Class RigidAnalyticFunction_disc

x.__init__(...) initializes x; see x.__class__.__doc__ for signature

Overrides: object.__init__

Returns:

a new object with type S, a subtype of T

Overrides: structure.sage_object.SageObject.__new__

File: sage/rings/padics/rigid_functions.pyx (starting at line 57)

Returns the base ring of this function.

Will eventually be replaced by element's method.

File: sage/rings/padics/rigid_functions.pyx (starting at line 99)

Returns the object defining the coefficients of self.  This object should satisfy the following specifications.

self.coeffs().__iter__() returns an iterator over the coefficients of self (an object that has a next method and iter returns self).  The coefficients should be elements of self.base_ring()
self.coeffs()[i] returns the coefficient of x^i.  The coefficients should be elements of self.base_ring().
self.coeffs().start_term() returns smallest i so that the coefficient of x^i is nonzero.
self.coeffs().valuation(i) returns the valuation of self.coeffs()[i]
self.coeffs().denom_iter() returns an iterator over the denominators of the coefficients of self.
self.coeffs().numer_iter() returns an iterator over the numerators of the coefficients of self.  The nth term of numer_iter divided by the nth term of denom_iter, cast into the base ring, should be the nth term of iter.
self.coeffs().denom(i) returns the denominator of self.coeffs()[i]
self.coeffs().numer(i) returns the numerator of self.coeffs()[i]
self.coeffs().numer_all_one() returns True iff the numerators of all coefficients are 1 after the start_term.
self.coeffs().denom_all_one() returns True iff the denominators of all coefficients are 1 after the start term.

File: sage/rings/padics/rigid_functions.pyx (starting at line 89)

Returns the logarithmic offset of self.

If n = log_order, L = log_of_radius and C = log_offset, then the valuation of the ith coefficient
(normalized so that the valuation of p is 1) must be bounded below by 
i*L - n*log_p(i) - C

File: sage/rings/padics/rigid_functions.pyx (starting at line 79)

Returns the logarithmic order of self.

If n = self.log_order() and C = self.log_offset(), then the valuation of the ith coefficient
(normalized so that the valuation of p is 1) is bounded below by 
i*L - n*log_p(i) - C

File: sage/rings/padics/rigid_functions.pyx (starting at line 149)

Returns the indices needed to compute the value of this function to absolute precision absprec if the input has valuation val.

INPUT:
  self -- a RigidAnalyticFunction_disc
  absprec -- the absolute precision desired of the answer.
  val -- the valuation of the element which is being plugged in (normalized so that the valuation of the uniformizer of the base ring is 1) [default None].  Defaults to the minimum valuation that's strictly greater than -self.log_of_radius() * self.base_ring().e()
  empty_list -- boolean (default False).  Whether to use self.coeffs() to decrease max_contiguous and put outliers into L.  If True, does not do so.
OUTPUT:
  max_contiguous -- non-negative integer.  Use the iterator for indices 0 <= i < max_contiguous
  L -- list of non-negative integers.  The additional terms needed that affect the return value below absolute precision absprec.

File: sage/rings/padics/rigid_functions.pyx (starting at line 264)

        

File: sage/rings/padics/rigid_functions.pyx (starting at line 194)

Returns the valuation of this function when evaluated on something of valuation input_valuation.

Neglects possible cancellation (so this is a lower bound on the valuation of the answer) and with valuation normalized so that the valuation of the uniformizer is 1.

File: sage/rings/padics/rigid_functions.pyx (starting at line 71)

Returns the radius of the disc on which this function converges.

This radius may be larger than the radius of convergence of the parent.

File: sage/rings/padics/rigid_functions.pyx (starting at line 139)

Returns a lower bound on the valuation of a_i * x^i when x has valuation i, as an RIF.

If val is infinity, returns RIF(0)

File: sage/rings/padics/rigid_functions.pyx (starting at line 252)

Returns an index i that is within 1 of the one that minimizes the function i * (input_valuation + e * log_p(r)) - e * n * log_p(i) - e * C

If input_valuation is infinity, returns RIF(0.5)