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

def __init__ (self, row, column, compo=0, coeff_ring=0)
 
def __truediv__ (self, other)
 
def toSubspace (self, isbasis=None)
 
def kernel (self)
 
def image (self)
 
def rank (self)
 
def inverseImage (self, V)
 
def solve (self, B)
 
def columnEchelonForm (self)
 
- 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 toFieldMatrix (self)
 
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

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

Private Member Functions

def _initialize (self, row, column, compo=0, coeff_ring=0)
 
def _selectMatrix (self)
 
def _cohensSimplify (self)
 

Private Attributes

 __class__
 

Static Private Attributes

def __div__ = __truediv__
 

Additional Inherited Members

- Static Public Attributes inherited from nzmath.matrix.RingMatrix
def HNF = hermiteNormalForm
 
def extHNF = exthermiteNormalForm
 

Detailed Description

FieldMatrix is a class for matrices whose elements are in field.

Definition at line 1178 of file matrix.py.

Constructor & Destructor Documentation

◆ __init__()

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

Reimplemented from nzmath.matrix.RingMatrix.

Reimplemented in nzmath.matrix.FieldSquareMatrix.

Definition at line 1183 of file matrix.py.

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

Member Function Documentation

◆ __truediv__()

def nzmath.matrix.FieldMatrix.__truediv__ (   self,
  other 
)
division by a scalar.

Definition at line 1206 of file matrix.py.

◆ _cohensSimplify()

def nzmath.matrix.FieldMatrix._cohensSimplify (   self)
private
_cohensSimplify is a common process used in image() and kernel()

Return a tuple of modified matrix M, image data c and kernel data d.

Definition at line 1219 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().

Referenced by nzmath.matrix.FieldMatrix.image(), and nzmath.matrix.FieldMatrix.kernel().

◆ _initialize()

def nzmath.matrix.FieldMatrix._initialize (   self,
  row,
  column,
  compo = 0,
  coeff_ring = 0 
)
private
initialize matrix

Reimplemented from nzmath.matrix.Matrix.

Definition at line 1190 of file matrix.py.

References nzmath.matrix.Matrix.coeff_ring.

◆ _selectMatrix()

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

Reimplemented from nzmath.matrix.RingMatrix.

Definition at line 1196 of file matrix.py.

References nzmath.matrix.Matrix.__class__.

◆ columnEchelonForm()

def nzmath.matrix.FieldMatrix.columnEchelonForm (   self)
Return a Matrix in column echelon form whose image is equal to 
the image of self.

Definition at line 1404 of file matrix.py.

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

◆ image()

def nzmath.matrix.FieldMatrix.image (   self)

◆ inverseImage()

◆ kernel()

def nzmath.matrix.FieldMatrix.kernel (   self)
Return a Matrix whose column vectors are one basis of self's kernel,
or return None if self's kernel is 0.

Definition at line 1250 of file matrix.py.

References nzmath.matrix.FieldMatrix._cohensSimplify(), nzmath.matrix.Matrix.coeff_ring, nzmath.matrix.Matrix.column, nzmath.lattice.LatticeElement.column, nzmath.bigrange.range(), and nzmath.matrix.zeroMatrix().

◆ rank()

def nzmath.matrix.FieldMatrix.rank (   self)
Return rank of self.

Definition at line 1298 of file matrix.py.

References nzmath.matrix.FieldMatrix.image().

◆ solve()

def nzmath.matrix.FieldMatrix.solve (   self,
  B 
)
Return solution X for self * X = B (B is a vector).
This function returns tuple (V, M) below.
  V: one solution as vector
  M: kernel of self as list of basis vectors.
If you want only one solution, use 'inverseImage'.

Warning: B should not be a matrix instead of a vector

Definition at line 1375 of file matrix.py.

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

◆ toSubspace()

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

Reimplemented from nzmath.matrix.RingMatrix.

Definition at line 1214 of file matrix.py.

References nzmath.matrix.Matrix.__class__.

Member Data Documentation

◆ __class__

nzmath.matrix.FieldMatrix.__class__
private

Definition at line 1202 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().

◆ __div__

def nzmath.matrix.FieldMatrix.__div__ = __truediv__
staticprivate

Definition at line 1212 of file matrix.py.

◆ coeff_ring

nzmath.matrix.FieldMatrix.coeff_ring

Definition at line 1194 of file matrix.py.

◆ isbasis

nzmath.matrix.FieldMatrix.isbasis

Definition at line 1217 of file matrix.py.

Referenced by nzmath.matrix.Subspace.toBasis().

◆ row

nzmath.matrix.FieldMatrix.row

Definition at line 1201 of file matrix.py.


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