Inheritance diagram for nzmath.poly.hensel.HenselLiftPair:

Collaboration diagram for nzmath.poly.hensel.HenselLiftPair:

Public Member Functions
def	__init__ (self, target, factor1, factor2, ladder1, ladder2, p, q=None)

def	from_factors (cls, target, factor1, factor2, p)

def	lift_factors (self)

def	lift_ladder (self)

def	lift (self)

Public Attributes
	f

	a1

	a2

	u1

	u2

	p

	q

Properties
	factors = property(_get_factors)

Private Member Functions
def	_get_factors (self)

Detailed Description

A class represents integer polynomial pair which will be lifted by
Hensel's method.

Definition at line 67 of file hensel.py.

Constructor & Destructor Documentation

◆ init()

def nzmath.poly.hensel.HenselLiftPair.__init__	(	self,
		target,
		factor1,
		factor2,
		ladder1,
		ladder2,
		p,
		q = `None`
	)

HenselLiftPair(f, a1, a2, u1, u2, p, q)

The parameters satisfy that:
  a1 and a2 are monic,
  f == a1*a2 (mod q) and
  a1*u1 + a2*u2 == 1 (mod p),
with positive integers p dividing q.

If p==q, q can be omit from the argument.

Definition at line 72 of file hensel.py.

Member Function Documentation

◆ _get_factors()

def nzmath.poly.hensel.HenselLiftPair._get_factors ( self )

private

getter for factors of target mod q

Definition at line 154 of file hensel.py.

References nzmath.poly.hensel.HenselLiftPair.a1, nzmath.elliptic.ECGeneric.a1, nzmath.elliptic.ECoverQ.a1, nzmath.elliptic.ECoverGF.a1, nzmath.poly.hensel.HenselLiftPair.a2, nzmath.elliptic.ECGeneric.a2, nzmath.elliptic.ECoverQ.a2, and nzmath.elliptic.ECoverGF.a2.

◆ from_factors()

def nzmath.poly.hensel.HenselLiftPair.from_factors	(	cls,
		target,
		factor1,
		factor2,
		p
	)

Create and return an instance of HenselLiftPair.

HenselLiftPair.from_factors(f, a1, a2, p)

The parameters satisfy that:
  f == a1*a2 (mod p)
with a prime number p.

Definition at line 96 of file hensel.py.

References nzmath.poly.hensel._extgcdp().

◆ lift()

def nzmath.poly.hensel.HenselLiftPair.lift ( self )

The lift.

Definition at line 147 of file hensel.py.

References nzmath.poly.hensel.HenselLiftPair.lift_factors(), and nzmath.poly.hensel.HenselLiftPair.lift_ladder().

◆ lift_factors()

def nzmath.poly.hensel.HenselLiftPair.lift_factors ( self )

Update factors by lifted integer coefficient polynomials Ai's:
  f == A1*A2 (mod p*q) and
  Ai == ai (mod q) (i = 1, 2).
Moreover, q is updated by p*q

PRECONDITIONS (automatically satisfied):
  f == a1*a1 (mod q)
  a1*u1 + a2*u2 == 1 (mod p)
  p | q

Definition at line 109 of file hensel.py.

References nzmath.poly.hensel.HenselLiftPair.a1, nzmath.elliptic.ECGeneric.a1, nzmath.elliptic.ECoverQ.a1, nzmath.elliptic.ECoverGF.a1, nzmath.poly.hensel.HenselLiftPair.a2, nzmath.elliptic.ECGeneric.a2, nzmath.elliptic.ECoverQ.a2, nzmath.elliptic.ECoverGF.a2, nzmath.poly.hensel.HenselLiftPair.f, nzmath.ecpp.Elliptic.f, nzmath.poly.hensel.HenselLiftPair.p, nzmath.poly.hensel.HenselLiftPair.q, nzmath.poly.hensel.HenselLiftPair.u1, and nzmath.poly.hensel.HenselLiftPair.u2.

Referenced by nzmath.poly.hensel.HenselLiftPair.lift(), and nzmath.poly.hensel.HenselLiftMulti.lift().

◆ lift_ladder()

def nzmath.poly.hensel.HenselLiftPair.lift_ladder ( self )

Update u1 and u2 with U1 and U2:
  a1*U1 + a2*U2 == 1 (mod p**2)
  Ui == ui (mod p) (i = 1, 2)
then, update p with p**2.

PRECONDITIONS (automatically satisfied):
  a1*u1 + a2*u2 == 1 (mod p)

Definition at line 130 of file hensel.py.

References nzmath.poly.hensel.HenselLiftPair.a1, nzmath.elliptic.ECGeneric.a1, nzmath.elliptic.ECoverQ.a1, nzmath.elliptic.ECoverGF.a1, nzmath.poly.hensel.HenselLiftPair.a2, nzmath.elliptic.ECGeneric.a2, nzmath.elliptic.ECoverQ.a2, nzmath.elliptic.ECoverGF.a2, nzmath.poly.hensel.HenselLiftPair.p, nzmath.poly.hensel.HenselLiftPair.u1, and nzmath.poly.hensel.HenselLiftPair.u2.