nzmath.poly.uniutil.DivisionProvider Class Reference

Inheritance diagram for nzmath.poly.uniutil.DivisionProvider:

Collaboration diagram for nzmath.poly.uniutil.DivisionProvider:

Public Member Functions
def	__init__ (self)
def	__divmod__ (self, other)
def	__floordiv__ (self, other)
def	__mod__ (self, other)
def	mod (self, dividend)
def	mod_pow (self, polynom, index)
def	__truediv__ (self, other)
def	scalar_exact_division (self, scale)
def	gcd (self, other)
def	extgcd (self, other)

Private Member Functions
def	_populate_reduced (self, degree, lc, upperbound)
def	_populate_reduced_more (self, degrees)

Private Attributes
	_reduced

Detailed Description

DivisionProvider provides all kind of divisions for univariate
polynomials.  It is assumed that the coefficient ring of the
polynomials is a field.

The class should be used as a mix-in.

REQUIRE: OrderProvider

Definition at line 78 of file uniutil.py.

Constructor & Destructor Documentation

__init__()

def nzmath.poly.uniutil.DivisionProvider.__init__

(

self

)

Do not instantiate DivisionProvider.
This initializer should be called from descendant.

Definition at line 88 of file uniutil.py.

References nzmath.matrix.Matrix.__class__, nzmath.matrix.RingMatrix.__class__, nzmath.matrix.RingSquareMatrix.__class__, nzmath.matrix.FieldMatrix.__class__, nzmath.matrix.MatrixRing.__class__, and nzmath.matrix.Subspace.__class__.

Member Function Documentation

__divmod__()

def nzmath.poly.uniutil.DivisionProvider.__divmod__	(		self,
			other
	)

divmod(self, other)

The method does, as the built-in divmod, return a tuple of
(self // other, self % other).

Definition at line 97 of file uniutil.py.

References nzmath.poly.univar.PolynomialInterface.construct_with_default(), nzmath.poly.formalsum.FormalSumContainerInterface.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.poly.multiutil.OrderProvider.order, nzmath.poly.uniutil.OrderProvider.order, nzmath.finitefield.FiniteField.order(), nzmath.finitefield.FinitePrimeFieldElement.order(), nzmath.permute.Permute.order(), nzmath.group.GroupElement.order(), nzmath.permute.ExPermute.order(), and nzmath.elliptic.ECoverGF.order().

__floordiv__()

def nzmath.poly.uniutil.DivisionProvider.__floordiv__	(		self,
			other
	)

self // other

Definition at line 114 of file uniutil.py.

References nzmath.poly.univar.PolynomialInterface.construct_with_default(), nzmath.poly.formalsum.FormalSumContainerInterface.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.poly.multiutil.OrderProvider.order, nzmath.poly.uniutil.OrderProvider.order, nzmath.finitefield.FiniteField.order(), nzmath.finitefield.FinitePrimeFieldElement.order(), nzmath.permute.Permute.order(), nzmath.group.GroupElement.order(), nzmath.permute.ExPermute.order(), and nzmath.elliptic.ECoverGF.order().

__mod__()

def nzmath.poly.uniutil.DivisionProvider.__mod__	(		self,
			other
	)

self % other

Definition at line 127 of file uniutil.py.

References nzmath.poly.multiutil.OrderProvider.order, nzmath.poly.uniutil.OrderProvider.order, nzmath.finitefield.FiniteField.order(), nzmath.finitefield.FinitePrimeFieldElement.order(), nzmath.permute.Permute.order(), nzmath.group.GroupElement.order(), nzmath.permute.ExPermute.order(), and nzmath.elliptic.ECoverGF.order().

__truediv__()

def nzmath.poly.uniutil.DivisionProvider.__truediv__	(		self,
			other
	)

self / other

The result is a rational function.

Definition at line 285 of file uniutil.py.

_populate_reduced()

def nzmath.poly.uniutil.DivisionProvider._populate_reduced (   self,   degree,   lc,   upperbound  )

private

Populate self._reduced.

degree, lc is of self, and self._reduced is populated up to
the given upperbound.

Definition at line 202 of file uniutil.py.

