NZMATH  1.2.0 About: NZMATH is a Python based number theory oriented calculation system.   Fossies Dox: NZMATH-1.2.0.tar.gz  ("inofficial" and yet experimental doxygen-generated source code documentation)
nzmath.module.Ideal Class Reference
Inheritance diagram for nzmath.module.Ideal:
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## 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

lcm = Module.intersect

## Private Member Functions

def _precompute_for_different (cls, number_field)

__doc__

## Additional Inherited Members

Public Attributes inherited from nzmath.module.Module
number_field

base

denominator

mat_repr

## Detailed Description

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

Definition at line 666 of file module.py.

## ◆ __init__()

 def nzmath.module.Ideal.__init__ ( self, pair_mat_repr, number_field, 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 module.py.

## ◆ __pow__()

 def nzmath.module.Ideal.__pow__ ( self, other )
self ** other (based on ideal multiplication)

Reimplemented from nzmath.module.Module.

Definition at line 683 of file module.py.

## ◆ _precompute_for_different()

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

Definition at line 721 of file module.py.

## ◆ inverse()

 def nzmath.module.Ideal.inverse ( self )
Return the inverse ideal of self

Definition at line 696 of file module.py.

## ◆ isIntegral()

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

Definition at line 755 of file module.py.

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

## ◆ isPrime()

 def nzmath.module.Ideal.isPrime ( self )
determine whether self is prime ideal or not

Definition at line 762 of file module.py.

## ◆ 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 module.py.

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

## ◆ twoElementRepresentation()

 def nzmath.module.Ideal.twoElementRepresentation ( self )

Definition at line 740 of file module.py.

## ◆ __doc__

 nzmath.module.Ideal.__doc__
staticprivate

Definition at line 694 of file module.py.

## ◆ gcd

static

Definition at line 680 of file module.py.

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

## ◆ issubideal

 nzmath.module.Ideal.issubideal = Module.issubmodule
static

Definition at line 677 of file module.py.

## ◆ issuperideal

 nzmath.module.Ideal.issuperideal = Module.issupermodule
static

Definition at line 678 of file module.py.

## ◆ lcm

 nzmath.module.Ideal.lcm = Module.intersect
static

Definition at line 681 of file module.py.

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