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


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)


 _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.

from nzmath.plugins import SETPRECISION

Then, the following computations will be done in such precision, if

Function Documentation

◆ _initialize()

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

Definition at line 216 of file

References nzmath.equation._upper_bound_of_roots(), nzmath.equation.Newton(), and nzmath.bigrange.range().

Referenced by nzmath.equation._SimMethod().

◆ _SimMethod()

def nzmath.equation._SimMethod (   g,
  initials = None,
  newtoninitial = None,
  repeat = 250 
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

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)
Return an upper bound of roots.

Definition at line 240 of file

Referenced by nzmath.equation._initialize().

◆ allroots_Fp()

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

Definition at line 296 of file

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

◆ e1()

def nzmath.equation.e1 (   x)
0 = x[0] + x[1]*t

Definition at line 33 of file

◆ e1_ZnZ()

def nzmath.equation.e1_ZnZ (   x,
Return the solution of x[0] + x[1]*t = 0 (mod n).
x[0], x[1] and n must be positive integers.

Definition at line 42 of file

Referenced by nzmath.equation.e2_Fp().

◆ e2()

def nzmath.equation.e2 (   x)
0 = x[0] + x[1]*t + x[2]*t**2

Definition at line 52 of file

◆ e2_Fp()

def nzmath.equation.e2_Fp (   x,
p is prime
f = x[0] + x[1]*t + x[2]*t**2

Definition at line 64 of file

References nzmath.equation.e1_ZnZ().

Referenced by nzmath.equation.e3_Fp().

◆ e3()

def nzmath.equation.e3 (   x)
0 = x[0] + x[1]*t + x[2]*t**2 + x[3]*t**3

Definition at line 88 of file

References nzmath.bigrange.range().

◆ e3_Fp()

def nzmath.equation.e3_Fp (   x,
p is prime
0 = x[0] + x[1]*t + x[2]*t**2 + x[3]*t**3

Definition at line 114 of file

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[0] + f[1] * x + ... + f[n] * x ** n

Definition at line 136 of file

References nzmath.bigrange.range().

Referenced by nzmath.equation._initialize().

◆ root_Fp()

def nzmath.equation.root_Fp (   g,
  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

References nzmath.bigrange.range().

◆ roots_loop()

def nzmath.equation.roots_loop (   g,

Definition at line 316 of file

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

References nzmath.equation._SimMethod().

Variable Documentation

◆ _log

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

Definition at line 28 of file