4.5.1.8 Order_QQ Objects

class Order_QQ
Instances of class Order_QQ have the following methods (in addition to inherited methods and special methods):

commutator_ideal,$  $ left_ideal,$  $ left_ideal_classes,$  $ prime_ideal,$  $ right_ideal,$  $ right_ideal_classes,$  $ two_sided_ideal_classes,$  $ units

These methods are defined as follows:

commutator_ideal( )

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

left_ideal( v)

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

left_ideal_classes( )

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

prime_ideal( 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( v)

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

right_ideal_classes( )

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

two_sided_ideal_classes( )

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

units( )

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

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