In[1]: M = Manifold('m004')

In[2]: G = M.fundamental_group?
Docstring:
Manifold.fundamental_group(self, simplify_presentation=True, fillings_may_affect_generators=True, minimize_number_of_generators=True, try_hard_to_shorten_relators=True)

In[3]: G = M.fundamental_group()

In[4]: G
Out[4]:
Generators:
   a,b
Relators:
   aaabABBAb

In[5]: m=G.meridian(); G.meridian()
Out[5]: 'ab'

In[6]: l=G.longitude(); G.longitude()
Out[6]: 'aBAbABab'

In[7]: M.dehn_fill((5,1),0)

In[8]: H = M.fundamental_group(fillings_may_affect_generators=False)

In[9]: H
Out[9]:
Generators:
   a,b
Relators:
   aaabABBAb
   ababababababaBAbAB

def egcd(r, s):
   if r == 0:
     return (s, 0, 1)
   else:
     g, x, y = egcd(s % r, r)
     return (g, y - (b // a) * x, x)