nzmath.algfield.MatAlgNumber Class Reference

Inheritance diagram for nzmath.algfield.MatAlgNumber:

Collaboration diagram for nzmath.algfield.MatAlgNumber:

Public Member Functions
def	__init__ (self, coefficient, polynomial)
def	__repr__ (self)
def	__neg__ (self)
def	__add__ (self, other)
def	__sub__ (self, other)
def	__mul__ (self, other)
def	__truediv__ (self, other)
def	__pow__ (self, other)
def	inverse (self)
def	norm (self)
def	trace (self)
def	getRing (self)
def	ch_basic (self)

Public Attributes
	coeff
	degree
	matrix
	polynomial
	field

Static Private Attributes
def	__radd__ = __add__
def	__rmul__ = __mul__
def	__div__ = __truediv__
def	__floordiv__ = __truediv__

Detailed Description

The class for algebraic number represented by matrix.

Definition at line 595 of file algfield.py.

Constructor & Destructor Documentation

__init__()

def nzmath.algfield.MatAlgNumber.__init__	(		self,
			coefficient,
			polynomial
	)

Definition at line 599 of file algfield.py.

Member Function Documentation

__add__()

def nzmath.algfield.MatAlgNumber.__add__	(		self,
			other
	)

Definition at line 651 of file algfield.py.

References nzmath.algfield.NumberField.degree, nzmath.algfield.BasicAlgNumber.degree, nzmath.algfield.MatAlgNumber.degree, nzmath.algfield.MatAlgNumber.matrix, nzmath.algfield.NumberField.polynomial, nzmath.algfield.BasicAlgNumber.polynomial, nzmath.algfield.MatAlgNumber.polynomial, and nzmath.bigrange.range().

__mul__()

def nzmath.algfield.MatAlgNumber.__mul__	(		self,
			other
	)

Definition at line 677 of file algfield.py.

References nzmath.algfield.MatAlgNumber.matrix, nzmath.algfield.NumberField.polynomial, nzmath.algfield.BasicAlgNumber.polynomial, nzmath.algfield.MatAlgNumber.polynomial, and nzmath.bigrange.range().

__neg__()

def nzmath.algfield.MatAlgNumber.__neg__

(

self

)

Definition at line 644 of file algfield.py.

References nzmath.algfield.MatAlgNumber.matrix, nzmath.algfield.NumberField.polynomial, nzmath.algfield.BasicAlgNumber.polynomial, nzmath.algfield.MatAlgNumber.polynomial, and nzmath.bigrange.range().

__pow__()

def nzmath.algfield.MatAlgNumber.__pow__	(		self,
			other
	)

Definition at line 707 of file algfield.py.

References nzmath.algfield.MatAlgNumber.matrix, nzmath.algfield.NumberField.polynomial, nzmath.algfield.BasicAlgNumber.polynomial, nzmath.algfield.MatAlgNumber.polynomial, and nzmath.bigrange.range().

__repr__()

def nzmath.algfield.MatAlgNumber.__repr__

(

self

)

Definition at line 640 of file algfield.py.

References nzmath.matrix.Matrix.__class__, nzmath.matrix.RingMatrix.__class__, nzmath.matrix.RingSquareMatrix.__class__, nzmath.matrix.FieldMatrix.__class__, nzmath.matrix.MatrixRing.__class__, nzmath.matrix.Subspace.__class__, nzmath.algfield.MatAlgNumber.matrix, nzmath.algfield.NumberField.polynomial, nzmath.algfield.BasicAlgNumber.polynomial, and nzmath.algfield.MatAlgNumber.polynomial.

__sub__()

def nzmath.algfield.MatAlgNumber.__sub__	(		self,
			other
	)

Definition at line 665 of file algfield.py.

References nzmath.algfield.NumberField.degree, nzmath.algfield.BasicAlgNumber.degree, nzmath.algfield.MatAlgNumber.degree, nzmath.algfield.MatAlgNumber.matrix, nzmath.algfield.NumberField.polynomial, nzmath.algfield.BasicAlgNumber.polynomial, nzmath.algfield.MatAlgNumber.polynomial, and nzmath.bigrange.range().

__truediv__()

def nzmath.algfield.MatAlgNumber.__truediv__	(		self,
			other
	)

Definition at line 691 of file algfield.py.

