nzmath.poly.uniutil.PseudoDivisionProvider Class Reference

Inheritance diagram for nzmath.poly.uniutil.PseudoDivisionProvider:

Collaboration diagram for nzmath.poly.uniutil.PseudoDivisionProvider:

Public Member Functions
def	pseudo_divmod (self, other)
def	pseudo_floordiv (self, other)
def	pseudo_mod (self, other)
def	__truediv__ (self, other)
def	exact_division (self, other)
def	scalar_exact_division (self, scale)
def	monic_divmod (self, other)
def	monic_floordiv (self, other)
def	monic_mod (self, other)
def	monic_pow (self, index, mod)

Detailed Description

PseudoDivisionProvider provides pseudo divisions for univariate
polynomials.  It is assumed that the coefficient ring of the
polynomials is a domain.

The class should be used as a mix-in.

Definition at line 338 of file uniutil.py.

Member Function Documentation

__truediv__()

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

self / other

Return the result as a rational function.

Definition at line 434 of file uniutil.py.

exact_division()

def nzmath.poly.uniutil.PseudoDivisionProvider.exact_division	(		self,
			other
	)

Return quotient of exact division.

Definition at line 443 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(), nzmath.elliptic.ECoverGF.order(), nzmath.poly.multiutil.PseudoDivisionProvider.pseudo_divmod(), and nzmath.poly.uniutil.PseudoDivisionProvider.pseudo_divmod().

monic_divmod()

def nzmath.poly.uniutil.PseudoDivisionProvider.monic_divmod	(		self,
			other
	)

self.monic_divmod(other) -> (Q, R)

Q, R are polynomials such that
self == other * Q + R.

The leading coefficient of other MUST be one.

Definition at line 465 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().

monic_floordiv()

def nzmath.poly.uniutil.PseudoDivisionProvider.monic_floordiv	(		self,
			other
	)

self.monic_floordiv(other) -> Q

Q is a polynomial such that
self == other * Q + R,
where R is a polynomial whose degree is smaller than other's.

The leading coefficient of other MUST be one.

Definition at line 492 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().

monic_mod()

def nzmath.poly.uniutil.PseudoDivisionProvider.monic_mod	(		self,
			other
	)

self.monic_mod(other) -> R

R is a polynomial such that
self == other * Q + R,
where Q is another polynomial.

The leading coefficient of other MUST be one.

Definition at line 520 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().

Referenced by nzmath.poly.uniutil.PseudoDivisionProvider.monic_pow().

monic_pow()

def nzmath.poly.uniutil.PseudoDivisionProvider.monic_pow	(		self,
			index,
			mod
	)

Return self**index % mod.

The leading coefficient of mod MUST be one.

Definition at line 545 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.uniutil.PseudoDivisionProvider.monic_mod(), nzmath.poly.univar.PolynomialInterface.square(), nzmath.poly.univar.BasicPolynomial.square(), nzmath.poly.multivar.BasicPolynomial.square(), nzmath.poly.univar.SortedPolynomial.square(), and nzmath.poly.uniutil.FinitePrimeFieldPolynomial.square().

Referenced by nzmath.poly.uniutil.DomainPolynomial.__pow__().

pseudo_divmod()

def nzmath.poly.uniutil.PseudoDivisionProvider.pseudo_divmod	(		self,
			other
	)

self.pseudo_divmod(other) -> (Q, R)

Q, R are polynomials such that
d**(deg(self) - deg(other) + 1) * self == other * Q + R,
where d is the leading coefficient of other.

Definition at line 346 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().

Referenced by nzmath.poly.uniutil.PseudoDivisionProvider.exact_division().

pseudo_floordiv()

def nzmath.poly.uniutil.PseudoDivisionProvider.pseudo_floordiv	(		self,
			other
	)

self.pseudo_floordiv(other) -> Q

Q is a polynomial such that
d**(deg(self) - deg(other) + 1) * self == other * Q + R,
where d is the leading coefficient of other and R is a
polynomial.

Definition at line 377 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().

pseudo_mod()

def nzmath.poly.uniutil.PseudoDivisionProvider.pseudo_mod	(		self,
			other
	)

self.pseudo_mod(other) -> R

R is a polynomial such that
d**(deg(self) - deg(other) + 1) * self == other * Q + R,
where d is the leading coefficient of other and Q a
polynomial.

Definition at line 406 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().

scalar_exact_division()

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

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

Definition at line 458 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().

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

• nzmath/poly/uniutil.py