Coverage for local/lib/python2.7/site-packages/sage/rings/padics/qadic_flint_CR.pyx : 59%

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

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

include "CR_template.pxi" 

cdef class PowComputer_(PowComputer_flint_unram): 

""" 

A PowComputer for a capped-relative unramified ring or field. 

""" 

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> = ZqCR(125) 

sage: type(R.prime_pow) 

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

sage: R.prime_pow._prec_type 

'capped-rel' 

""" 

self._prec_type = 'capped-rel' 

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

cdef class qAdicCappedRelativeElement(CRElement): 

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)``. 

Raises an error if ``self`` has negative valuation. 

EXAMPLES:: 

sage: R.<a> = QqCR(5^5,5) 

sage: b = (5 + 15*a)^3 

sage: b.matrix_mod_pn() 

[ 125 1125 3375 3375 0] 

[ 0 125 1125 3375 3375] 

[380500 377125 125 1125 3375] 

[380500 367000 377125 125 1125] 

[387250 376000 367000 377125 125] 

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

True 

sage: M.base_ring() 

Ring of integers modulo 125 

Check that :trac:`13617` has been fixed:: 

sage: R(0).matrix_mod_pn() 

[0 0 0 0 0] 

[0 0 0 0 0] 

[0 0 0 0 0] 

[0 0 0 0 0] 

[0 0 0 0 0] 

""" 

if self.ordp < 0: 

raise ValueError("self must be integral") 

if exactzero(self.ordp): 

from sage.matrix.all import matrix 

return matrix(ZZ, self.prime_pow.deg, self.prime_pow.deg) 

else: 

return cmatrix_mod_pn(self.unit, self.ordp + self.relprec, self.ordp, self.prime_pow) 

def _flint_rep(self, var='x'): 

""" 

Replacement for _ntl_rep for use in printing and debugging. 

EXAMPLES:: 

sage: R.<a> = Qq(27, 4) 

sage: (~(1+a))._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.unit, var) 

def _flint_rep_abs(self, var='x'): 

""" 

Replacement for _ntl_rep_abs for use in printing and debugging. 

EXAMPLES:: 

sage: R.<a> = Qq(27, 4) 

sage: (~(3+3*a))._flint_rep_abs() 

(41*x^2 + 40*x + 42, -1) 

sage: (3+3*a)*(41*a^2+40*a+42) 

3 + O(3^5) 

sage: (3+3*a)._flint_rep_abs() 

(3*x + 3, 0) 

""" 

if self.ordp < 0: 

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

cshift(self.prime_pow.poly_flint_rep, self.unit, self.ordp, self.ordp + self.relprec, self.prime_pow, False) 

return self.prime_pow._new_fmpz_poly(self.prime_pow.poly_flint_rep, var), Integer(0) 

def __hash__(self): 

r""" 

Raise a ``TypeError`` since this element is not hashable 

(:trac:`11895`.) 

TESTS:: 

sage: K.<a> = Qq(9) 

sage: hash(a) 

Traceback (most recent call last): 

... 

TypeError: unhashable type: 'sage.rings.padics.qadic_flint_CR.qAdicCappedRelativeElement' 

""" 

# Eventually, hashing will be disabled for all (non-fixed-mod) p-adic 

# elements (#11895), until then, we only to this for types which did 

# not support hashing before we switched some elements to FLINT 

raise TypeError("unhashable type: 'sage.rings.padics.qadic_flint_CR.qAdicCappedRelativeElement'")