nzmath.algfield.BasicAlgNumber Class Reference

Inheritance diagram for nzmath.algfield.BasicAlgNumber:

Collaboration diagram for nzmath.algfield.BasicAlgNumber:

Public Member Functions
def	__init__ (self, valuelist, polynomial, precompute=False)
def	__repr__ (self)
def	__neg__ (self)
def	__add__ (self, other)
def	__sub__ (self, other)
def	__mul__ (self, other)
def	__pow__ (self, exponent, mod=None)
def	inverse (self)
def	__truediv__ (self, other)
def	getConj (self)
def	getApprox (self)
def	getCharPoly (self)
def	getRing (self)
def	trace (self)
def	norm (self)
def	isAlgInteger (self)
def	ch_matrix (self)

Public Attributes
	value
	coeff
	denom
	degree
	polynomial
	field
	conj
	approx
	charpoly

Private Member Functions
def	_int_to_algnumber (self, other)
def	_rational_to_algnumber (self, other)

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

Detailed Description

The class for algebraic number.

Definition at line 341 of file algfield.py.

Constructor & Destructor Documentation

__init__()

def nzmath.algfield.BasicAlgNumber.__init__	(		self,
			valuelist,
			polynomial,
			precompute = False
	)

Definition at line 345 of file algfield.py.

Member Function Documentation

__add__()

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

Definition at line 388 of file algfield.py.

References nzmath.algfield.BasicAlgNumber._int_to_algnumber(), nzmath.algfield.BasicAlgNumber._rational_to_algnumber(), nzmath.algfield.BasicAlgNumber.coeff, nzmath.algfield.BasicAlgNumber.denom, nzmath.algfield.NumberField.polynomial, nzmath.algfield.BasicAlgNumber.polynomial, and nzmath.bigrange.range().

Referenced by nzmath.algfield.BasicAlgNumber.__sub__().

__mul__()

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

Definition at line 408 of file algfield.py.

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

__neg__()

def nzmath.algfield.BasicAlgNumber.__neg__

(

self

)

Definition at line 368 of file algfield.py.

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

__pow__()

def nzmath.algfield.BasicAlgNumber.__pow__	(		self,
			exponent,
			mod = None
	)

Definition at line 434 of file algfield.py.

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

__repr__()

def nzmath.algfield.BasicAlgNumber.__repr__

(

self

)

Definition at line 364 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.BasicAlgNumber.coeff, nzmath.algfield.BasicAlgNumber.denom, nzmath.algfield.NumberField.polynomial, and nzmath.algfield.BasicAlgNumber.polynomial.

__sub__()

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

Definition at line 405 of file algfield.py.

References nzmath.algfield.BasicAlgNumber.__add__().

__truediv__()

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

Definition at line 465 of file algfield.py.

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

_int_to_algnumber()

def nzmath.algfield.BasicAlgNumber._int_to_algnumber (   self,   other  )

private

other (integer) -> BasicAlgNumber (over self.field)

Definition at line 374 of file algfield.py.

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

Referenced by nzmath.algfield.BasicAlgNumber.__add__().

_rational_to_algnumber()

def nzmath.algfield.BasicAlgNumber._rational_to_algnumber (   self,   other  )

private

other (rational) -> BasicAlgNumber (over self.field)

Definition at line 381 of file algfield.py.

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

Referenced by nzmath.algfield.BasicAlgNumber.__add__().

ch_matrix()

def nzmath.algfield.BasicAlgNumber.ch_matrix

(

self

)

Change style to MatAlgNumber.

Definition at line 583 of file algfield.py.

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

getApprox()

def nzmath.algfield.BasicAlgNumber.getApprox

(

self

)

Return the approximations of all conjugates of self.

Definition at line 488 of file algfield.py.

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

Referenced by nzmath.algfield.BasicAlgNumber.getCharPoly().

getCharPoly()

def nzmath.algfield.BasicAlgNumber.getCharPoly

(

self

)

Return the characteristic polynomial of self
by compute products of (x-self^{(i)}).

Definition at line 502 of file algfield.py.

References nzmath.algfield.NumberField.degree, nzmath.algfield.BasicAlgNumber.degree, nzmath.algfield.BasicAlgNumber.getApprox(), and nzmath.bigrange.range().

getConj()

def nzmath.algfield.BasicAlgNumber.getConj

(

self

)

Return (approximate) solutions of self.polynomial.
We can discriminate the conjugate field of self by these values.

Definition at line 479 of file algfield.py.

Referenced by nzmath.algfield.BasicAlgNumber.getApprox().

getRing()

def nzmath.algfield.BasicAlgNumber.getRing

(

self

)

Return the algebraic number field contained self.

Definition at line 522 of file algfield.py.

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

(

self

)

Definition at line 446 of file algfield.py.

References nzmath.algfield.BasicAlgNumber.coeff, nzmath.algfield.NumberField.degree, nzmath.algfield.BasicAlgNumber.degree, nzmath.algfield.BasicAlgNumber.denom, nzmath.algfield.NumberField.polynomial, nzmath.algfield.BasicAlgNumber.polynomial, nzmath.algfield.qpoly(), 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__().

isAlgInteger()

def nzmath.algfield.BasicAlgNumber.isAlgInteger

(

self

)

Determine whether self is an algebraic integer or not.

Definition at line 573 of file algfield.py.

References nzmath.algfield.BasicAlgNumber.norm().

norm()

def nzmath.algfield.BasicAlgNumber.norm

(

self

)

Compute the norm of self in K.

Definition at line 553 of file algfield.py.

