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

def __init__ (self, row, column=0, compo=0, coeff_ring=0)
 
def __pow__ (self, other)
 
def toFieldMatrix (self)
 
def getRing (self)
 
def isOrthogonalMatrix (self)
 
def isAlternatingMatrix (self)
 
def isSingular (self)
 
def trace (self)
 
def determinant (self)
 
def cofactor (self, i, j)
 
def commutator (self, other)
 
def characteristicMatrix (self)
 
def characteristicPolynomial (self)
 
def adjugateMatrix (self)
 
def cofactorMatrix (self)
 
def smithNormalForm (self)
 
def extsmithNormalForm (self)
 
- Public Member Functions inherited from nzmath.matrix.SquareMatrix
def isUpperTriangularMatrix (self)
 
def isLowerTriangularMatrix (self)
 
def isDiagonalMatrix (self)
 
def isScalarMatrix (self)
 
def isSymmetricMatrix (self)
 
- Public Member Functions inherited from nzmath.matrix.Matrix
def __getitem__ (self, index)
 
def __setitem__ (self, key, value)
 
def __eq__ (self, other)
 
def __hash__ (self)
 
def __ne__ (self, other)
 
def __nonzero__ (self)
 
def __contains__ (self, item)
 
def __repr__ (self)
 
def __str__ (self)
 
def __call__ (self, arg)
 
def map (self, function)
 
def reduce (self, function, initializer=None)
 
def copy (self)
 
def set (self, compo)
 
def setRow (self, m, arg)
 
def setColumn (self, n, arg)
 
def getRow (self, i)
 
def getColumn (self, j)
 
def swapRow (self, m1, m2)
 
def swapColumn (self, n1, n2)
 
def insertRow (self, i, arg)
 
def insertColumn (self, j, arg)
 
def extendRow (self, arg)
 
def extendColumn (self, arg)
 
def deleteRow (self, i)
 
def deleteColumn (self, j)
 
def transpose (self)
 
def getBlock (self, i, j, row, column=None)
 
def subMatrix (self, I, J=None)
 
def toMatrix (self, flag=True)
 
- Public Member Functions inherited from nzmath.matrix.RingMatrix
def __add__ (self, other)
 
def __sub__ (self, other)
 
def __mul__ (self, other)
 
def __rmul__ (self, other)
 
def __mod__ (self, other)
 
def __pos__ (self)
 
def __neg__ (self)
 
def getCoefficientRing (self)
 
def toSubspace (self, isbasis=None)
 
def hermiteNormalForm (self, non_zero=False)
 
def exthermiteNormalForm (self, non_zero=False)
 
def kernelAsModule (self)
 
- Public Member Functions inherited from nzmath.ring.RingElement
def __init__ (self, *args, **kwd)
 
def __eq__ (self, other)
 
def __hash__ (self)
 
def __ne__ (self, other)
 

Public Attributes

 coeff_ring
 
 row
 
- Public Attributes inherited from nzmath.matrix.Matrix
 row
 
 column
 
 compo
 
 coeff_ring
 
- Public Attributes inherited from nzmath.matrix.RingMatrix
 row
 
 coeff_ring
 

Static Public Attributes

def isAntisymmetricMatrix = isAlternatingMatrix
 
def isSkewsymmetricMatrix = isAlternatingMatrix
 
def cofactors = cofactorMatrix
 
def SNF = smithNormalForm
 
def elementary_divisor = smithNormalForm
 
def extSNF = extsmithNormalForm
 
- Static Public Attributes inherited from nzmath.matrix.RingMatrix
def HNF = hermiteNormalForm
 
def extHNF = exthermiteNormalForm
 

Private Member Functions

def _characteristicPolyList (self)
 

Private Attributes

 __class__
 

Detailed Description

RingSquareMatrix is a class for square matrices whose elements are in ring.

Definition at line 860 of file matrix.py.

Constructor & Destructor Documentation

◆ __init__()

def nzmath.matrix.RingSquareMatrix.__init__ (   self,
  row,
  column = 0,
  compo = 0,
  coeff_ring = 0 
)
RingSquareMatrix(row [, column ,components, coeff_ring])
RingSquareMatrix must be row == column .

Reimplemented from nzmath.matrix.SquareMatrix.

Reimplemented in nzmath.matrix.FieldSquareMatrix.

Definition at line 865 of file matrix.py.

References nzmath.matrix.Matrix._initialize().

Member Function Documentation

◆ __pow__()

◆ _characteristicPolyList()

◆ adjugateMatrix()

def nzmath.matrix.RingSquareMatrix.adjugateMatrix (   self)

◆ characteristicMatrix()

def nzmath.matrix.RingSquareMatrix.characteristicMatrix (   self)
Return the characteristic matrix (i.e. xI-A) of self.

Definition at line 995 of file matrix.py.

References nzmath.matrix.Matrix.coeff_ring, nzmath.matrix.Matrix.row, nzmath.lattice.LatticeElement.row, and nzmath.matrix.unitMatrix().

◆ characteristicPolynomial()

def nzmath.matrix.RingSquareMatrix.characteristicPolynomial (   self)
characteristicPolynomial() -> Polynomial

Definition at line 1022 of file matrix.py.

