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.equation Namespace Reference

Functions

def e1 (x)

def e1_ZnZ (x, n)

def e2 (x)

def e2_Fp (x, p)

def e3 (x)

def e3_Fp (x, p)

def Newton (f, initial=1, repeat=250)

def SimMethod (f, NewtonInitial=1, repeat=250)

def _SimMethod (g, initials=None, newtoninitial=None, repeat=250)

def _initialize (g, newtoninitial=None)

def _upper_bound_of_roots (g)

def root_Fp (g, p, flag=True)

def allroots_Fp (g, p)

def roots_loop (g, deg_g, p, Fp)

Variables

_log = logging.getLogger('nzmath.equation')

Detailed Description

equation -- methods to solve algebraic equations.

If you would like to solve an equation in the complex field and need
more precision, then you can import and use plugins.SETPRECISION.

e.g:
from nzmath.plugins import SETPRECISION
SETPRECISION(200)

Then, the following computations will be done in such precision, if
plugins.PRECISION_CHANGEABLE is true.

◆ _initialize()

 def nzmath.equation._initialize ( g, newtoninitial = None )
private
create initial values of equation given as a list g.

Definition at line 216 of file equation.py.

Referenced by nzmath.equation._SimMethod().

◆ _SimMethod()

 def nzmath.equation._SimMethod ( g, initials = None, newtoninitial = None, repeat = 250 )
private
Return zeros of a polynomial given as a list.

- g is the list of the polynomial coefficient in ascending order.
- initial (optional) is a list of initial approximations of zeros.
- newtoninitial (optional) is an initial value for Newton method to
obtain an initial approximations of zeros if 'initial' is not given.
- repeat (optional) is the number of iteration. The default is 250.

Definition at line 172 of file equation.py.

References nzmath.equation._initialize(), and nzmath.bigrange.range().

Referenced by nzmath.equation.SimMethod().

◆ _upper_bound_of_roots()

 def nzmath.equation._upper_bound_of_roots ( g )
private
Return an upper bound of roots.

Definition at line 240 of file equation.py.

Referenced by nzmath.equation._initialize().

◆ allroots_Fp()

 def nzmath.equation.allroots_Fp ( g, p )
Return roots over F_p of nonzero polynomial g.
p must be prime.

Definition at line 296 of file equation.py.

References nzmath.bigrange.range(), and nzmath.equation.roots_loop().

◆ e1()

 def nzmath.equation.e1 ( x )
0 = x + x*t

Definition at line 33 of file equation.py.

◆ e1_ZnZ()

 def nzmath.equation.e1_ZnZ ( x, n )
Return the solution of x + x*t = 0 (mod n).
x, x and n must be positive integers.

Definition at line 42 of file equation.py.

Referenced by nzmath.equation.e2_Fp().

◆ e2()

 def nzmath.equation.e2 ( x )
0 = x + x*t + x*t**2

Definition at line 52 of file equation.py.

◆ e2_Fp()

 def nzmath.equation.e2_Fp ( x, p )
p is prime
f = x + x*t + x*t**2

Definition at line 64 of file equation.py.

References nzmath.equation.e1_ZnZ().

Referenced by nzmath.equation.e3_Fp().

◆ e3()

 def nzmath.equation.e3 ( x )
0 = x + x*t + x*t**2 + x*t**3

Definition at line 88 of file equation.py.

References nzmath.bigrange.range().

◆ e3_Fp()

 def nzmath.equation.e3_Fp ( x, p )
p is prime
0 = x + x*t + x*t**2 + x*t**3

Definition at line 114 of file equation.py.

References nzmath.equation.e2_Fp(), and nzmath.arith1.inverse().

◆ Newton()

 def nzmath.equation.Newton ( f, initial = 1, repeat = 250 )
Compute x s.t. 0 = f + f * x + ... + f[n] * x ** n

Definition at line 136 of file equation.py.

References nzmath.bigrange.range().

Referenced by nzmath.equation._initialize().

◆ root_Fp()

 def nzmath.equation.root_Fp ( g, p, flag = True )
Return a root over F_p of nonzero polynomial g.
p must be prime.
If flag = False, return a root randomly

Definition at line 248 of file equation.py.

References nzmath.bigrange.range().

◆ roots_loop()

 def nzmath.equation.roots_loop ( g, deg_g, p, Fp )

Definition at line 316 of file equation.py.

Referenced by nzmath.equation.allroots_Fp().

◆ SimMethod()

 def nzmath.equation.SimMethod ( f, NewtonInitial = 1, repeat = 250 )
Return zeros of a polynomial given as a list.

Definition at line 161 of file equation.py.

References nzmath.equation._SimMethod().

◆ _log

 nzmath.equation._log = logging.getLogger('nzmath.equation')
private

Definition at line 28 of file equation.py.