NZMATH  1.2.0 About: NZMATH is a Python based number theory oriented calculation system.   Fossies Dox: NZMATH-1.2.0.tar.gz  ("inofficial" and yet experimental doxygen-generated source code documentation)
nzmath.poly.hensel Namespace Reference

## Classes

class  HenselLiftMulti

class  HenselLiftPair

class  HenselLiftSimultaneously

## Functions

def _extgcdp (f, g, p)

def _init_cofactors (factors)

def lift_upto (target, factors, p, bound)

## Variables

the_ring = polyring.PolynomialRing(rational.theIntegerRing)

the_one = the_ring.one

the_zero = the_ring.zero

## Detailed Description

```hensel -- Hensel Lift classes for factorization
of integer coefficient polynomials

If you need lifted factors only once, you may want to use lift_upto
function.  On the other hand, if you might happen to need another
lift, you would directly use one of the lifters and its lift method
for consecutive lifts.
```

## ◆ _extgcdp()

 def nzmath.poly.hensel._extgcdp ( f, g, p )
private
```_extgcdp(f,g,p) -> u,v,w

Find u,v,w such that f*u + g*v = w = gcd(f,g) mod p.
p should be a prime number.

This is a private function.
```

Definition at line 25 of file hensel.py.

## ◆ _init_cofactors()

 def nzmath.poly.hensel._init_cofactors ( factors )
private
```Return list of bi's; bi = a{i+1}*...*ar where ai's are of factors.

This is a private function.
```

Definition at line 54 of file hensel.py.

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

## ◆ lift_upto()

 def nzmath.poly.hensel.lift_upto ( target, factors, p, bound )
```Hensel lift factors mod p of target upto bound and return factors
mod q and q.

PRECONDITIONS:
target == product(factors) mod p
POSTCONDITIONS:
there exist k s.t. q == p**k >= bound and
target == product(result) mod q
```

Definition at line 493 of file hensel.py.

## ◆ the_one

 nzmath.poly.hensel.the_one = the_ring.one

Definition at line 21 of file hensel.py.

## ◆ the_ring

 nzmath.poly.hensel.the_ring = polyring.PolynomialRing(rational.theIntegerRing)

Definition at line 20 of file hensel.py.

## ◆ the_zero

 nzmath.poly.hensel.the_zero = the_ring.zero

Definition at line 22 of file hensel.py.