Coverage for local/lib/python2.7/site-packages/sage/monoids/free_abelian_monoid_element.py : 69%

""" 

Abelian Monoid Elements 

AUTHORS: 

- David Kohel (2005-09) 

EXAMPLES: 

Recall the example from abelian monoids:: 

sage: F = FreeAbelianMonoid(5,names = list("abcde")) 

sage: (a,b,c,d,e) = F.gens() 

sage: a*b^2*e*d 

a*b^2*d*e 

sage: x = b^2*e*d*a^7 

sage: x 

a^7*b^2*d*e 

sage: x.list() 

[7, 2, 0, 1, 1] 

The list is a copy, so changing the list does not change the element:: 

sage: x.list()[0] = 0 

sage: x 

a^7*b^2*d*e 

""" 

#***************************************************************************** 

# Copyright (C) 2006 William Stein <wstein@gmail.com> 

# Copyright (C) 2005 David Kohel <kohel@maths.usyd.edu> 

# 

# Distributed under the terms of the GNU General Public License (GPL) 

# http://www.gnu.org/licenses/ 

#***************************************************************************** 

from six import integer_types 

from sage.structure.richcmp import richcmp 

from sage.rings.integer import Integer 

from sage.structure.element import MonoidElement 

def is_FreeAbelianMonoidElement(x): 

r""" 

Queries whether ``x`` is an object of type ``FreeAbelianMonoidElement``. 

INPUT: 

- ``x`` -- an object. 

OUTPUT: 

- ``True`` if ``x`` is an object of type ``FreeAbelianMonoidElement``; 

``False`` otherwise. 

""" 

return isinstance(x, FreeAbelianMonoidElement) 

class FreeAbelianMonoidElement(MonoidElement): 

def __init__(self, F, x): 

""" 

Create the element x of the FreeAbelianMonoid F. 

EXAMPLES:: 

sage: F = FreeAbelianMonoid(5, 'abcde') 

sage: F 

Free abelian monoid on 5 generators (a, b, c, d, e) 

sage: F(1) 

1 

sage: a, b, c, d, e = F.gens() 

sage: a^2 * b^3 * a^2 * b^4 

a^4*b^7 

sage: F = FreeAbelianMonoid(5, 'abcde') 

sage: a, b, c, d, e = F.gens() 

sage: a in F 

True 

sage: a*b in F 

True 

""" 

MonoidElement.__init__(self, F) 

n = F.ngens() 

if isinstance(x, integer_types + (Integer,)) and x == 1: 

self._element_vector = tuple([0]*n) 

elif isinstance(x, (list, tuple)): 

if len(x) != n: 

raise IndexError("argument length (= %s) must be %s"%(len(x), n)) 

self._element_vector = tuple(x) 

else: 

raise TypeError("argument x (= %s) is of wrong type"%x) 

def _repr_(self): 

""" 

Return a string representation of ``self``. 

EXAMPLES:: 

sage: F = FreeAbelianMonoid(5, 'abcde') 

sage: F(1) 

1 

sage: a, b, c, d, e = F.gens() 

sage: a^2 * b^3 * a^2 * b^4 

a^4*b^7 

""" 

s = "" 

A = self.parent() 

n = A.ngens() 

x = A.variable_names() 

v = self._element_vector 

for i in range(n): 

if v[i] == 0: 

continue 

elif v[i] == 1: 

if len(s) > 0: s += "*" 

s += "%s"%x[i] 

else: 

if len(s) > 0: s += "*" 

s += "%s^%s"%(x[i],v[i]) 

if not s: 

s = "1" 

return s 

def _richcmp_(self, other, op): 

""" 

Rich comparison. 

EXAMPLES:: 

sage: F = FreeAbelianMonoid(5, 'abcde') 

sage: F(1) 

1 

sage: a, b, c, d, e = F.gens() 

sage: x = a^2 * b^3 

sage: F(1) < x 

True 

sage: x > b 

True 

sage: x <= a^4 

True 

sage: x != a*b 

True 

sage: a*b == b*a 

True 

sage: x > a^3*b^2 

False 

""" 

return richcmp(self._element_vector, other._element_vector, op) 

def __mul__(self, y): 

if not isinstance(y, FreeAbelianMonoidElement): 

raise TypeError("argument y (= %s) is of wrong type"%y) 

M = self.parent() 

z = M.element_class(M, 1) 

xelt = self._element_vector 

yelt = y._element_vector 

z._element_vector = tuple([xelt[i]+yelt[i] for i in range(len(xelt))]) 

return z 

def __pow__(self, n): 

""" 

Raises self to the power of `n`. 

AUTHORS: 

- Tom Boothby (2007-08): Replaced O(log n) time, O(n) space 

algorithm with O(1) time and space"algorithm". 

EXAMPLES:: 

sage: F = FreeAbelianMonoid(5,names = list("abcde")) 

sage: (a,b,c,d,e) = F.gens() 

sage: x = a*b^2*e*d; x 

a*b^2*d*e 

sage: x^3 

a^3*b^6*d^3*e^3 

sage: x^0 

1 

""" 

if not isinstance(n, integer_types + (Integer,)): 

raise TypeError("argument n (= %s) must be an integer"%(n,)) 

if n < 0: 

raise IndexError("argument n (= %s) must be positive"%n) 

elif n == 1: 

return self 

M = self.parent() 

z = M.element_class(M, 1) 

if n == 0: 

return z 

else: 

z._element_vector = tuple([i*n for i in self._element_vector]) 

return z 

def __hash__(self): 

""" 

Return the hash of ``self``. 

EXAMPLES:: 

sage: F = FreeAbelianMonoid(5,names = list("abcde")) 

sage: (a,b,c,d,e) = F.gens() 

sage: x = a*b^2*e*d 

sage: hash(x) == hash(x) 

True 

""" 

return hash(self._element_vector) 

def list(self): 

""" 

Return (a reference to) the underlying list used to represent this 

element. If this is a monoid in an abelian monoid on `n` 

generators, then this is a list of nonnegative integers of length 

`n`. 

EXAMPLES:: 

sage: F = FreeAbelianMonoid(5, 'abcde') 

sage: (a, b, c, d, e) = F.gens() 

sage: a.list() 

[1, 0, 0, 0, 0] 

""" 

return list(self._element_vector)