NZMATH  1.2.0
About: NZMATH is a Python based number theory oriented calculation system.
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nzmath.module Namespace Reference

Classes

class  Ideal
 
class  Ideal_with_generator
 
class  Module
 
class  Submodule
 

Functions

def _toIntegerMatrix (mat, option=0)
 functions for internal computations More...
 
def _symmetric_element (i, j, mat)
 
def _base_multiplication (base, number_field)
 

Variables

list mono_method = ["index", "smallest_rational", "inverse", "norm"]
 
list di_method
 

Detailed Description

module, ideal etc. for number field

Function Documentation

◆ _base_multiplication()

def nzmath.module._base_multiplication (   base,
  number_field 
)
private
return [base[i] * base[j]] (as a numberfield element)
this is a precomputation for computing _module_mul

Definition at line 1018 of file module.py.

References nzmath.module._toIntegerMatrix(), and nzmath.bigrange.range().

◆ _symmetric_element()

def nzmath.module._symmetric_element (   i,
  j,
  mat 
)
private
get (i, j)-element from lst ordered (1, 1), (1, 2), (2, 2), ...
we assume that
1: (j, i)-element is same as (i, j)-element (i.e. symmetric)
2: index of mat starts 1 (i.e. for Matrix only)

Definition at line 1006 of file module.py.

Referenced by nzmath.module.Module._module_mul(), nzmath.module.Ideal._precompute_for_different(), and nzmath.module.Module._scalar_mul().

◆ _toIntegerMatrix()

def nzmath.module._toIntegerMatrix (   mat,
  option = 0 
)
private

functions for internal computations

transform a (including integral) rational matrix to 
    some integral matrix as the following
[option]
0: return integral-matrix, denominator
   (mat = 1/denominator * integral-matrix)
1: return integral-matrix, denominator, numerator
   (mat = numerator/denominator * reduced-int-matrix)
2: return integral-matrix, numerator (assuming mat is integral)
   (mat = numerator * numerator-reduced-rational-matrix)

Definition at line 954 of file module.py.

Referenced by nzmath.module.Module.__contains__(), nzmath.module._base_multiplication(), nzmath.module.Module._module_mul(), nzmath.module.Module._scalar_mul(), nzmath.module.Module._simplify(), nzmath.module.Module.change_base_module(), nzmath.module.Ideal.inverse(), nzmath.module.Module.smallest_rational(), and nzmath.module.Ideal_with_generator.to_HNFRepresentation().

Variable Documentation

◆ di_method

list nzmath.module.di_method
Initial value:
1 = ["__eq__", "__ne__", "__contains__", "intersect",
2  "issubideal", "issuperideal"]

Definition at line 937 of file module.py.

◆ mono_method

list nzmath.module.mono_method = ["index", "smallest_rational", "inverse", "norm"]

Definition at line 936 of file module.py.