◆ cofactor()

def nzmath.matrix.RingSquareMatrix.cofactor (   self,
  i,
  j 
)
Return (i, j)-cofactor of self.

Definition at line 979 of file matrix.py.

References nzmath.matrix.RingSquareMatrix.determinant(), and nzmath.matrix.Matrix.subMatrix().

◆ cofactorMatrix()

def nzmath.matrix.RingSquareMatrix.cofactorMatrix (   self)
Return cofactor matrix.

Definition at line 1046 of file matrix.py.

References nzmath.matrix.RingSquareMatrix.adjugateMatrix(), and nzmath.matrix.Matrix.transpose().

◆ commutator()

def nzmath.matrix.RingSquareMatrix.commutator (   self,
  other 
)
Return commutator defined as follows:
[self, other] = self * other - other * self .

Definition at line 988 of file matrix.py.

◆ determinant()

◆ extsmithNormalForm()

def nzmath.matrix.RingSquareMatrix.extsmithNormalForm (   self)
Find the Smith Normal Form M for square matrix,
Computing U,V which satisfied M=U*self*V.
Return matrices tuple,(U,V,M).

Definition at line 1116 of file matrix.py.

References nzmath.matrix.Matrix.coeff_ring, nzmath.factor.misc.FactoredInteger.copy(), nzmath.imaginary.Complex.copy(), nzmath.matrix.Matrix.copy(), nzmath.bigrange.range(), and nzmath.matrix.unitMatrix().

◆ getRing()

def nzmath.matrix.RingSquareMatrix.getRing (   self)

◆ isAlternatingMatrix()

def nzmath.matrix.RingSquareMatrix.isAlternatingMatrix (   self)
Check whether self is alternating matrix or not.
Alternating (skew symmetric, or antisymmetric) matrix satisfies M=-M^T.

Definition at line 917 of file matrix.py.

References nzmath.matrix.Matrix.column, nzmath.lattice.LatticeElement.column, nzmath.bigrange.range(), nzmath.matrix.Matrix.row, and nzmath.lattice.LatticeElement.row.

◆ isOrthogonalMatrix()

def nzmath.matrix.RingSquareMatrix.isOrthogonalMatrix (   self)
Check whether self is orthogonal matrix or not.
Orthogonal matrix satisfies M*M^T equals unit matrix.

Definition at line 910 of file matrix.py.

References nzmath.matrix.Matrix.coeff_ring, nzmath.matrix.Matrix.row, nzmath.lattice.LatticeElement.row, nzmath.matrix.Matrix.transpose(), nzmath.factor.mpqs.Elimination.transpose(), and nzmath.matrix.unitMatrix().

◆ isSingular()

def nzmath.matrix.RingSquareMatrix.isSingular (   self)
Check determinant == 0 or not.

Definition at line 931 of file matrix.py.

References nzmath.matrix.RingSquareMatrix.determinant().

◆ smithNormalForm()

def nzmath.matrix.RingSquareMatrix.smithNormalForm (   self)
Find the Smith Normal Form for square non-singular integral matrix.
Return the list of diagonal elements.

Definition at line 1054 of file matrix.py.

References nzmath.matrix.Matrix.coeff_ring, nzmath.factor.misc.FactoredInteger.copy(), nzmath.imaginary.Complex.copy(), nzmath.matrix.Matrix.copy(), and nzmath.bigrange.range().

◆ toFieldMatrix()

def nzmath.matrix.RingSquareMatrix.toFieldMatrix (   self)
RingSquareMatrix -> FieldSquareMatrix

Reimplemented from nzmath.matrix.RingMatrix.

Definition at line 899 of file matrix.py.

◆ trace()

def nzmath.matrix.RingSquareMatrix.trace (   self)

Member Data Documentation

◆ __class__

nzmath.matrix.RingSquareMatrix.__class__
private

Definition at line 901 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().

◆ coeff_ring

nzmath.matrix.RingSquareMatrix.coeff_ring

Definition at line 902 of file matrix.py.

◆ cofactors

def nzmath.matrix.RingSquareMatrix.cofactors = cofactorMatrix
static

Definition at line 1052 of file matrix.py.

◆ elementary_divisor

def nzmath.matrix.RingSquareMatrix.elementary_divisor = smithNormalForm
static

Definition at line 1114 of file matrix.py.

◆ extSNF

def nzmath.matrix.RingSquareMatrix.extSNF = extsmithNormalForm
static

Definition at line 1175 of file matrix.py.

◆ isAntisymmetricMatrix

def nzmath.matrix.RingSquareMatrix.isAntisymmetricMatrix = isAlternatingMatrix
static

Definition at line 928 of file matrix.py.

◆ isSkewsymmetricMatrix

def nzmath.matrix.RingSquareMatrix.isSkewsymmetricMatrix = isAlternatingMatrix
static

Definition at line 929 of file matrix.py.

◆ row

nzmath.matrix.RingSquareMatrix.row

Definition at line 1028 of file matrix.py.

◆ SNF

def nzmath.matrix.RingSquareMatrix.SNF = smithNormalForm
static

Definition at line 1113 of file matrix.py.


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