Inheritance diagram for nzmath.poly.hensel.HenselLiftMulti:

Collaboration diagram for nzmath.poly.hensel.HenselLiftMulti:

Public Member Functions
def	__init__ (self, target, factors, cofactors, ladder, p, q=None)

def	from_factors (cls, target, factors, p)

def	lift_factors (self)

def	lift_ladder (self)

def	lift (self)

Public Attributes
	f

	a

	r

	b

	s

	t

	p

	q

Properties
	factors = property(_get_factors)

Private Member Functions
def	_get_factors (self)

Detailed Description

A class represents integer polynomials which will be lifted by
Hensel's lemma.

If the number of factors is two, you should use HenselLiftPair.

Definition at line 163 of file hensel.py.

Constructor & Destructor Documentation

◆ init()

def nzmath.poly.hensel.HenselLiftMulti.__init__	(	self,
		target,
		factors,
		cofactors,
		ladder,
		p,
		q = `None`
	)

HenselLiftMulti(f, factors, ladder, p, q)

The parameters satisfy that:
 +  ai's of factors and f are all monic
 +  bi's of cofactors are product of aj's for i < j
 +  f == a1*...*ar (mod q)
 +  ladder is a tuple (sis, tis) and si's of sis and ti's of tis
    satisfy: ai*si + bi*ti == 1 (mod p),
with positive integers p dividing q.

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

Definition at line 170 of file hensel.py.

Member Function Documentation

◆ _get_factors()

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

private

getter for factors of target mod q

Definition at line 268 of file hensel.py.

References nzmath.elliptic.ECGeneric.a, nzmath.poly.hensel.HenselLiftMulti.a, and nzmath.elliptic.ECoverGF.a.

◆ from_factors()

def nzmath.poly.hensel.HenselLiftMulti.from_factors	(	cls,
		target,
		factors,
		p
	)

Create and return an instance of HenselLiftMulti.

HenselLiftMulti.from_factors(f, factors, p)

The parameters satisfy that:
  f == a1*...*ar (mod p)
with a prime number p and ai's in factors.

Definition at line 197 of file hensel.py.

References nzmath.poly.hensel._extgcdp(), and nzmath.poly.hensel._init_cofactors().

◆ lift()

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

The lift.

Definition at line 261 of file hensel.py.

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

◆ lift_factors()

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

Find a lifted integer coefficient polynomials such that:
  f = A1*A2*...*Ar (mod q*p),
  Ai = ai (mod q) (i=1,2,...,r),
then, update q with q*p.

PRECONDITIONS (automatically satisfied):
  f = a1*a2*...*ar (mod q),
  ai*si + bi*ti = 1 (mod p) (i=1,2,...,r) and
  p | q.

Definition at line 215 of file hensel.py.

Referenced by nzmath.poly.hensel.HenselLiftMulti.lift().

◆ lift_ladder()

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

Update ladder si's and ti's with Si's and Ti's:
  ai*Si + bi*Ti == 1 (mod p**2) (i = 1, 2, ..., r),
  Si == si (mod p) (i = 1, 2, ..., r) and
  Ti == ti (mod p) (i = 1, 2, ..., r)
then, update p with p**2.

PRECONDITIONS (automatically satisfied):
  ai*si + bi*ti == 1 (mod p)

Definition at line 241 of file hensel.py.