NZMATH  1.2.0
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nzmath.module.Ideal Class Reference
Inheritance diagram for nzmath.module.Ideal:
Collaboration diagram for nzmath.module.Ideal:

Public Member Functions

def __init__ (self, pair_mat_repr, number_field, base=None, ishnf=False)
def __pow__ (self, other)
def inverse (self)
def twoElementRepresentation (self)
def norm (self)
def isIntegral (self)
def isPrime (self)
- Public Member Functions inherited from nzmath.module.Module
def toHNF (self)
def __repr__ (self)
def __str__ (self)
def __eq__ (self, other)
def __ne__ (self, other)
def __contains__ (self, other)
def __add__ (self, other)
def __mul__ (self, other)
def copy (self)
def intersect (self, other)
def issubmodule (self, other)
def issupermodule (self, other)
def represent_element (self, other)
def change_base_module (self, other_base)
def index (self)
def smallest_rational (self)

Static Public Attributes

 issubideal = Module.issubmodule
 issuperideal = Module.issupermodule
 gcd = Module.__add__
 lcm = Module.intersect

Private Member Functions

def _precompute_for_different (cls, number_field)

Static Private Attributes


Additional Inherited Members

- Public Attributes inherited from nzmath.module.Module

Detailed Description

for computing ideal with HNF (as Z-module).

Definition at line 666 of file

Constructor & Destructor Documentation

◆ __init__()

def nzmath.module.Ideal.__init__ (   self,
  base = None,
  ishnf = False 
Ideal is subclass of Module.
Please refer to Module.__init__.__doc__

Reimplemented from nzmath.module.Module.

Definition at line 670 of file

Member Function Documentation

◆ __pow__()

◆ _precompute_for_different()

def nzmath.module.Ideal._precompute_for_different (   cls,
Return T such that T^-1 represents HNF of inverse of different (codifferent)

Definition at line 721 of file

References nzmath.module.Module._base_multiplication(), nzmath.module._symmetric_element(), and nzmath.bigrange.range().

◆ inverse()

◆ isIntegral()

def nzmath.module.Ideal.isIntegral (   self)
determine whether self is integral ideal or not

Definition at line 755 of file

References nzmath.module.Module.change_base_module(), and nzmath.module.Module.number_field.

Referenced by nzmath.module.Ideal.isPrime().

◆ isPrime()

◆ norm()

def nzmath.module.Ideal.norm (   self)
return the norm of self
(Note that Norm(I)=[Z_K : I] for an ideal I and an integral ring Z_K)

Definition at line 746 of file

References nzmath.module.Module.change_base_module(), nzmath.module.Module.index(), and nzmath.module.Module.number_field.

Referenced by nzmath.module.Ideal.isPrime().

◆ twoElementRepresentation()

def nzmath.module.Ideal.twoElementRepresentation (   self)

Definition at line 740 of file

Member Data Documentation

◆ __doc__


Definition at line 694 of file

◆ gcd

nzmath.module.Ideal.gcd = Module.__add__

Definition at line 680 of file

Referenced by nzmath.rational.IntegerRing.lcm().

◆ issubideal

nzmath.module.Ideal.issubideal = Module.issubmodule

Definition at line 677 of file

◆ issuperideal

nzmath.module.Ideal.issuperideal = Module.issupermodule

Definition at line 678 of file

◆ lcm

nzmath.module.Ideal.lcm = Module.intersect

Definition at line 681 of file

The documentation for this class was generated from the following file: