Coverage for local/lib/python2.7/site-packages/sage/combinat/species/series_order.py : 58%

""" 

Series Order 

This file provides some utility classes which are useful when 

working with unknown, known, and infinite series orders for 

univariate power series. 

This code is based on the work of Ralf Hemmecke and Martin Rubey's 

Aldor-Combinat, which can be found at 

http://www.risc.uni-linz.ac.at/people/hemmecke/aldor/combinat/index.html. 

In particular, the relevant section for this file can be found at 

http://www.risc.uni-linz.ac.at/people/hemmecke/AldorCombinat/combinatsu30.html. 

""" 

from sage.rings.all import Integer 

class SeriesOrderElement: 

pass 

class InfiniteSeriesOrder(SeriesOrderElement): 

def __repr__(self): 

""" 

EXAMPLES:: 

sage: from sage.combinat.species.series_order import * 

sage: o = InfiniteSeriesOrder(); o 

Infinite series order 

""" 

return "Infinite series order" 

def __add__(self, x): 

""" 

EXAMPLES:: 

sage: from sage.combinat.species.series_order import * 

sage: o = InfiniteSeriesOrder() 

sage: o + 2 

Infinite series order 

sage: o + o 

Infinite series order 

:: 

sage: u = UnknownSeriesOrder() 

sage: o + u 

Unknown series order 

TESTS:: 

sage: o + -1 

Traceback (most recent call last): 

... 

ValueError: x must be a positive integer 

""" 

if isinstance(x, (int, Integer)): 

if x < 0: 

raise ValueError("x must be a positive integer") 

return self 

if isinstance(x, InfiniteSeriesOrder): 

return self 

if isinstance(x, UnknownSeriesOrder): 

return x 

raise TypeError("x must be a positive integer or a SeriesOrderElement") 

__radd__ = __add__ 

def __mul__(self, x): 

""" 

EXAMPLES:: 

sage: from sage.combinat.species.series_order import * 

sage: o = InfiniteSeriesOrder() 

sage: o * 2 

Infinite series order 

sage: o * o 

Infinite series order 

:: 

sage: u = UnknownSeriesOrder() 

sage: o * u 

Unknown series order 

TESTS:: 

sage: o * -1 

Traceback (most recent call last): 

... 

ValueError: x must be a positive integer 

""" 

if isinstance(x, (int, Integer)): 

if x < 0: 

raise ValueError("x must be a positive integer") 

elif x == 0: 

return x 

return self 

if isinstance(x, InfiniteSeriesOrder): 

return self 

if isinstance(x, UnknownSeriesOrder): 

return x 

raise TypeError("x must be a positive integer or a SeriesOrderElement") 

__rmul__ = __mul__ 

def __lt__(self, x): 

""" 

EXAMPLES:: 

sage: from sage.combinat.species.series_order import * 

sage: o = InfiniteSeriesOrder() 

sage: o < 2 

False 

sage: o < o 

False 

:: 

sage: u = UnknownSeriesOrder() 

sage: o < u 

False 

sage: 2 < o # TODO: Not Implemented 

True 

""" 

if isinstance(x, (int, Integer)): 

if x < 0: 

raise ValueError("x must be a positive integer") 

return False 

if isinstance(x, InfiniteSeriesOrder): 

return False 

if isinstance(x, UnknownSeriesOrder): 

return False 

raise TypeError("x must be a positive integer or a SeriesOrderElement") 

def __gt__(self, x): 

""" 

EXAMPLES:: 

sage: from sage.combinat.species.series_order import * 

sage: o = InfiniteSeriesOrder() 

sage: o > 2 

True 

""" 

return True 

class UnknownSeriesOrder(SeriesOrderElement): 

def __repr__(self): 

""" 

EXAMPLES:: 

sage: from sage.combinat.species.series_order import * 

sage: u = UnknownSeriesOrder(); u 

Unknown series order 

""" 

return "Unknown series order" 

def __add__(self, x): 

""" 

EXAMPLES:: 

sage: from sage.combinat.species.series_order import * 

sage: u = UnknownSeriesOrder() 

sage: u + 2 

Unknown series order 

sage: u + u 

Unknown series order 

""" 

if isinstance(x, (int, Integer)): 

if x < 0: 

raise ValueError("x must be a positive integer") 

return self 

if isinstance(x, SeriesOrderElement): 

return self 

raise TypeError("x must be a positive integer or a SeriesOrderElement") 

__radd__ = __add__ 

def __mul__(self, x): 

""" 

EXAMPLES:: 

sage: from sage.combinat.species.series_order import * 

sage: u = UnknownSeriesOrder() 

sage: u * 2 

Unknown series order 

sage: u * u 

Unknown series order 

""" 

if isinstance(x, (int, Integer)): 

if x < 0: 

raise ValueError("x must be a positive integer") 

return self 

if isinstance(x, SeriesOrderElement): 

return self 

raise TypeError("x must be a positive integer or a SeriesOrderElement") 

__rmul__ = __mul__ 

def __lt__(self, x): 

""" 

EXAMPLES:: 

sage: from sage.combinat.species.series_order import * 

sage: u = UnknownSeriesOrder() 

sage: u < 2 

True 

sage: o = InfiniteSeriesOrder() 

sage: u < o 

True 

""" 

if isinstance(x, (int, Integer)): 

if x < 0: 

raise ValueError("x must be a positive integer") 

return True 

if isinstance(x, SeriesOrderElement): 

return True 

raise TypeError("x must be a positive integer or a SeriesOrderElement") 

def __gt__(self, x): 

""" 

EXAMPLES:: 

sage: from sage.combinat.species.series_order import * 

sage: u = UnknownSeriesOrder() 

sage: u > 2 

False 

""" 

return False 

def bounded_decrement(x): 

""" 

EXAMPLES:: 

sage: from sage.combinat.species.series_order import * 

sage: u = UnknownSeriesOrder() 

sage: bounded_decrement(u) 

Unknown series order 

sage: bounded_decrement(4) 

3 

sage: bounded_decrement(0) 

0 

""" 

if isinstance(x, SeriesOrderElement): 

return x 

if isinstance(x, (int, Integer)): 

if x < 0: 

raise ValueError("x must be a positive integer") 

return max(0, x - 1) 

raise TypeError("x must be a positive integer or a SeriesOrderElement") 

def increment(x): 

""" 

EXAMPLES:: 

sage: from sage.combinat.species.series_order import * 

sage: u = UnknownSeriesOrder() 

sage: increment(u) 

Unknown series order 

sage: increment(2) 

3 

""" 

if isinstance(x, SeriesOrderElement): 

return x + 1 

if isinstance(x, (int, Integer)): 

if x < 0: 

raise ValueError("x must be a positive integer") 

return x+1 

raise TypeError("x must be a positive integer or a SeriesOrderElement") 

inf = InfiniteSeriesOrder() 

unk = UnknownSeriesOrder()