attachment:find_gamma.sage of days22/wuthrich

   1 def Gamma(E,r):
   2    alpha = r.numerator()
   3    beta = r.denominator()
   4    N = E.conductor()
   5    newcusp=0
   6    epsilon=var('epsilon')
   7    if gcd(beta,N) == 1:
   8        [c,d] = xgcd(N*alpha,beta)[1:3]
   9        c=-c
  10        d=-d
  11        Gamma = matrix(ZZ,[[-beta,alpha],[c*N,d]])
  12        #Gamma = Gamma0(N)([-beta,alpha,c*N,d])
  13        A = 0
  14        B = 1
  15        [C,D] = xgcd(-B,A)[1:3]
  16        M = matrix(ZZ,[[A,B],[C,D]])
  17        #M = SL2Z([A,C,B,D])
  18        M = M.transpose()
  19 
  20 
  21 
  22        Q = N/B
  23 
  24        #[x,y] = xgcd(Q^2,N)[1:3]
  25 
  26        #x = -x/A
  27        #y=-y
  28 
  29        #wQ = matrix(ZZ,[[Q*x,y],[N,-A*Q]])
  30 
  31        print solve(epsilon == 1/Q * imag(SL2Z(M.inverse()).acton(SL2Z(Gamma).acton(r+i*epsilon)) ), epsilon)
  32 
  33    else:
  34        [c,d] = xgcd(N*alpha,beta)[1:3]
  35        [a,b] = xgcd(d,-c*N)[1:3]
  36        newcusp = (a*alpha + b*beta)/(c*N*alpha + d*beta)
  37        Gamma = matrix(ZZ,[[a,b],[c*N,d]])
  38        #Gamma = Gamma0(N)([-beta,alpha,c*N,d])
  39        A = newcusp.numerator()
  40        B = newcusp.denominator()
  41        [C,D] = xgcd(-B,A)[1:3]
  42        M = matrix(ZZ,[[A,B],[C,D]])
  43        #M = SL2Z([A,C,B,D])
  44        M = M.transpose()
  45 
  46        Q = N/B
  47 
  48        #[x,y] = xgcd(Q^2,N)[1:3]
  49 
  50        #x = -x/A
  51        #y=-y
  52 
  53        #wQ = matrix(ZZ,[[Q*x,y],[N,-A*Q]])
  54 
  55        print solve(epsilon == 1/Q * imag(SL2Z(M.inverse()).acton(SL2Z(Gamma).acton(r+i*epsilon)) ), epsilon)
  56 
  57 
  58 
  59    return [Gamma,newcusp]