NZMATH  1.2.0
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nzmath.matrix.MatrixRing Class Reference
Inheritance diagram for nzmath.matrix.MatrixRing:
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Collaboration diagram for nzmath.matrix.MatrixRing:
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Public Member Functions

def __init__ (self, size, scalars)
 
def __eq__ (self, other)
 
def __hash__ (self)
 
def __repr__ (self)
 
def __str__ (self)
 
def getInstance (cls, size, scalars)
 
def unitMatrix (self)
 
def zeroMatrix (self)
 
def createElement (self, compo)
 
def getCharacteristic (self)
 
def issubring (self, other)
 
def issuperring (self, other)
 
def getCommonSuperring (self, other)
 
- Public Member Functions inherited from nzmath.ring.Ring
def __init__ (self)
 
def __ne__ (self, other)
 

Public Attributes

 size
 
 scalars
 

Properties

 one = property(_getOne, None, None, "multiplicative unit")
 
 zero = property(_getZero, None, None, "additive unit")
 

Private Member Functions

def _getOne (self)
 
def _getZero (self)
 

Private Attributes

 __class__
 
 _one
 
 _zero
 

Static Private Attributes

dictionary _instances = {}
 

Detailed Description

MatrixRing is a class for matrix rings.

Definition at line 1586 of file matrix.py.

Constructor & Destructor Documentation

◆ __init__()

def nzmath.matrix.MatrixRing.__init__ (   self,
  size,
  scalars 
)
MatrixRing(size, scalars)

size: size of matrices (positive integer)
scalars: ring of scalars

Definition at line 1593 of file matrix.py.

Member Function Documentation

◆ __eq__()

◆ __hash__()

def nzmath.matrix.MatrixRing.__hash__ (   self)

Reimplemented from nzmath.ring.Ring.

Definition at line 1612 of file matrix.py.

References nzmath.matrix.MatrixRing.scalars, and nzmath.matrix.MatrixRing.size.

◆ __repr__()

def nzmath.matrix.MatrixRing.__repr__ (   self)

Definition at line 1615 of file matrix.py.

References nzmath.matrix.MatrixRing.scalars, and nzmath.matrix.MatrixRing.size.

◆ __str__()

def nzmath.matrix.MatrixRing.__str__ (   self)

Definition at line 1618 of file matrix.py.

References nzmath.matrix.MatrixRing.scalars, and nzmath.matrix.MatrixRing.size.

◆ _getOne()

◆ _getZero()

◆ createElement()

def nzmath.matrix.MatrixRing.createElement (   self,
  compo 
)
Return a newly created matrix from 'compo'.

'compo' must be a list of n*n components in the scalar ring,
where n = self.size.

Reimplemented from nzmath.ring.Ring.

Definition at line 1667 of file matrix.py.

References nzmath.matrix.createMatrix(), nzmath.matrix.MatrixRing.scalars, and nzmath.matrix.MatrixRing.size.

Referenced by nzmath.finitefield.FiniteField.random_element(), and nzmath.finitefield.FiniteField.TonelliShanks().

◆ getCharacteristic()

def nzmath.matrix.MatrixRing.getCharacteristic (   self)
Return the characteristic of the ring.

Reimplemented from nzmath.ring.Ring.

Definition at line 1676 of file matrix.py.

References nzmath.matrix.MatrixRing.scalars.

◆ getCommonSuperring()

def nzmath.matrix.MatrixRing.getCommonSuperring (   self,
  other 
)
Return common super ring of self and another ring.

Reimplemented from nzmath.ring.Ring.

Definition at line 1703 of file matrix.py.

References nzmath.matrix.MatrixRing.scalars, and nzmath.matrix.MatrixRing.size.

◆ getInstance()

def nzmath.matrix.MatrixRing.getInstance (   cls,
  size,
  scalars 
)
Return the cached instance of the specified matrix ring.  If
the specified ring is not cached, it is created, cached and
returned.

The method is a class method.

Definition at line 1622 of file matrix.py.

References nzmath.finitefield.FinitePrimeField._instances, nzmath.intresidue.IntegerResidueClassRing._instances, and nzmath.matrix.MatrixRing._instances.

◆ issubring()

def nzmath.matrix.MatrixRing.issubring (   self,
  other 
)
Report whether another ring contains the ring as a subring.

Reimplemented from nzmath.ring.Ring.

Definition at line 1682 of file matrix.py.