References nzmath.algfield.MatAlgNumber.matrix, nzmath.algfield.NumberField.polynomial, nzmath.algfield.BasicAlgNumber.polynomial, nzmath.algfield.MatAlgNumber.polynomial, and nzmath.bigrange.range().

ch_basic()

def nzmath.algfield.MatAlgNumber.ch_basic

(

self

)

Definition at line 734 of file algfield.py.

References nzmath.algfield.BasicAlgNumber.coeff, nzmath.algfield.MatAlgNumber.coeff, nzmath.algfield.NumberField.degree, nzmath.algfield.BasicAlgNumber.degree, nzmath.algfield.MatAlgNumber.degree, nzmath.algfield.NumberField.polynomial, nzmath.algfield.BasicAlgNumber.polynomial, nzmath.algfield.MatAlgNumber.polynomial, and nzmath.bigrange.range().

getRing()

def nzmath.algfield.MatAlgNumber.getRing

(

self

)

Return the algebraic number field contained self.

Definition at line 728 of file algfield.py.

References nzmath.algfield.NumberField.polynomial, nzmath.algfield.BasicAlgNumber.polynomial, and nzmath.algfield.MatAlgNumber.polynomial.

Referenced by nzmath.poly.multiutil.RingPolynomial.__add__(), nzmath.ring.QuotientFieldElement.__add__(), nzmath.poly.uniutil.RingPolynomial.__add__(), nzmath.ring.QuotientFieldElement.__eq__(), nzmath.poly.uniutil.FieldPolynomial.__pow__(), nzmath.poly.multiutil.RingPolynomial.__radd__(), nzmath.poly.uniutil.RingPolynomial.__radd__(), nzmath.poly.multiutil.RingPolynomial.__rsub__(), nzmath.ring.QuotientFieldElement.__rsub__(), nzmath.poly.uniutil.RingPolynomial.__rsub__(), nzmath.ring.QuotientFieldElement.__rtruediv__(), nzmath.poly.multiutil.RingPolynomial.__sub__(), nzmath.ring.QuotientFieldElement.__sub__(), nzmath.poly.uniutil.RingPolynomial.__sub__(), nzmath.ring.QuotientFieldElement.__truediv__(), nzmath.poly.uniutil.PrimeCharacteristicFunctionsProvider._small_index_mod_pow(), nzmath.ring.CommutativeRingElement.exact_division(), nzmath.poly.uniutil.DivisionProvider.extgcd(), nzmath.poly.uniutil.PrimeCharacteristicFunctionsProvider.factor(), nzmath.poly.uniutil.DivisionProvider.mod_pow(), nzmath.poly.uniutil.PrimeCharacteristicFunctionsProvider.mod_pow(), nzmath.poly.uniutil.PseudoDivisionProvider.monic_pow(), nzmath.ring.CommutativeRingElement.mul_module_action(), and nzmath.poly.uniutil.SubresultantGcdProvider.subresultant_gcd().

inverse()

def nzmath.algfield.MatAlgNumber.inverse

(

self

)

Definition at line 714 of file algfield.py.

References nzmath.algfield.MatAlgNumber.matrix, nzmath.algfield.NumberField.polynomial, nzmath.algfield.BasicAlgNumber.polynomial, nzmath.algfield.MatAlgNumber.polynomial, and nzmath.bigrange.range().

Referenced by nzmath.permute.Permute.__pow__(), nzmath.intresidue.IntegerResidueClass.__pow__(), nzmath.permute.ExPermute.__pow__(), nzmath.module.Ideal.__pow__(), nzmath.matrix.RingSquareMatrix.__pow__(), nzmath.permute.Permute.__rdiv__(), nzmath.permute.ExPermute.__rdiv__(), and nzmath.ring.QuotientFieldElement.__rtruediv__().

norm()

def nzmath.algfield.MatAlgNumber.norm

(

self

)

Definition at line 722 of file algfield.py.

References nzmath.algfield.MatAlgNumber.matrix.

Referenced by nzmath.module.Ideal.isPrime().

trace()

def nzmath.algfield.MatAlgNumber.trace

(

self

)

Definition at line 725 of file algfield.py.

References nzmath.algfield.MatAlgNumber.matrix.

Referenced by nzmath.matrix.RingSquareMatrix._characteristicPolyList(), and nzmath.elliptic.ECoverGF.order().

Member Data Documentation

__div__

def nzmath.algfield.MatAlgNumber.__div__ = __truediv__

staticprivate

Definition at line 704 of file algfield.py.

