u=-(2^62 + 2^55 +1)

p=36*u^4+36*u^3+24*u^2+6*u+1
r=36*u^4+36*u^3+18*u^2+6*u+1
t=6*u^2+1
#-------------- Fp--------------
Fp=GF(p)
#-------------------------------
b=2
#--------------Fp^2--------------
K2.<i>=PolynomialRing(Fp)
Fp2.<i>=FiniteField(p^2,modulus=i^2+1)
#------------------------------------
#-------------Fp^6---------------------
K6.<v>=PolynomialRing(Fp2)
Fp6.<v>=Fp2.extension(v^3-i-1)
#-------------------------------------

#---------------Fp^12-------------------

K12.<z>=PolynomialRing(Fp6)
Fp12.<z>=Fp6.extension(z^2-v)
Fp12.is_field=lambda:True
#---------------------------------------

f1=Fp12.random_element()

f=(f1^(p^6-1))^(p^2+1)

#algorithm 7: New variant of Devegili et al.
def algorithm_7 (f,u):
    
     t0=f^(-2*u)
     t1=t0^2
     t0=t0*t1
     t1=f^(-1)
     t1=t0*t1
     t2=(t1)^p

     t1=t1^2
     t1=t1*t2

     t2=t0^(-u)
     t0=t2^2
     t0=t0^p
     t1=t1*t0

     t2=t2*f
     t0=t2^(p^2)
     t1=t0*t1

     t0=t2^(-6*u-5)
     t1=t1*t0

     t0=t0^p
     t1=t1*t0

     t0=f^2
     t2=t0^2
     t2=t2*f
     t1=t2*t1

     t2=t2*t0
     t2=t2^p
     t1=t1*t2

     t2=f^(p^3)
     t1=t1*t2
     
     return t1

algorithm_7 (f,u)==f^((p^4-p^2+1)/r)

#algorithm 8 : precomputations for new addition chain

t0=f^(-u)
y3=t0^2
y0=t0*y3
y2=y3^p
y2=y3*y2
y2=y2^2
y2=y2*y3
     
t0=y0^(-u)
y0=f^(-1)
y1=t0^(p^2)
y1=y0*y1
t0=t0^(-1)
y3=t0^p
y3=t0*y3
t0=t0^2
y1=t0*y1
     
t0=y3^(-u)
t0=t0^2
t0=t0^(-1)
y3=t0*y3
    
t0=f^p
y0=f^(p^2)
y0=t0*y0
t0=f^(p^3)
y0=t0*y0

y0==f^p*f^(p^2)*f^(p^3)

y1==(f^(3*u^2))^(p^2)*f^(-1)*f^(-6*u^2)

y2==(f^p*f)^(-4*u)*f^(-2*u)

y3==(f^p*f)^(-6*u^3)*(f^p*f)^(-3*u^2)

#algorithm 9: New addition chain

def algorithm_9(f,u):
    t0=f^(-u)
    y3=t0^2
    y0=t0*y3
    y2=y3^p
    y2=y3*y2
    y2=y2^2
    y2=y2*y3
     
    t0=y0^(-u)
    y0=f^(-1)
    y1=t0^(p^2)
    y1=y0*y1
    t0=t0^(-1)
    y3=t0^p
    y3=t0*y3
    t0=t0^2
    y1=t0*y1
     
    t0=y3^(-u)
    t0=t0^2
    t0=t0^(-1)
    y3=t0*y3
    
    t0=f^p
    y0=f^(p^2)
    y0=t0*y0
    t0=f^(p^3)
    y0=t0*y0
    
    t0=y3^2
    t0=t0*y2
    y3=t0*y0
    t0=t0*y1
    t0=t0^2
    t0=t0*y3
    
    return t0

algorithm_9(f,u)==f^((p^4-p^2+1)/r)

#algorithm10: New Variant of Fuentes et al

def algorithm_10(f,u):
    t0=f^(-u)
    t0=t0^2
    t2=t0^(-u)
    t1=t2^2
    t2=t2*t1
    t2=t2*f
    
    t1=t2^(-2*u-1)
    t3=t1^(-1)
    t1=t0^2
    t1=t1*f
    t1=t1^(-1)
    t1=t1*t3
    
    t0=t0*t1
    t2=t2*t1
    t3=t1^(p^2)
    t2=t2*t3
    
    t3=f^(-1)
    t3=t0*t3
    t1=t3^(p^3)
    
    t2=t2*t1
    t1=t0^p
    
    t1=t2*t1
    
    return t1

#algorithm11: New multiple of d

def algorithm_11(f,u):
    t0=f^(-u)
    t0=t0^2
    t1=t0^2
    t0=t0*t1
    t1=f*t0
    t2=f^2
    t2=t2^2
    t2=t2*t1
    t2=t2^(-1)
    t2=t2^(p^3)
    
    t1=t1^2
    t1=t1*f
    t1=t1^(-1)
    t1=t1^(p^2)
    t1=t1*t2
    
    t2=t0^(-u)
    t2=f*t2
    t1=t1*t2
    
    t0=t2^(-1)
    t2=t0^(p^3)
    t1=t1*t2
    
    t2=t0^(-6*u-4)
    t0=t2^(p^2)
    t1=t1*t0
    
    t2=t0^p
    t1=t1*t2
    
    t0=f^p
    t1=t1*t0
    return t1

algorithm_11(f,u)==(f^((p^4-p^2+1)/r))^(36*u^3+18*u^2+6*u+1)

For the arithmetic in the finite fields Fp2, Fp6 and Fp12 please consult  this link: https://cloud.sagemath.com/#projects/332de229-174f-4d90-ae79-ca9d3b0fc1f7/files/arithmetic.sagews