References nzmath.matrix.MatrixRing.scalars, and nzmath.matrix.MatrixRing.size.

Referenced by nzmath.ring.Ring.getCommonSuperring(), nzmath.rational.RationalField.getCommonSuperring(), and nzmath.rational.IntegerRing.getCommonSuperring().

◆ issuperring()

◆ unitMatrix()

◆ zeroMatrix()

Member Data Documentation

◆ __class__

nzmath.matrix.MatrixRing.__class__
private

Definition at line 1608 of file matrix.py.

Referenced by nzmath.imaginary.Complex.__add__(), nzmath.vector.Vector.__add__(), nzmath.real.Real.__add__(), nzmath.poly.multivar.TermIndices.__add__(), nzmath.intresidue.IntegerResidueClass.__add__(), nzmath.module.Module.__add__(), nzmath.ring.QuotientFieldElement.__add__(), nzmath.ring.Ideal.__add__(), nzmath.ring.ResidueClass.__add__(), nzmath.poly.multivar.BasicPolynomial.__call__(), nzmath.imaginary.Complex.__div__(), nzmath.intresidue.IntegerResidueClass.__div__(), nzmath.quad.ReducedQuadraticForm.__eq__(), nzmath.real.RealField.__eq__(), nzmath.poly.multivar.TermIndices.__hash__(), nzmath.poly.ring.PolynomialRing.__hash__(), nzmath.rational.Rational.__hash__(), nzmath.poly.multivar.BasicPolynomial.__hash__(), nzmath.poly.multiutil.PolynomialRingAnonymousVariables.__hash__(), nzmath.poly.multiutil.OrderProvider.__init__(), nzmath.poly.termorder.TermOrderInterface.__init__(), nzmath.poly.uniutil.OrderProvider.__init__(), nzmath.poly.uniutil.DivisionProvider.__init__(), nzmath.poly.multiutil.RingElementProvider.__init__(), nzmath.poly.uniutil.PrimeCharacteristicFunctionsProvider.__init__(), nzmath.poly.uniutil.VariableProvider.__init__(), nzmath.poly.uniutil.RingElementProvider.__init__(), nzmath.vector.Vector.__mod__(), nzmath.quad.ReducedQuadraticForm.__mul__(), nzmath.intresidue.IntegerResidueClass.__mul__(), nzmath.vector.Vector.__mul__(), nzmath.imaginary.Complex.__mul__(), nzmath.real.Real.__mul__(), nzmath.factor.misc.FactoredInteger.__mul__(), nzmath.poly.multivar.TermIndices.__mul__(), nzmath.ring.QuotientFieldElement.__mul__(), nzmath.ring.Ideal.__mul__(), nzmath.ring.ResidueClass.__mul__(), nzmath.prime.FactoredInteger.__mul__(), nzmath.rational.Integer.__mul__(), nzmath.vector.Vector.__neg__(), nzmath.intresidue.IntegerResidueClass.__neg__(), nzmath.imaginary.Complex.__neg__(), nzmath.ring.QuotientFieldElement.__neg__(), nzmath.imaginary.Complex.__pos__(), nzmath.intresidue.IntegerResidueClass.__pos__(), nzmath.ring.ResidueClass.__pos__(), nzmath.quad.ReducedQuadraticForm.__pow__(), nzmath.factor.misc.FactoredInteger.__pow__(), nzmath.permute.Permute.__pow__(), nzmath.imaginary.Complex.__pow__(), nzmath.intresidue.IntegerResidueClass.__pow__(), nzmath.ring.QuotientFieldElement.__pow__(), nzmath.finitefield.ExtendedFieldElement.__pow__(), nzmath.prime.FactoredInteger.__pow__(), nzmath.real.Real.__radd__(), nzmath.imaginary.Complex.__rdiv__(), nzmath.intresidue.IntegerResidueClass.__rdiv__(), nzmath.algfield.NumberField.__repr__(), nzmath.poly.ratfunc.RationalFunction.__repr__(), nzmath.poly.ring.PolynomialRing.__repr__(), nzmath.real.RealField.__repr__(), nzmath.imaginary.ComplexField.__repr__(), nzmath.finitefield.FinitePrimeField.__repr__(), nzmath.module.Module.__repr__(), nzmath.poly.ring.PolynomialIdeal.__repr__(), nzmath.rational.Rational.__repr__(), nzmath.poly.multiutil.RingPolynomial.__repr__(), nzmath.poly.univar.BasicPolynomial.__repr__(), nzmath.poly.formalsum.DictFormalSum.