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

def __init__ (self, row, column, compo=0, coeff_ring=0)
 
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 toFieldMatrix (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.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 Attributes

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

Static Public Attributes

def HNF = hermiteNormalForm
 
def extHNF = exthermiteNormalForm
 

Private Member Functions

def _selectMatrix (self)
 
def _SimplifyHNF (self)
 

Private Attributes

 __class__
 
 _coeff_ring
 

Detailed Description

RingMatrix is a class for matrices whose elements are in ring.

Definition at line 543 of file matrix.py.

Constructor & Destructor Documentation

◆ __init__()

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

Reimplemented from nzmath.matrix.Matrix.

Reimplemented in nzmath.matrix.FieldSquareMatrix, nzmath.matrix.RingSquareMatrix, and nzmath.matrix.FieldMatrix.

Definition at line 548 of file matrix.py.

References nzmath.matrix.Matrix._initialize(), and nzmath.matrix.Matrix._selectMatrix().

Member Function Documentation

◆ __add__()

def nzmath.matrix.RingMatrix.__add__ (   self,
  other 
)

◆ __mod__()

def nzmath.matrix.RingMatrix.__mod__ (   self,
  other 
)

◆ __mul__()

def nzmath.matrix.RingMatrix.__mul__ (   self,
  other 
)

◆ __neg__()

def nzmath.matrix.RingMatrix.__neg__ (   self)
return -self.

Definition at line 679 of file matrix.py.

References nzmath.matrix.Matrix.coeff_ring, and nzmath.matrix.Matrix.map().

◆ __pos__()

def nzmath.matrix.RingMatrix.__pos__ (   self)

◆ __rmul__()

◆ __sub__()

def nzmath.matrix.RingMatrix.__sub__ (   self,
  other 
)

◆ _selectMatrix()

def nzmath.matrix.RingMatrix._selectMatrix (   self)
private
Select Matrix class.

Reimplemented from nzmath.matrix.Matrix.

Reimplemented in nzmath.matrix.FieldMatrix.

Definition at line 555 of file matrix.py.

◆ _SimplifyHNF()

◆ exthermiteNormalForm()

def nzmath.matrix.RingMatrix.exthermiteNormalForm (   self,
  non_zero = False 
)
Find the Hermite Normal Form M for integer matrix.
Computing U which satisfied M=self*U.
Return matrices tuple,(U, M).

Definition at line 824 of file matrix.py.

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

◆ getCoefficientRing()

◆ hermiteNormalForm()

def nzmath.matrix.RingMatrix.hermiteNormalForm (   self,
  non_zero = False 
)

◆ kernelAsModule()

def nzmath.matrix.RingMatrix.kernelAsModule (   self)

◆ toFieldMatrix()

def nzmath.matrix.RingMatrix.toFieldMatrix (   self)
RingMatrix -> FieldMatrix

Reimplemented in nzmath.matrix.Subspace, and nzmath.matrix.RingSquareMatrix.

Definition at line 711 of file matrix.py.

References nzmath.matrix.Matrix.__class__, and nzmath.matrix.Matrix.coeff_ring.

Referenced by nzmath.matrix.RingMatrix.toSubspace().

◆ toSubspace()

def nzmath.matrix.RingMatrix.toSubspace (   self,
  isbasis = None 
)
RingMatrix -> Subspace

Reimplemented in nzmath.matrix.FieldMatrix.

Definition at line 716 of file matrix.py.

References nzmath.matrix.RingMatrix.toFieldMatrix(), and nzmath.matrix.RingMatrix.toSubspace().

Referenced by nzmath.matrix.RingMatrix.toSubspace().

Member Data Documentation

◆ __class__

nzmath.matrix.RingMatrix.__class__
private

Definition at line 560 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.RingMatrix._coeff_ring
private

Definition at line 708 of file matrix.py.

◆ coeff_ring

nzmath.matrix.RingMatrix.coeff_ring

Definition at line 708 of file matrix.py.

◆ extHNF

def nzmath.matrix.RingMatrix.extHNF = exthermiteNormalForm
static

Definition at line 845 of file matrix.py.

◆ HNF

def nzmath.matrix.RingMatrix.HNF = hermiteNormalForm
static

Definition at line 773 of file matrix.py.

◆ row

nzmath.matrix.RingMatrix.row

Definition at line 559 of file matrix.py.


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