Package sage :: Package algebras :: Package old :: Module quatalg :: Class Algebra_QQ
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Class Algebra_QQ

Gens --+    
       |    
Ring --+    
       |    
 Algebra --+
           |
          Algebra_QQ


Method Summary
  discriminant(self)
  is_definite(self)
  is_indefinite(self)
  maximal_order(self)
Return a maximal order.
  quaternion_order(self, M)
Return a maximal order.
  ramified_primes(self)
    Inherited from Algebra
  __init__(self, K, a, b, gens)
Create the quaternion algebra over the field K with generators i and j and relations i^2 = a, j^2 = b, and i*j=-j*i.
  __call__(self, x)
Coerce x into the ring.
  __cmp__(self, other)
  __contains__(self, x)
  __repr__(self)
  assign_names(self, s)
  base_field(self)
  base_ring(self)
  basis(self)
  characteristic(self)
  constants(self)
  gen(self, i)
  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.
  is_field(self)
  name(self)
  names(self)
  ngens(self)
  random(self, bound)
  set_gens(self, g)
Changes the chosen generators of self.
  vector_space(self)
    Inherited from Ring
  __hash__(self)
  type(self)
    Inherited from Gens
  __getattr__(self, attrname)
  __getitem__(self, n)
  __getslice__(self, n, m)
  gens(self)
  list(self)

Method Details

maximal_order(self)

Return a maximal order.

quaternion_order(self, M=1)

Return a maximal order.

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