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.ring.Ideal Class Reference
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## Public Member Functions

def __init__ (self, generators, aring)

def __add__ (self, other)

def __mul__ (self, other)

def __eq__ (self, other)

def __hash__ (self)

def __ne__ (self, other)

def __contains__ (self, element)

def issubset (self, other)

def issuperset (self, other)

def reduce (self, element)

ring

generators

## Detailed Description

```Ideal class is an abstract class to represent the finitely
generated ideals.  Because the finitely-generatedness is not a
restriction for Noetherian rings and in the most cases only
Noetherian rings are used, it is general enough.
```

Definition at line 460 of file ring.py.

## ◆ __init__()

 def nzmath.ring.Ideal.__init__ ( self, generators, aring )
```Ideal(generators, ring) creates an ideal of the ring genarated
by the generators.  generators must be an element of the ring
or a list of elements of the ring.
```

Reimplemented in nzmath.poly.ring.PolynomialIdeal, and nzmath.poly.multiutil.PolynomialIdeal.

Definition at line 468 of file ring.py.

## Member Function Documentation

 def nzmath.ring.Ideal.__add__ ( self, other )
```I + J <=> I.__add__(J)

where I+J = {i+j | i in I and j in J}
```

Definition at line 484 of file ring.py.

## ◆ __contains__()

 def nzmath.ring.Ideal.__contains__ ( self, element )
```e in I  <=>  I.__contains__(e)

for e in the ring, to which the ideal I belongs.
```

Reimplemented in nzmath.poly.multiutil.PolynomialIdeal, and nzmath.poly.ring.PolynomialIdeal.

Definition at line 528 of file ring.py.

## ◆ __eq__()

 def nzmath.ring.Ideal.__eq__ ( self, other )
```I == J <=> I.__eq__(J)
```

Definition at line 508 of file ring.py.

Referenced by nzmath.ring.Ideal.__ne__().

## ◆ __hash__()

 def nzmath.ring.Ideal.__hash__ ( self )

Definition at line 519 of file ring.py.

## ◆ __mul__()

 def nzmath.ring.Ideal.__mul__ ( self, other )
```I * J <=> I.__mul__(J)

where I*J = {sum of i*j | i in I and j in J}
```

Definition at line 495 of file ring.py.

## ◆ issubset()

 def nzmath.ring.Ideal.issubset ( self, other )
```Report whether another ideal contains this ideal.
```

Reimplemented in nzmath.poly.ring.PolynomialIdeal.

Definition at line 536 of file ring.py.

Referenced by nzmath.ring.Ideal.__eq__().

## ◆ issuperset()

 def nzmath.ring.Ideal.issuperset ( self, other )
```Report whether this ideal contains another ideal.
```

Reimplemented in nzmath.poly.ring.PolynomialIdeal.

Definition at line 544 of file ring.py.

Referenced by nzmath.ring.Ideal.__eq__().

## ◆ reduce()

 def nzmath.ring.Ideal.reduce ( self, element )
```Reduce an element with the ideal to simpler representative.
```

Reimplemented in nzmath.poly.ring.PolynomialIdeal.

Definition at line 552 of file ring.py.

## ◆ generators

 nzmath.ring.Ideal.generators

Definition at line 478 of file ring.py.

Referenced by nzmath.ring.Ideal.__add__(), and nzmath.ring.Ideal.__mul__().

## ◆ ring

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