References nzmath.poly.uniutil.DivisionProvider._reduced, nzmath.poly.univar.PolynomialInterface.construct_with_default(), nzmath.poly.formalsum.FormalSumContainerInterface.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.poly.formalsum.FormalSumContainerInterface.itercoefficients(), nzmath.poly.univar.BasicPolynomial.itercoefficients(), nzmath.poly.formalsum.DictFormalSum.itercoefficients(), nzmath.poly.multivar.BasicPolynomial.itercoefficients(), nzmath.poly.formalsum.ListFormalSum.itercoefficients(), nzmath.poly.univar.SortedPolynomial.itercoefficients(), nzmath.poly.multiutil.OrderProvider.order, nzmath.poly.uniutil.OrderProvider.order, nzmath.finitefield.FiniteField.order(), nzmath.finitefield.FinitePrimeFieldElement.order(), nzmath.permute.Permute.order(), nzmath.group.GroupElement.order(), nzmath.permute.ExPermute.order(), nzmath.elliptic.ECoverGF.order(), nzmath.bigrange.range(), nzmath.poly.univar.PolynomialInterface.scalar_mul(), nzmath.poly.array.ArrayPoly.scalar_mul(), nzmath.poly.multivar.BasicPolynomial.scalar_mul(), nzmath.poly.array.ArrayPolyMod.scalar_mul(), nzmath.poly.formalsum.DictFormalSum.scalar_mul(), nzmath.poly.formalsum.ListFormalSum.scalar_mul(), and nzmath.poly.univar.SortedPolynomial.scalar_mul().

Referenced by nzmath.poly.uniutil.DivisionProvider.mod().

_populate_reduced_more()

def nzmath.poly.uniutil.DivisionProvider._populate_reduced_more (   self,   degrees  )

private

Populate self._reduced more for much higher degree dividend.
This method has to be called after _populate_reduced.

self._reduced is populated so that it will include all of
degrees > degree * 2.  The degrees are recommended to be
sorted in descending order.

Definition at line 223 of file uniutil.py.

References nzmath.poly.uniutil.DivisionProvider._populate_reduced_more(), nzmath.poly.uniutil.DivisionProvider._reduced, nzmath.poly.uniutil.DivisionProvider.mod(), nzmath.poly.array.ArrayPolyMod.mod, nzmath.poly.multiutil.OrderProvider.order, nzmath.poly.uniutil.OrderProvider.order, nzmath.finitefield.FiniteField.order(), nzmath.finitefield.FinitePrimeFieldElement.order(), nzmath.permute.Permute.order(), nzmath.group.GroupElement.order(), nzmath.permute.ExPermute.order(), and nzmath.elliptic.ECoverGF.order().

Referenced by nzmath.poly.uniutil.DivisionProvider._populate_reduced_more(), and nzmath.poly.uniutil.DivisionProvider.mod().

extgcd()

def nzmath.poly.uniutil.DivisionProvider.extgcd	(		self,
			other
	)

Return a tuple (u, v, d); they are the greatest common divisor
d of two polynomials self and other and u, v such that
d = self * u + other * v.

see nzmath.gcd.extgcd

Definition at line 316 of file uniutil.py.

References nzmath.poly.ratfunc.RationalFunction.getRing(), nzmath.poly.multiutil.RingElementProvider.getRing(), nzmath.real.Real.getRing(), nzmath.finitefield.FinitePrimeFieldElement.getRing(), nzmath.imaginary.Complex.getRing(), nzmath.intresidue.IntegerResidueClass.getRing(), nzmath.ring.RingElement.getRing(), nzmath.poly.multiutil.RingPolynomial.getRing(), nzmath.finitefield.ExtendedFieldElement.getRing(), nzmath.rational.Rational.getRing(), nzmath.algfield.BasicAlgNumber.getRing(), nzmath.ring.ResidueClass.getRing(), nzmath.algfield.MatAlgNumber.getRing(), nzmath.rational.Integer.getRing(), nzmath.matrix.RingSquareMatrix.getRing(), nzmath.poly.uniutil.RingElementProvider.getRing(), nzmath.poly.uniutil.RingPolynomial.getRing(), nzmath.poly.multiutil.OrderProvider.order, nzmath.poly.uniutil.OrderProvider.order, nzmath.finitefield.FiniteField.order(), nzmath.finitefield.FinitePrimeFieldElement.order(), nzmath.permute.Permute.order(), nzmath.group.GroupElement.order(), nzmath.permute.ExPermute.order(), and nzmath.elliptic.ECoverGF.order().

gcd()

def nzmath.poly.uniutil.DivisionProvider.gcd	(		self,
			other
	)

Return a greatest common divisor of self and other.
Returned polynomial is always monic.

