nzmath.algfield Namespace Reference

Classes
class	BasicAlgNumber
class	MatAlgNumber
class	NumberField

Functions
def	prime_decomp (p, polynomial)
def	_easy_prime_decomp (p, polynomial)
def	_main_prime_decomp (p, polynomial)
def	changetype (a, polynomial=[0, 1])
def	disc (A)
def	qpoly (coeffs)
def	zpoly (coeffs)
def	fppoly (coeffs, p)

Function Documentation

_easy_prime_decomp()

def nzmath.algfield._easy_prime_decomp (   p,   polynomial  )

private

prime decomposition by factoring polynomial

Definition at line 758 of file algfield.py.

References nzmath.algfield.fppoly(), and nzmath.bigrange.range().

Referenced by nzmath.algfield.prime_decomp().

_main_prime_decomp()

def nzmath.algfield._main_prime_decomp (   p,   polynomial  )

private

main step of prime decomposition

Definition at line 782 of file algfield.py.

Referenced by nzmath.algfield.prime_decomp().

changetype()

def nzmath.algfield.changetype	(		a,
			polynomial = [0, 1]
	)

Change 'a' to be an element of field K defined polynomial

Definition at line 789 of file algfield.py.

References nzmath.bigrange.range().

Referenced by nzmath.algfield.NumberField.POLRED().

disc()

def nzmath.algfield.disc

(

A

)

Compute the discriminant of a_i, where A=[a_1,...,a_n]

Definition at line 812 of file algfield.py.

References nzmath.bigrange.range().

fppoly()

def nzmath.algfield.fppoly	(		coeffs,
			p
	)

Return a Z_p coefficient polynomial constructed from given
coeffs.  The coeffs is a list of coefficients in ascending order.

Definition at line 840 of file algfield.py.

Referenced by nzmath.algfield._easy_prime_decomp().

prime_decomp()

def nzmath.algfield.prime_decomp	(		p,
			polynomial
	)

Return prime decomposition of (p) over Q[x]/(polynomial).

Definition at line 747 of file algfield.py.

References nzmath.algfield._easy_prime_decomp(), and nzmath.algfield._main_prime_decomp().

qpoly()

def nzmath.algfield.qpoly

(

coeffs

)

Return a rational coefficient polynomial constructed from given
coeffs.  The coeffs is a list of coefficients in ascending order.

Definition at line 825 of file algfield.py.

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

zpoly()

def nzmath.algfield.zpoly

(

coeffs

)

Return an integer coefficient polynomial constructed from given
coeffs.  The coeffs is a list of coefficients in ascending order.

Definition at line 833 of file algfield.py.

Referenced by nzmath.algfield.NumberField.__mul__(), nzmath.algfield.BasicAlgNumber.__mul__(), nzmath.algfield.BasicAlgNumber.__pow__(), nzmath.algfield.BasicAlgNumber.__truediv__(), nzmath.algfield.BasicAlgNumber.norm(), nzmath.algfield.NumberField.POLRED(), and nzmath.algfield.NumberField.signature().