Coverage for local/lib/python2.7/site-packages/sage/categories/examples/semigroups_cython.pyx : 80%

r""" 

Examples of semigroups in cython 

""" 

from sage.structure.parent cimport Parent 

from sage.structure.element cimport Element 

from sage.categories.all import Category, Semigroups 

from sage.categories.examples.semigroups import LeftZeroSemigroup as LeftZeroSemigroupPython 

from cpython.object cimport PyObject_RichCompare 

class IdempotentSemigroups(Category): 

def super_categories(self): 

""" 

EXAMPLES:: 

sage: from sage.categories.examples.semigroups_cython import IdempotentSemigroups 

sage: IdempotentSemigroups().super_categories() 

[Category of semigroups] 

""" 

return [Semigroups()] 

class ElementMethods: 

def _pow_int(self, i): 

""" 

EXAMPLES:: 

sage: from sage.categories.examples.semigroups_cython import LeftZeroSemigroup 

sage: S = LeftZeroSemigroup() 

sage: S(2)._pow_int(3) 

2 

""" 

assert i > 0 

return self 

def is_idempotent(self): 

""" 

EXAMPLES:: 

sage: from sage.categories.examples.semigroups_cython import LeftZeroSemigroup 

sage: S = LeftZeroSemigroup() 

sage: S(2).is_idempotent() 

True 

""" 

return True 

cdef class LeftZeroSemigroupElement(Element): 

cdef object _value 

def __init__(self, parent, value): 

""" 

EXAMPLES:: 

sage: from sage.categories.examples.semigroups_cython import LeftZeroSemigroup 

sage: S = LeftZeroSemigroup() 

sage: x = S(3) 

sage: TestSuite(x).run() 

""" 

Element.__init__(self, parent = parent) 

self._value = value 

def _repr_(self): 

""" 

EXAMPLES:: 

sage: from sage.categories.examples.semigroups_cython import LeftZeroSemigroup 

sage: S = LeftZeroSemigroup() 

sage: S(3) # indirect doctest 

3 

""" 

return repr(self._value) 

def __reduce__(self): 

""" 

EXAMPLES:: 

sage: from sage.categories.examples.semigroups_cython import LeftZeroSemigroup 

sage: S = LeftZeroSemigroup() 

sage: x = S(3) 

sage: x.__reduce__() 

(<type 'sage.categories.examples.semigroups_cython.LeftZeroSemigroupElement'>, 

(An example of a semigroup: the left zero semigroup, 3)) 

""" 

return LeftZeroSemigroupElement, (self._parent, self._value) 

cpdef _richcmp_(self, other, int op): 

""" 

EXAMPLES:: 

sage: from sage.categories.examples.semigroups_cython import LeftZeroSemigroup 

sage: S = LeftZeroSemigroup() 

sage: S(3) == S(3) 

True 

sage: S(3) == S(2) 

False 

""" 

left = (<LeftZeroSemigroupElement>self)._value 

right = (<LeftZeroSemigroupElement>other)._value 

return PyObject_RichCompare(left, right, op) 

cpdef _mul_(self, other): 

""" 

EXAMPLES:: 

sage: from sage.categories.examples.semigroups_cython import LeftZeroSemigroup 

sage: S = LeftZeroSemigroup() 

sage: S(2) * S(3) 

2 

sage: S(2)._mul_(S(3)) 

2 

""" 

return self.parent().product(self, other) 

def __pow__(self, i, dummy): 

""" 

EXAMPLES:: 

sage: from sage.categories.examples.semigroups_cython import LeftZeroSemigroup 

sage: S = LeftZeroSemigroup() 

sage: S(2)^3 

2 

""" 

return self._pow_int(i) 

class LeftZeroSemigroup(LeftZeroSemigroupPython): 

r""" 

An example of semigroup 

This class illustrates a minimal implementation of a semi-group 

where the element class is an extension type, and still gets code 

from the category. The category itself must be a Python class 

though. 

This is purely a proof of concept. The code obviously needs refactorisation! 

Comments: 

- one cannot play ugly class surgery tricks (as with _mul_parent). 

available operations should really be declared to the coercion model! 

EXAMPLES:: 

sage: from sage.categories.examples.semigroups_cython import LeftZeroSemigroup 

sage: S = LeftZeroSemigroup(); S 

An example of a semigroup: the left zero semigroup 

This is the semigroup which contains all sort of objects:: 

sage: S.some_elements() 

[3, 42, 'a', 3.4, 'raton laveur'] 

with product rule is given by $a \times b = a$ for all $a,b$. :: 

sage: S('hello') * S('world') 

'hello' 

sage: S(3)*S(1)*S(2) 

3 

sage: S(3)^12312321312321 

3 

sage: TestSuite(S).run(verbose = True) 

running ._test_an_element() . . . pass 

running ._test_associativity() . . . pass 

running ._test_cardinality() . . . pass 

running ._test_category() . . . pass 

running ._test_elements() . . . 

Running the test suite of self.an_element() 

running ._test_category() . . . pass 

running ._test_eq() . . . pass 

running ._test_new() . . . pass 

running ._test_not_implemented_methods() . . . pass 

running ._test_pickling() . . . pass 

pass 

running ._test_elements_eq_reflexive() . . . pass 

running ._test_elements_eq_symmetric() . . . pass 

running ._test_elements_eq_transitive() . . . pass 

running ._test_elements_neq() . . . pass 

running ._test_eq() . . . pass 

running ._test_new() . . . pass 

running ._test_not_implemented_methods() . . . pass 

running ._test_pickling() . . . pass 

running ._test_some_elements() . . . pass 

That's really the only method which is obtained from the category ... :: 

sage: S(42).is_idempotent 

<bound method IdempotentSemigroups.element_class.is_idempotent of 42> 

sage: S(42).is_idempotent() 

True 

sage: S(42)._pow_int 

<bound method IdempotentSemigroups.element_class._pow_int of 42> 

sage: S(42)^10 

42 

sage: S(42).is_idempotent 

<bound method IdempotentSemigroups.element_class.is_idempotent of 42> 

sage: S(42).is_idempotent() 

True 

""" 

def __init__(self): 

""" 

TESTS:: 

sage: from sage.categories.examples.semigroups_cython import LeftZeroSemigroup 

sage: S = LeftZeroSemigroup() 

sage: S.category() 

Category of idempotent semigroups 

sage: TestSuite(S).run() 

""" 

Parent.__init__(self, category = IdempotentSemigroups()) 

Element = LeftZeroSemigroupElement