nzmath.ring.CommutativeRingElement Class Reference

Inheritance diagram for nzmath.ring.CommutativeRingElement:

Collaboration diagram for nzmath.ring.CommutativeRingElement:

Public Member Functions
def	__init__ (self)
def	mul_module_action (self, other)
def	exact_division (self, other)
Public Member Functions inherited from nzmath.ring.RingElement
def	__init__ (self, *args, **kwd)
def	getRing (self)
def	__eq__ (self, other)
def	__hash__ (self)
def	__ne__ (self, other)

Detailed Description

CommutativeRingElement is an abstract class for elements of
commutative rings.

Definition at line 291 of file ring.py.

Constructor & Destructor Documentation

__init__()

def nzmath.ring.CommutativeRingElement.__init__

(

self

)

This class is abstract and cannot be instantiated.

Reimplemented in nzmath.poly.uniutil.RingElementProvider, nzmath.ring.FieldElement, nzmath.poly.multiutil.RingElementProvider, and nzmath.finitefield.FiniteFieldElement.

Definition at line 297 of file ring.py.

Member Function Documentation

exact_division()

def nzmath.ring.CommutativeRingElement.exact_division	(		self,
			other
	)

In UFD, if other divides self, return the quotient as a UFD
element.  The main difference with / is that / may return the
quotient as an element of quotient field.

Simple cases:
- in a euclidean domain, if remainder of euclidean division
  is zero, the division // is exact.
- in a field, there's no difference with /.

If other doesn't divide self, raise ValueError.

Reimplemented in nzmath.ring.FieldElement.

Definition at line 320 of file ring.py.

References nzmath.poly.ratfunc.RationalFunction.getRing(), nzmath.poly.multiutil.RingElementProvider.getRing(), nzmath.real.Real.getRing(), nzmath.finitefield.FinitePrimeFieldElement.getRing(), nzmath.imaginary.Complex.getRing(), nzmath.intresidue.IntegerResidueClass.getRing(), nzmath.ring.RingElement.getRing(), nzmath.poly.multiutil.RingPolynomial.getRing(), nzmath.finitefield.ExtendedFieldElement.getRing(), nzmath.rational.Rational.getRing(), nzmath.algfield.BasicAlgNumber.getRing(), nzmath.algfield.MatAlgNumber.getRing(), nzmath.rational.Integer.getRing(), nzmath.matrix.RingSquareMatrix.getRing(), nzmath.poly.uniutil.RingElementProvider.getRing(), and nzmath.poly.uniutil.RingPolynomial.getRing().

mul_module_action()

def nzmath.ring.CommutativeRingElement.mul_module_action	(		self,
			other
	)

Return the result of a module action.
other must be in one of the action rings of self's ring.

Definition at line 305 of file ring.py.

References nzmath.poly.ratfunc.RationalFunction.getRing(), nzmath.poly.multiutil.RingElementProvider.getRing(), nzmath.real.Real.getRing(), nzmath.finitefield.FinitePrimeFieldElement.getRing(), nzmath.imaginary.Complex.getRing(), nzmath.intresidue.IntegerResidueClass.getRing(), nzmath.ring.RingElement.getRing(), nzmath.poly.multiutil.RingPolynomial.getRing(), nzmath.finitefield.ExtendedFieldElement.getRing(), nzmath.rational.Rational.getRing(), nzmath.algfield.BasicAlgNumber.getRing(), nzmath.algfield.MatAlgNumber.getRing(), nzmath.rational.Integer.getRing(), nzmath.matrix.RingSquareMatrix.getRing(), nzmath.poly.uniutil.RingElementProvider.getRing(), and nzmath.poly.uniutil.RingPolynomial.getRing().

Referenced by nzmath.intresidue.IntegerResidueClass.__mul__(), nzmath.ring.QuotientFieldElement.__mul__(), and nzmath.intresidue.IntegerResidueClass.__rmul__().

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

• nzmath/ring.py