nzmath.poly.uniutil.SubresultantGcdProvider Class Reference

Inheritance diagram for nzmath.poly.uniutil.SubresultantGcdProvider:

Collaboration diagram for nzmath.poly.uniutil.SubresultantGcdProvider:

Public Member Functions
def	resultant (self, other)
def	subresultant_gcd (self, other)
def	subresultant_extgcd (self, other)

Detailed Description

SubresultantGcdProvider provides gcd method using subresultant
algorithm.

REQUIRE: PseudoDivisionProvider, ContentProvider

Definition at line 616 of file uniutil.py.

Member Function Documentation

resultant()

def nzmath.poly.uniutil.SubresultantGcdProvider.resultant	(		self,
			other
	)

Return the resultant of self and other.

Definition at line 623 of file uniutil.py.

References nzmath.ring.exact_division(), nzmath.poly.ring.PolynomialRing.getCoefficientRing(), nzmath.poly.multiutil.RingElementProvider.getCoefficientRing(), nzmath.poly.multiutil.RingPolynomial.getCoefficientRing(), nzmath.poly.multiutil.PolynomialRingAnonymousVariables.getCoefficientRing(), nzmath.poly.ring.RationalFunctionField.getCoefficientRing(), nzmath.matrix.RingMatrix.getCoefficientRing(), and nzmath.poly.uniutil.RingPolynomial.getCoefficientRing().

Referenced by nzmath.poly.uniutil.DomainPolynomial.discriminant(), and nzmath.poly.uniutil.FieldPolynomial.discriminant().

subresultant_extgcd()

def nzmath.poly.uniutil.SubresultantGcdProvider.subresultant_extgcd	(		self,
			other
	)

Return (A, B, P) s.t. A*self+B*other=P,
where P is the greatest common divisor of given polynomials.
They must be in the polynomial ring and its coefficient ring must
be a UFD.

Reference: Kida's paper p.18

Definition at line 700 of file uniutil.py.

References nzmath.ring.exact_division(), nzmath.poly.ring.PolynomialRing.getCoefficientRing(), nzmath.poly.multiutil.RingElementProvider.getCoefficientRing(), nzmath.poly.multiutil.RingPolynomial.getCoefficientRing(), nzmath.poly.multiutil.PolynomialRingAnonymousVariables.getCoefficientRing(), nzmath.poly.ring.RationalFunctionField.getCoefficientRing(), nzmath.matrix.RingMatrix.getCoefficientRing(), and nzmath.poly.uniutil.RingPolynomial.getCoefficientRing().

subresultant_gcd()

def nzmath.poly.uniutil.SubresultantGcdProvider.subresultant_gcd	(		self,
			other
	)

Return the greatest common divisor of given polynomials.  They
must be in the polynomial ring and its coefficient ring must
be a UFD.

Reference: Algorithm 3.3.1 of Cohen's book

Definition at line 653 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(), and nzmath.poly.uniutil.RingPolynomial.getRing().

---

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

• nzmath/poly/uniutil.py