Package sage :: Package rings :: Module padic_field :: Class pAdicField
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Class pAdicField

Ring --+
       |
      pAdicField


Field Q_p of p-adic numbers.
Method Summary
  __init__(self, p)
  __call__(self, x)
Coerce x into the ring.
  __cmp__(self, other)
  __repr__(self)
  characteristic(self)
The characteristic of the field Qp, which is always 0.
  is_field(self)
This function always returns true, because Qp is a field.
  name(self)
  prec(self, n)
  prime(self)
The prime p such that this is the field Qp.
  print_prec(self, n)
If you call print_prec(n), then printing of elements in this p-adic field is truncated at O(p^n).
  random(self, prec)
A random integral element of Q_p to precision O(p**prec).
  residue_characteristic(self)
The characteristic of the residue class field Qp.
  residue_class_field(self)
The residue class field of the ring Zp of integers of Qp, i.e., the field Z/pZ.
  series_print(self, n)
    Inherited from Ring
  __hash__(self)
  is_atomic_repr(self)
True if the elements have atomic string representations, in the sense that they print if they print at s, then -s means the negative of s.
  type(self)

Method Details

__call__(self, x, prec=Infinity)
(Call operator)

Coerce x into the ring.
Overrides:
sage.rings.ring.Ring.__call__ (inherited documentation)

characteristic(self)

The characteristic of the field Qp, which is always 0. >>> K = Qp(7) >>> K.characteristic() 0
Overrides:
sage.rings.ring.Ring.characteristic

is_field(self)

This function always returns true, because Qp is a field. >>> K = Qp(7) >>> K.is_field() True
Overrides:
sage.rings.ring.Ring.is_field

prime(self)

The prime p such that this is the field Qp. >>> K = Qp(7) >>> K.prime() 7

print_prec(self, n=None)

If you call print_prec(n), then printing of elements in this p-adic field is truncated at O(p^n). Calling print_prec() with no arguments returns n. This command only affects printing, and does not alter the actual values of elements of this field.

random(self, prec=10)

A random integral element of Q_p to precision O(p**prec).

residue_characteristic(self)

The characteristic of the residue class field Qp. >>> K = Qp(7) >>> K.residue_characteristic() 7

residue_class_field(self)

The residue class field of the ring Zp of integers of Qp, i.e., the field Z/pZ. >>> K = Qp(3) >>> K.residue_class_field() Z/3Z

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