__repr__(), nzmath.algfield.BasicAlgNumber.__repr__(), nzmath.poly.multiutil.PolynomialRingAnonymousVariables.__repr__(), nzmath.poly.ring.RationalFunctionField.__repr__(), nzmath.poly.formalsum.ListFormalSum.__repr__(), nzmath.finitefield.ExtendedFieldElement.__repr__(), nzmath.poly.multiutil.PolynomialIdeal.__repr__(), nzmath.algfield.MatAlgNumber.__repr__(), nzmath.finitefield.ExtendedField.__repr__(), nzmath.module.Ideal_with_generator.__repr__(), nzmath.poly.uniutil.RingPolynomial.__repr__(), nzmath.vector.Vector.__rmul__(), nzmath.real.Real.__rmul__(), nzmath.rational.Integer.__rmul__(), nzmath.imaginary.Complex.__rsub__(), nzmath.real.Real.__rsub__(), nzmath.intresidue.IntegerResidueClass.__rsub__(), nzmath.ring.QuotientFieldElement.__rsub__(), nzmath.real.Real.__rtruediv__(), nzmath.ring.QuotientFieldElement.__rtruediv__(), nzmath.vector.Vector.__sub__(), nzmath.imaginary.Complex.__sub__(), nzmath.real.Real.__sub__(), nzmath.poly.multivar.TermIndices.__sub__(), nzmath.intresidue.IntegerResidueClass.__sub__(), nzmath.ring.QuotientFieldElement.__sub__(), nzmath.ring.ResidueClass.__sub__(), nzmath.quad.ReducedQuadraticForm.__truediv__(), nzmath.vector.Vector.__truediv__(), nzmath.real.Real.__truediv__(), nzmath.ring.QuotientFieldElement.__truediv__(), nzmath.module.Module._module_mul(), nzmath.finitefield.ExtendedFieldElement._op(), nzmath.module.Module._rational_mul(), nzmath.module.Module._scalar_mul(), nzmath.module.Module.change_base_module(), nzmath.poly.multivar.BasicPolynomial.combine_similar_terms(), nzmath.imaginary.Complex.conjugate(), nzmath.poly.univar.PolynomialInterface.construct_with_default(), nzmath.poly.formalsum.DictFormalSum.construct_with_default(), nzmath.poly.multivar.BasicPolynomial.construct_with_default(), nzmath.poly.formalsum.ListFormalSum.construct_with_default(), nzmath.vector.Vector.copy(), nzmath.factor.misc.FactoredInteger.copy(), nzmath.imaginary.Complex.copy(), nzmath.module.Module.copy(), nzmath.prime.FactoredInteger.copy(), nzmath.module.Ideal_with_generator.copy(), nzmath.poly.multivar.BasicPolynomial.erase_variable(), nzmath.poly.multiutil.PseudoDivisionProvider.exact_division(), nzmath.poly.multivar.TermIndices.gcd(), nzmath.poly.ring.PolynomialRing.getCommonSuperring(), nzmath.poly.multiutil.PolynomialRingAnonymousVariables.getCommonSuperring(), nzmath.module.Module.intersect(), nzmath.quad.ReducedQuadraticForm.inverse(), nzmath.imaginary.Complex.inverse(), nzmath.intresidue.IntegerResidueClass.inverse(), nzmath.ring.QuotientFieldElement.inverse(), nzmath.finitefield.ExtendedFieldElement.inverse(), nzmath.module.Module.issubmodule(), nzmath.module.Module.issupermodule(), nzmath.poly.multivar.TermIndices.lcm(), nzmath.poly.termorder.TermOrderInterface.leading_coefficient(), nzmath.poly.termorder.TermOrderInterface.leading_term(), nzmath.prime.TestPrime.next(), nzmath.poly.multivar.TermIndices.pop(), nzmath.poly.univar.BasicPolynomial.square(), and nzmath.poly.multiutil.NestProvider.unnest().

◆ _instances

◆ _one

◆ _zero

◆ scalars

◆ size

Property Documentation

◆ one

◆ zero

nzmath.matrix.MatrixRing.zero = property(_getZero, None, None, "additive unit")
static

Definition at line 1665 of file matrix.py.

Referenced by nzmath.ring.Field.gcd(), and nzmath.matrix.MatrixRing.zeroMatrix().


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