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

def __init__ (self, row, column, compo=0, coeff_ring=0, isbasis=None)
 
def fromMatrix (cls, mat, isbasis=None)
 
def toFieldMatrix (self)
 
def isSubspace (self, other)
 
def toBasis (self)
 
def supplementBasis (self)
 
def sumOfSubspaces (self, other)
 
def intersectionOfSubspaces (self, other)
 
- Public Member Functions inherited from nzmath.matrix.FieldMatrix
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 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

 isbasis
 
 row
 
 compo
 
 column
 
- Public Attributes inherited from nzmath.matrix.FieldMatrix
 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 Attributes

 __class__
 

Additional Inherited Members

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

Detailed Description

Subspace is a class for subspaces.

Definition at line 1713 of file matrix.py.

Constructor & Destructor Documentation

◆ __init__()

def nzmath.matrix.Subspace.__init__ (   self,
  row,
  column,
  compo = 0,
  coeff_ring = 0,
  isbasis = None 
)
Subspace(row, column [,components, coeff_ring, isbasis])

Definition at line 1718 of file matrix.py.

References nzmath.matrix.Matrix._initialize().

Member Function Documentation

◆ fromMatrix()

def nzmath.matrix.Subspace.fromMatrix (   cls,
  mat,
  isbasis = None 
)
A constructor class method, which creates Subspace from a
Matrix instance.

Definition at line 1732 of file matrix.py.

◆ intersectionOfSubspaces()

◆ isSubspace()

def nzmath.matrix.Subspace.isSubspace (   self,
  other 
)
Check self is in other as subspace


Definition at line 1751 of file matrix.py.

◆ sumOfSubspaces()

def nzmath.matrix.Subspace.sumOfSubspaces (   self,
  other 
)

◆ supplementBasis()

◆ toBasis()

◆ toFieldMatrix()

def nzmath.matrix.Subspace.toFieldMatrix (   self)
Subspace -> Field(Square)Matrix

Reimplemented from nzmath.matrix.RingMatrix.

Definition at line 1742 of file matrix.py.

Member Data Documentation

◆ __class__

nzmath.matrix.Subspace.__class__
private

Definition at line 1747 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().

◆ column

nzmath.matrix.Subspace.column

Definition at line 1770 of file matrix.py.

◆ compo

◆ isbasis

nzmath.matrix.Subspace.isbasis

Definition at line 1729 of file matrix.py.

◆ row

nzmath.matrix.Subspace.row

Definition at line 1746 of file matrix.py.


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