
fact_n = 1;
for (n=0;n<=MYDIGITS;n++)
{
if (n!=0)
fact_n = fact_n*n;
log_Gamma[j][k][n] = pow(0.5,n)*(log_GAMMA((m[j]/2 + lambda[k]),n))/fact_n;
sum_log_Gamma[j][n] = sum_log_Gamma[j][n] + log_Gamma[j][k][n];
}
}
}
cout << endl;
// compute the exponential taylor series for gamma = exp(sum_log_Gamma)
Complex exp_sum_log_Gamma[N+1][MYDIGITS+1][MYDIGITS+1]; // symmetric functions
Complex gamma[N+1][MYDIGITS+1]; // gamma(s+m[j]) for j = 1 to N
Complex temp_gamma[MYDIGITS+1];
Complex temp_mult_gamma[MYDIGITS+1];
Complex temp_exp_sum_log_Gamma[MYDIGITS+1];
int fact_n_k;
for (j=1;j<=N;j++)
{
for (n=0;n<=MYDIGITS;n++)
exp_sum_log_Gamma[j][0][n] = 0;
exp_sum_log_Gamma[j][0][0] = exp(sum_log_Gamma[j][0]);
for (k=1;k<=MYDIGITS;k++)
{
fact_n_k = 1;
for (n=0;n<=MYDIGITS;n++)
{
if(n%k == 0)
{
if (n/k != 0)
fact_n_k = fact_n_k*(n/k);
exp_sum_log_Gamma[j][k][n] = pow(sum_log_Gamma[j][k],n/k)/fact_n_k;
}
else
exp_sum_log_Gamma[j][k][n] = 0;
}
}
}
for (j=1;j<=N;j++)
{
for (n=0;n<=MYDIGITS;n++)
temp_mult_gamma[n] = exp_sum_log_Gamma[j][0][n];
for (k=1;k<=MYDIGITS;k++)
{
for (n=0;n<=MYDIGITS;n++)
{
temp_exp_sum_log_Gamma[n] = exp_sum_log_Gamma[j][k][n];
temp_gamma[n] = temp_mult_gamma[n];
}
mult_poly_taylor(temp_gamma,temp_exp_sum_log_Gamma,temp_mult_gamma,MYDIGITS);
}
for (n=0;n<=MYDIGITS;n++)
gamma[j][n] = temp_mult_gamma[n];
}
cout << "-----------------------------------------------"<< endl;
cout << "The gamma(s+m[j]) coefficients are as follows"<< endl<<endl;
for(j=1;j<=N;j++)
{
cout<<"gamma(s+m["<<j<<"]) = "<<"gamma(s+"<<m[j]<<") = "<<gamma[j][0];
for (n=1;n<=MYDIGITS;n++)
cout << " + " << gamma[j][n] <<" s^"<<n;
cout<<endl;
}
cout << "-----------------------------------------------"<< endl;
}
#endif
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