Package sage :: Package algebras :: Module quatalg :: Class Order_QQ
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Class Order_QQ

Lattice --+    
          |    
 Lattice_QQ --+
              |
Lattice --+   |
          |   |
      Order --+
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             Order_QQ


Method Summary
  commutator_ideal(self)
Return the two-sides ideal of this order generated by elements of the form x*y - y*x.
  is_definite(self)
  is_isomorphic(self, other)
  left_ideal(self, v)
Returns the left ideal generated by the sequence of elements of the list v.
  left_ideal_classes(self)
Return a list of representatives for the left locally-free ideal classes of self.
  prime_ideal(self, p)
Returns the unique 2-sided prime ideal P this order S over the prime pZ.
  right_ideal(self, v)
Returns the right ideal generated by the sequence of elements of the list v.
  right_ideal_classes(self)
Return a list of representatives for the right locally-free ideal classes of self.
  two_sided_ideal_classes(self)
Return a list of representatives for the two-sided locally-free ideal classes of self.
  unit_group(self)
  units(self)
Returns a list of representatives for the units in self modulo the unit group of the base ring.
    Inherited from Lattice_QQ
  gram_matrix(self)
Return the Gram matrix with respect to the norm on the basis.
  reduced_basis(self)
Return a Minkowski-reduced basis for self.
  reduced_gram_matrix(self)
Return the unique Minkowski-reduced Gram matrix.
    Inherited from Order
  __init__(self, R, v)
  __repr__(self)
  base_ring(self)
  level(self)

Method Details

commutator_ideal(self)

Return the two-sides ideal of this order generated by elements of the form x*y - y*x.

left_ideal(self, v)

Returns the left ideal generated by the sequence of elements of the list v.

left_ideal_classes(self)

Return a list of representatives for the left locally-free ideal classes of self. The quaternion algebra must be definite.

prime_ideal(self, p)

Returns the unique 2-sided prime ideal P this order S over the prime pZ. If p is a ramified prime then P properly contains pS and need not be principal; otherwise P is equal to p*S.

right_ideal(self, v)

Returns the right ideal generated by the sequence of elements of the list v.

right_ideal_classes(self)

Return a list of representatives for the right locally-free ideal classes of self. The quaternion algebra must be definite.

two_sided_ideal_classes(self)

Return a list of representatives for the two-sided locally-free ideal classes of self. The quaternion algebra must be definite.

units(self)

Returns a list of representatives for the units in self modulo the unit group of the base ring.

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