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) |

## Classes | |

class | SquarefreeDecompositionMethod |

class | Undetermined |

## Functions | |

def | lenstra (n) |

def | trial_division (n) |

def | trivial_test (n) |

def | viafactor (n) |

def | lenstra_ternary (n) |

def | trivial_test_ternary (n) |

def | trial_division_ternary (n) |

## Variables | |

def | viafactor_ternary = viafactor |

viadecomposition = SquarefreeDecompositionMethod().issquarefree | |

Squarefreeness tests. Definition: n: squarefree <=> there is no p whose square divides n. Examples: - 0 is non-squarefree because any square of prime can divide 0. - 1 is squarefree because there is no prime dividing 1. - 2, 3, 5, and any other primes are squarefree. - 4, 8, 9, 12, 16 are non-squarefree composites. - 6, 10, 14, 15, 21 are squarefree composites.

def nzmath.squarefree.lenstra | ( | n | ) |

If return value is True, n is squarefree. Otherwise, the squarefreeness is still unknown and Undetermined is raised. The condition is so strong that it seems n is a prime or a Carmichael number. pre-condition: n & 1 reference: H.W.Lenstra 1973 ---

Definition at line 30 of file squarefree.py.

Referenced by nzmath.squarefree.trivial_test().

def nzmath.squarefree.lenstra_ternary | ( | n | ) |

Test the squarefreeness of n. The return value is one of the ternary logical constants. If return value is TRUE, n is squarefree. Otherwise, the squarefreeness is still unknown and UNKNOWN is returned. The condition is so strong that it seems n is a prime or a Carmichael number. pre-condition: n & 1 reference: H.W.Lenstra 1973 ---

Definition at line 119 of file squarefree.py.

References nzmath.bigrange.range().

Referenced by nzmath.squarefree.trivial_test_ternary().

def nzmath.squarefree.trial_division | ( | n | ) |

Test whether n is squarefree or not. The method is a kind of trial division.

Definition at line 50 of file squarefree.py.

References nzmath.squarefree.trivial_test().

def nzmath.squarefree.trial_division_ternary | ( | n | ) |

Test the squarefreeness of n. The return value is one of the True or False, not None. The method is a kind of trial division.

Definition at line 159 of file squarefree.py.

References nzmath.squarefree.trivial_test_ternary().

def nzmath.squarefree.trivial_test | ( | n | ) |

Test whether n is squarefree or not. This method do anything but factorization.

Definition at line 81 of file squarefree.py.

References nzmath.squarefree.lenstra().

Referenced by nzmath.squarefree.trial_division().

def nzmath.squarefree.trivial_test_ternary | ( | n | ) |

Test the squarefreeness of n. The return value is one of the ternary logical constants. The method uses a series of trivial tests.

Definition at line 141 of file squarefree.py.

References nzmath.squarefree.lenstra_ternary().

Referenced by nzmath.squarefree.SquarefreeDecompositionMethod.generate(), nzmath.squarefree.SquarefreeDecompositionMethod.issquarefree(), and nzmath.squarefree.trial_division_ternary().

def nzmath.squarefree.viafactor | ( | n | ) |

Test whether n is squarefree or not. It is obvious that if one knows the prime factorization of the number, he/she can tell whether the number is squarefree or not.

Definition at line 98 of file squarefree.py.

nzmath.squarefree.viadecomposition = SquarefreeDecompositionMethod().issquarefree |

Definition at line 264 of file squarefree.py.

def nzmath.squarefree.viafactor_ternary = viafactor |

Definition at line 190 of file squarefree.py.