nzmath.matrix.MatrixRing Class Reference

Inheritance diagram for nzmath.matrix.MatrixRing:

Collaboration diagram for nzmath.matrix.MatrixRing:

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__()

def nzmath.matrix.MatrixRing.__eq__	(		self,
			other
	)

self == other

Reimplemented from nzmath.ring.Ring.

Definition at line 1604 of file matrix.py.

Referenced by nzmath.poly.multivar.TermIndices.__ne__(), nzmath.poly.ring.PolynomialRing.__ne__(), nzmath.quad.ReducedQuadraticForm.__ne__(), nzmath.ring.Ring.__ne__(), nzmath.poly.formalsum.FormalSumContainerInterface.__ne__(), nzmath.poly.array.ArrayPoly.__ne__(), nzmath.real.RealField.__ne__(), nzmath.ring.Ideal.__ne__(), and nzmath.prime.FactoredInteger.__ne__().

__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()

def nzmath.matrix.MatrixRing._getOne (   self )

private

getter for one (unit matrix)

Definition at line 1641 of file matrix.py.

References nzmath.imaginary.ComplexField._one, nzmath.algfield.NumberField._one, nzmath.intresidue.IntegerResidueClassRing._one, nzmath.finitefield.FinitePrimeField._one, nzmath.finitefield.ExtendedField._one, and nzmath.matrix.MatrixRing._one.

_getZero()

def nzmath.matrix.MatrixRing._getZero (   self )

private

Return zero matrix.

Definition at line 1657 of file matrix.py.

References nzmath.imaginary.ComplexField._zero, nzmath.intresidue.IntegerResidueClassRing._zero, nzmath.algfield.NumberField._zero, nzmath.finitefield.FinitePrimeField._zero, nzmath.finitefield.ExtendedField._zero, and nzmath.matrix.MatrixRing._zero.

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()

def nzmath.matrix.MatrixRing.issuperring	(		self,
			other
	)

Report whether the ring is a superring of another ring.

Reimplemented from nzmath.ring.Ring.

Definition at line 1692 of file matrix.py.

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

Referenced by nzmath.ring.Ring.getCommonSuperring(), nzmath.poly.ring.PolynomialRing.getCommonSuperring(), nzmath.poly.multiutil.PolynomialRingAnonymousVariables.getCommonSuperring(), nzmath.poly.ring.RationalFunctionField.getCommonSuperring(), nzmath.rational.RationalField.getCommonSuperring(), nzmath.rational.IntegerRing.getCommonSuperring(), nzmath.real.RealField.issubring(), and nzmath.poly.ring.RationalFunctionField.issuperring().

unitMatrix()

def nzmath.matrix.MatrixRing.unitMatrix

(

self

)

Return the unit matrix.

Definition at line 1635 of file matrix.py.

References nzmath.imaginary.ComplexField.one, nzmath.intresidue.IntegerResidueClassRing.one, nzmath.algfield.NumberField.one, nzmath.finitefield.FinitePrimeField.one, nzmath.finitefield.ExtendedField.one, and nzmath.matrix.MatrixRing.one.

zeroMatrix()

def nzmath.matrix.MatrixRing.zeroMatrix

(

self

)

Return the zero matrix.

Definition at line 1651 of file matrix.py.

References nzmath.imaginary.ComplexField.zero, nzmath.intresidue.IntegerResidueClassRing.zero, nzmath.algfield.NumberField.zero, nzmath.finitefield.FinitePrimeField.zero, nzmath.finitefield.ExtendedField.zero, and nzmath.matrix.MatrixRing.zero.

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

dictionary nzmath.matrix.MatrixRing._instances = {}

staticprivate

Definition at line 1591 of file matrix.py.

Referenced by nzmath.poly.ring.PolynomialRing.getInstance(), nzmath.poly.multiutil.PolynomialRingAnonymousVariables.getInstance(), nzmath.poly.ring.RationalFunctionField.getInstance(), and nzmath.matrix.MatrixRing.getInstance().

_one

nzmath.matrix.MatrixRing._one

private

Definition at line 1646 of file matrix.py.

Referenced by nzmath.poly.ring.PolynomialRing._get_one(), nzmath.poly.ring.RationalFunctionField._get_one(), nzmath.real.RealField._getOne(), nzmath.poly.multiutil.PolynomialRingAnonymousVariables._getOne(), nzmath.ring.ResidueClassRing._getOne(), nzmath.rational.RationalField._getOne(), nzmath.rational.IntegerRing._getOne(), and nzmath.matrix.MatrixRing._getOne().

_zero

nzmath.matrix.MatrixRing._zero

private

Definition at line 1662 of file matrix.py.

Referenced by nzmath.poly.ring.PolynomialRing._get_zero(), nzmath.poly.ring.RationalFunctionField._get_zero(), nzmath.real.RealField._getZero(), nzmath.poly.multiutil.PolynomialRingAnonymousVariables._getZero(), nzmath.ring.ResidueClassRing._getZero(), nzmath.rational.RationalField._getZero(), nzmath.rational.IntegerRing._getZero(), and nzmath.matrix.MatrixRing._getZero().

scalars

nzmath.matrix.MatrixRing.scalars

Definition at line 1602 of file matrix.py.

Referenced by nzmath.matrix.MatrixRing.__hash__(), nzmath.matrix.MatrixRing.__repr__(), nzmath.matrix.MatrixRing.__str__(), nzmath.matrix.MatrixRing.createElement(), nzmath.matrix.MatrixRing.getCharacteristic(), nzmath.matrix.MatrixRing.getCommonSuperring(), nzmath.matrix.MatrixRing.issubring(), and nzmath.matrix.MatrixRing.issuperring().

size

nzmath.matrix.MatrixRing.size

Definition at line 1601 of file matrix.py.

Referenced by nzmath.prime.Zeta.__add__(), nzmath.prime.Zeta.__eq__(), nzmath.prime.Zeta.__getitem__(), nzmath.prime.Zeta.__hash__(), nzmath.matrix.MatrixRing.__hash__(), nzmath.prime.Zeta.__len__(), nzmath.prime.Zeta.__lshift__(), nzmath.prime.Zeta.__mod__(), nzmath.prime.Zeta.__mul__(), nzmath.prime.Zeta.__pos__(), nzmath.prime.Zeta.__pow__(), nzmath.matrix.MatrixRing.__repr__(), nzmath.prime.Zeta.__setitem__(), nzmath.matrix.MatrixRing.__str__(), nzmath.prime.Zeta._pow_mod(), nzmath.matrix.MatrixRing.createElement(), nzmath.matrix.MatrixRing.getCommonSuperring(), nzmath.matrix.MatrixRing.issubring(), nzmath.matrix.MatrixRing.issuperring(), and nzmath.prime.Zeta.promote().

Property Documentation

one

nzmath.matrix.MatrixRing.one = property(_getOne, None, None, "multiplicative unit")

static

Definition at line 1649 of file matrix.py.

Referenced by nzmath.ring.Field.gcd(), nzmath.finitefield.FiniteField.Legendre(), nzmath.finitefield.FiniteField.order(), nzmath.finitefield.FiniteField.sqrt(), nzmath.finitefield.FiniteField.TonelliShanks(), and nzmath.matrix.MatrixRing.unitMatrix().

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:

• nzmath/matrix.py