__floordiv__

def nzmath.algfield.MatAlgNumber.__floordiv__ = __truediv__

staticprivate

Definition at line 705 of file algfield.py.

__radd__

def nzmath.algfield.MatAlgNumber.__radd__ = __add__

staticprivate

Definition at line 663 of file algfield.py.

__rmul__

def nzmath.algfield.MatAlgNumber.__rmul__ = __mul__

staticprivate

Definition at line 689 of file algfield.py.

coeff

nzmath.algfield.MatAlgNumber.coeff

Definition at line 602 of file algfield.py.

Referenced by nzmath.algfield.MatAlgNumber.ch_basic().

degree

nzmath.algfield.MatAlgNumber.degree

Definition at line 603 of file algfield.py.

Referenced by nzmath.poly.array.ArrayPoly.__add__(), nzmath.algfield.MatAlgNumber.__add__(), nzmath.finitefield.ExtendedField.__eq__(), nzmath.finitefield.ExtendedField.__hash__(), nzmath.poly.array.ArrayPoly.__mul__(), nzmath.poly.array.ArrayPolyMod.__mul__(), nzmath.finitefield.ExtendedField.__repr__(), nzmath.poly.array.ArrayPoly.__sub__(), nzmath.algfield.MatAlgNumber.__sub__(), nzmath.finitefield.ExtendedField.card(), nzmath.algfield.MatAlgNumber.ch_basic(), nzmath.poly.array.ArrayPoly.coefficients_to_dict(), nzmath.poly.uniutil.DomainPolynomial.discriminant(), nzmath.poly.uniutil.FieldPolynomial.discriminant(), nzmath.poly.array.ArrayPoly.downshift_degree(), nzmath.poly.array.ArrayPoly.FFT_mul(), nzmath.poly.array.ArrayPolyMod.FFT_mul(), nzmath.finitefield.ExtendedField.issubring(), nzmath.poly.array.ArrayPoly.power(), nzmath.poly.array.ArrayPolyMod.power(), nzmath.poly.array.ArrayPoly.split_at(), and nzmath.poly.array.ArrayPolyMod.split_at().

field

nzmath.algfield.MatAlgNumber.field

Definition at line 638 of file algfield.py.

Referenced by nzmath.finitefield.ExtendedFieldElement.__add__(), nzmath.finitefield.ExtendedFieldElement.__eq__(), nzmath.finitefield.ExtendedFieldElement.__mul__(), nzmath.finitefield.ExtendedFieldElement.__neg__(), nzmath.finitefield.ExtendedFieldElement.__pow__(), nzmath.finitefield.ExtendedFieldElement.__repr__(), nzmath.finitefield.ExtendedFieldElement.__sub__(), nzmath.finitefield.ExtendedFieldElement._op(), nzmath.finitefield.ExtendedFieldElement.getRing(), nzmath.finitefield.ExtendedFieldElement.inverse(), nzmath.finitefield.ExtendedFieldElement.norm(), and nzmath.finitefield.ExtendedFieldElement.trace().

matrix

nzmath.algfield.MatAlgNumber.matrix

Definition at line 636 of file algfield.py.

Referenced by nzmath.algfield.MatAlgNumber.__add__(), nzmath.algfield.MatAlgNumber.__mul__(), nzmath.algfield.MatAlgNumber.__neg__(), nzmath.algfield.MatAlgNumber.__pow__(), nzmath.algfield.MatAlgNumber.__repr__(), nzmath.algfield.MatAlgNumber.__sub__(), nzmath.algfield.MatAlgNumber.__truediv__(), nzmath.algfield.MatAlgNumber.inverse(), nzmath.algfield.MatAlgNumber.norm(), and nzmath.algfield.MatAlgNumber.trace().

polynomial

nzmath.algfield.MatAlgNumber.polynomial

Definition at line 637 of file algfield.py.

Referenced by nzmath.algfield.MatAlgNumber.__add__(), nzmath.algfield.MatAlgNumber.__mul__(), nzmath.algfield.MatAlgNumber.__neg__(), nzmath.algfield.MatAlgNumber.__pow__(), nzmath.algfield.MatAlgNumber.__repr__(), nzmath.algfield.MatAlgNumber.__sub__(), nzmath.algfield.MatAlgNumber.__truediv__(), nzmath.algfield.MatAlgNumber.ch_basic(), nzmath.algfield.MatAlgNumber.getRing(), and nzmath.algfield.MatAlgNumber.inverse().

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

• nzmath/algfield.py