Definition at line 300 of file uniutil.py.

References nzmath.poly.multiutil.OrderProvider.order, nzmath.poly.uniutil.OrderProvider.order, nzmath.finitefield.FiniteField.order(), nzmath.finitefield.FinitePrimeFieldElement.order(), nzmath.permute.Permute.order(), nzmath.group.GroupElement.order(), nzmath.permute.ExPermute.order(), and nzmath.elliptic.ECoverGF.order().

Referenced by nzmath.rational.IntegerRing.lcm().

mod()

def nzmath.poly.uniutil.DivisionProvider.mod	(		self,
			dividend
	)

Return dividend % self.

self should have attribute _reduced to cache reduced monomials.

Definition at line 143 of file uniutil.py.

References nzmath.poly.uniutil.DivisionProvider._populate_reduced(), nzmath.poly.uniutil.DivisionProvider._populate_reduced_more(), nzmath.poly.uniutil.DivisionProvider._reduced, nzmath.poly.univar.PolynomialInterface.construct_with_default(), nzmath.poly.formalsum.FormalSumContainerInterface.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.poly.multiutil.OrderProvider.order, nzmath.poly.uniutil.OrderProvider.order, nzmath.finitefield.FiniteField.order(), nzmath.finitefield.FinitePrimeFieldElement.order(), nzmath.permute.Permute.order(), nzmath.group.GroupElement.order(), nzmath.permute.ExPermute.order(), and nzmath.elliptic.ECoverGF.order().

Referenced by nzmath.poly.uniutil.DivisionProvider._populate_reduced_more(), nzmath.poly.uniutil.PrimeCharacteristicFunctionsProvider._small_index_mod_pow(), nzmath.poly.uniutil.DivisionProvider.mod_pow(), nzmath.poly.uniutil.PrimeCharacteristicFunctionsProvider.mod_pow(), and nzmath.poly.uniutil.PrimeCharacteristicFunctionsProvider.split_same_degrees().

mod_pow()

def nzmath.poly.uniutil.DivisionProvider.mod_pow	(		self,
			polynom,
			index
	)

Return polynom ** index % self.

Definition at line 179 of file uniutil.py.

References nzmath.poly.univar.PolynomialInterface.construct_with_default(), nzmath.poly.formalsum.FormalSumContainerInterface.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.poly.ratfunc.RationalFunction.getRing(), nzmath.poly.multiutil.RingElementProvider.getRing(), nzmath.real.Real.getRing(), nzmath.finitefield.FinitePrimeFieldElement.getRing(), nzmath.imaginary.Complex.getRing(), nzmath.intresidue.IntegerResidueClass.getRing(), nzmath.ring.RingElement.getRing(), nzmath.poly.multiutil.RingPolynomial.getRing(), nzmath.finitefield.ExtendedFieldElement.getRing(), nzmath.rational.Rational.getRing(), nzmath.algfield.BasicAlgNumber.getRing(), nzmath.ring.ResidueClass.getRing(), nzmath.algfield.MatAlgNumber.getRing(), nzmath.rational.Integer.getRing(), nzmath.matrix.RingSquareMatrix.getRing(), nzmath.poly.uniutil.RingElementProvider.getRing(), nzmath.poly.uniutil.RingPolynomial.getRing(), nzmath.poly.uniutil.DivisionProvider.mod(), and nzmath.poly.array.ArrayPolyMod.mod.

scalar_exact_division()

def nzmath.poly.uniutil.DivisionProvider.scalar_exact_division	(		self,
			scale
	)

Return quotient by a scalar which can divide each coefficient
exactly.

Definition at line 293 of file uniutil.py.

References nzmath.poly.formalsum.FormalSumContainerInterface.coefficients_map().

Referenced by nzmath.poly.uniutil.PrimeCharacteristicFunctionsProvider.factor(), and nzmath.poly.uniutil.ContentProvider.primitive_part().

Member Data Documentation

_reduced

nzmath.poly.uniutil.DivisionProvider._reduced

private

Definition at line 95 of file uniutil.py.

Referenced by nzmath.poly.uniutil.DivisionProvider._populate_reduced(), nzmath.poly.uniutil.DivisionProvider._populate_reduced_more(), and nzmath.poly.uniutil.DivisionProvider.mod().

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

• nzmath/poly/uniutil.py