Coverage for local/lib/python2.7/site-packages/sage/rings/padics/qadic_flint_FM.pyx : 42%

include "sage/libs/linkages/padics/fmpz_poly_unram.pxi" 

include "sage/libs/linkages/padics/unram_shared.pxi" 

include "FM_template.pxi" 

cdef class PowComputer_(PowComputer_flint_unram): 

""" 

A PowComputer for a fixed-modulus unramified ring. 

""" 

def __init__(self, Integer prime, long cache_limit, long prec_cap, long ram_prec_cap, bint in_field, poly=None): 

""" 

Initialization. 

EXAMPLES:: 

sage: R.<a> = ZqFM(125) 

sage: type(R.prime_pow) 

<type 'sage.rings.padics.qadic_flint_FM.PowComputer_'> 

sage: R.prime_pow._prec_type 

'fixed-mod' 

""" 

self._prec_type = 'fixed-mod' 

PowComputer_flint_unram.__init__(self, prime, cache_limit, prec_cap, ram_prec_cap, in_field, poly) 

cdef class qAdicFixedModElement(FMElement): 

frobenius = frobenius_unram 

trace = trace_unram 

norm = norm_unram 

def matrix_mod_pn(self): 

""" 

Returns the matrix of right multiplication by the element on 

the power basis `1, x, x^2, \ldots, x^{d-1}` for this 

extension field. Thus the *rows* of this matrix give the 

images of each of the `x^i`. The entries of the matrices are 

IntegerMod elements, defined modulo ``p^(self.absprec() / e)``. 

EXAMPLES:: 

sage: R.<a> = ZqFM(5^5,5) 

sage: b = (5 + 15*a)^3 

sage: b.matrix_mod_pn() 

[ 125 1125 250 250 0] 

[ 0 125 1125 250 250] 

[2375 2125 125 1125 250] 

[2375 1375 2125 125 1125] 

[2875 1000 1375 2125 125] 

sage: M = R(0,3).matrix_mod_pn(); M == 0 

True 

sage: M.base_ring() 

Ring of integers modulo 3125 

""" 

return cmatrix_mod_pn(self.value, self.prime_pow.prec_cap, 0, self.prime_pow) 

def _flint_rep(self, var='x'): 

""" 

Replacement for _ntl_rep for use in printing and debugging. 

EXAMPLES:: 

sage: R.<a> = ZqFM(27, 4) 

sage: (1+a).inverse_of_unit()._flint_rep() 

41*x^2 + 40*x + 42 

sage: (1+a)*(41*a^2+40*a+42) 

1 + O(3^4) 

""" 

return self.prime_pow._new_fmpz_poly(self.value, var) 

def _flint_rep_abs(self, var='x'): 

""" 

Replacement for _ntl_rep_abs for use in printing and debugging. 

EXAMPLES:: 

sage: R.<a> = ZqFM(27, 4) 

sage: (3+3*a)._flint_rep_abs() 

(3*x + 3, 0) 

""" 

return self._flint_rep(var), Integer(0)