References nzmath.algfield.BasicAlgNumber.coeff, nzmath.algfield.NumberField.degree, nzmath.algfield.BasicAlgNumber.degree, nzmath.algfield.BasicAlgNumber.denom, nzmath.algfield.NumberField.polynomial, nzmath.algfield.BasicAlgNumber.polynomial, and nzmath.algfield.zpoly().

Referenced by nzmath.algfield.BasicAlgNumber.isAlgInteger(), and nzmath.module.Ideal.isPrime().

trace()

def nzmath.algfield.BasicAlgNumber.trace

(

self

)

Compute the trace of self in K.

Definition at line 528 of file algfield.py.

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

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

Member Data Documentation

__div__

def nzmath.algfield.BasicAlgNumber.__div__ = __truediv__

staticprivate

Definition at line 476 of file algfield.py.

__floordiv__

def nzmath.algfield.BasicAlgNumber.__floordiv__ = __truediv__

staticprivate

Definition at line 477 of file algfield.py.

__radd__

def nzmath.algfield.BasicAlgNumber.__radd__ = __add__

staticprivate

Definition at line 403 of file algfield.py.

__rmul__

def nzmath.algfield.BasicAlgNumber.__rmul__ = __mul__

staticprivate

Definition at line 432 of file algfield.py.

approx

nzmath.algfield.BasicAlgNumber.approx

Definition at line 499 of file algfield.py.

charpoly

nzmath.algfield.BasicAlgNumber.charpoly

Definition at line 519 of file algfield.py.

coeff

nzmath.algfield.BasicAlgNumber.coeff

Definition at line 349 of file algfield.py.

Referenced by nzmath.algfield.BasicAlgNumber.__add__(), nzmath.algfield.BasicAlgNumber.__mul__(), nzmath.algfield.BasicAlgNumber.__neg__(), nzmath.algfield.BasicAlgNumber.__pow__(), nzmath.algfield.BasicAlgNumber.__repr__(), nzmath.algfield.BasicAlgNumber.__truediv__(), nzmath.algfield.MatAlgNumber.ch_basic(), nzmath.algfield.BasicAlgNumber.ch_matrix(), nzmath.algfield.BasicAlgNumber.getApprox(), nzmath.algfield.BasicAlgNumber.inverse(), nzmath.algfield.BasicAlgNumber.norm(), and nzmath.algfield.BasicAlgNumber.trace().

conj

nzmath.algfield.BasicAlgNumber.conj

Definition at line 485 of file algfield.py.

degree

nzmath.algfield.BasicAlgNumber.degree

Definition at line 351 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.algfield.BasicAlgNumber.__mul__(), nzmath.algfield.BasicAlgNumber.__pow__(), nzmath.finitefield.ExtendedField.__repr__(), nzmath.poly.array.ArrayPoly.__sub__(), nzmath.algfield.MatAlgNumber.__sub__(), nzmath.algfield.BasicAlgNumber.__truediv__(), nzmath.algfield.BasicAlgNumber._int_to_algnumber(), nzmath.algfield.BasicAlgNumber._rational_to_algnumber(), nzmath.finitefield.ExtendedField.card(), nzmath.algfield.MatAlgNumber.ch_basic(), nzmath.algfield.BasicAlgNumber.ch_matrix(), 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.algfield.BasicAlgNumber.getApprox(), nzmath.algfield.BasicAlgNumber.getCharPoly(), nzmath.algfield.BasicAlgNumber.inverse(), nzmath.finitefield.ExtendedField.issubring(), nzmath.algfield.BasicAlgNumber.norm(), nzmath.poly.array.ArrayPoly.power(), nzmath.poly.array.ArrayPolyMod.power(), nzmath.poly.array.ArrayPoly.split_at(), and nzmath.poly.array.ArrayPolyMod.split_at().

denom

nzmath.algfield.BasicAlgNumber.denom

Definition at line 350 of file algfield.py.

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

field

nzmath.algfield.BasicAlgNumber.field

Definition at line 353 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().

polynomial

nzmath.algfield.BasicAlgNumber.polynomial

Definition at line 352 of file algfield.py.

Referenced by nzmath.algfield.BasicAlgNumber.__add__(), nzmath.algfield.MatAlgNumber.__add__(), nzmath.algfield.BasicAlgNumber.__mul__(), nzmath.algfield.MatAlgNumber.__mul__(), nzmath.algfield.BasicAlgNumber.__neg__(), nzmath.algfield.MatAlgNumber.__neg__(), nzmath.algfield.BasicAlgNumber.__pow__(), nzmath.algfield.MatAlgNumber.__pow__(), nzmath.algfield.BasicAlgNumber.__repr__(), nzmath.algfield.MatAlgNumber.__repr__(), nzmath.algfield.MatAlgNumber.__sub__(), nzmath.algfield.BasicAlgNumber.__truediv__(), nzmath.algfield.MatAlgNumber.__truediv__(), nzmath.algfield.BasicAlgNumber._int_to_algnumber(), nzmath.algfield.BasicAlgNumber._rational_to_algnumber(), nzmath.algfield.MatAlgNumber.ch_basic(), nzmath.algfield.BasicAlgNumber.ch_matrix(), nzmath.algfield.BasicAlgNumber.getRing(), nzmath.algfield.MatAlgNumber.getRing(), nzmath.algfield.BasicAlgNumber.inverse(), nzmath.algfield.MatAlgNumber.inverse(), nzmath.algfield.BasicAlgNumber.norm(), and nzmath.algfield.BasicAlgNumber.trace().

value

nzmath.algfield.BasicAlgNumber.value

Definition at line 348 of file algfield.py.

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

• nzmath/algfield.py