attachment:flipper_nf_conversion.py of days96

   1 r"""
   2 This module provides a simple function to convert flipper
   3 number field elements into Sage number field elements.
   4 
   5 EXAMPLES::
   6 
   7     sage: import flipper
   8     sage: import flipper_nf_conversion
   9 
  10     sage: S = flipper.load('S_2_1')
  11     sage: h = S.mapping_class('acBD')
  12     sage: F = h.flat_structure()
  13     sage: x = F.edge_vectors.values()[0].x
  14     sage: flipper_nf_conversion.flipper_nf_element_to_sage(x)
  15     2*a^3 - 14*a^2 + 26*a - 14
  16 """
  17 
  18 from sage.rings.all import ZZ, QQ, AA, RIF, NumberField
  19 
  20 def flipper_nf_to_sage(K, name='a'):
  21     r"""
  22     Convert a flipper number field to Sage.
  23 
  24     .. NOTE::
  25 
  26         Currently, the code is not careful at all with root isolation.
  27     """
  28     r = K.lmbda.interval_approximation()
  29     l = r.lower * ZZ(10)**(-r.precision)
  30     u = r.upper * ZZ(10)**(-r.precision)
  31 
  32     p = QQ['x'](K.polynomial.coefficients)
  33     s = AA.polynomial_root(p, RIF(l,u))
  34     return NumberField(p, name, embedding=s)
  35 
  36 def flipper_nf_element_to_sage(x):
  37     r"""
  38     Convert a flipper nf element to Sage.
  39     """
  40     return flipper_nf_to_sage(x.number_field)(x.linear_combination)