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test.py
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test.py
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from sage.categories.realizations import Category_realization_of_parent
from sage.structure.element import Element
from sage.misc.bindable_class import BindableClass
from sage.structure.parent import Parent
from sage.structure.unique_representation import UniqueRepresentation
from sage.structure.element_wrapper import ElementWrapper
from sage.categories.rings import Rings
from sage.categories.sets_cat import Sets
from sage.categories.homset import Hom
from sage.rings.integer import Integer
class RingOfIntegers(Parent, UniqueRepresentation):
r"""
An example of parent endowed with several realizations.
The RingOfIntegers, redone (much slower of course, but to test the idea on a simple case before constructing more complicated parents).
EXAMPLES::
sage: A = RingOfIntegers(); A
Integer Ring (redone)
Two notations of ``A``:
sage: SageIntegers = A.SageIntegers(); SageIntegers
Integer Ring (redone) in the realization SageIntegers
sage: LongIntegers = A.LongIntegers(); LongIntegers
Integer Ring (redone) in the realization LongIntegers
Some conversions::
sage: SageIntegers(LongIntegers("3242"))
3242
sage: LongIntegers(SageIntegers(4243))
'4243'
We can now mix expressions::
sage: LongIntegers(SageIntegers(4243)) + LongIntegers("523") # broken
"""
def __repr__(self):
return "Integer Ring (redone)"
def __init__(self):
r"""
EXAMPLES::
sage: A = RingOfIntegers(); A
Integer Ring (redone)
sage: TestSuite(A).run()
TESTS::
sage: A = Sets().WithRealizations().example(); A
The subset algebra of {1, 2, 3} over Rational Field
sage: SageIntegers, LongIntegers = A.realizations()
sage: type(LongIntegers.coerce_map_from(SageIntegers))
<type 'sage.categories.morphism.SetMorphism'>
sage: type(SageIntegers.coerce_map_from(LongIntegers))
<type 'sage.categories.morphism.SetMorphism'>
"""
Parent.__init__(self, category = Rings().WithRealizations())
category = self.Notations()
SageIntegers = self.SageIntegers()
LongIntegers = self.LongIntegers()
f_Sage_to_Long = lambda self: LongIntegers(str(self))
Sage_to_Long = \
Hom(SageIntegers, LongIntegers, Sets().Realizations())(f_Sage_to_Long)
f_Long_to_Sage = lambda self:(SageIntegers(Integer(self.value)))
Long_to_Sage = \
Hom(LongIntegers, SageIntegers, Sets().Realizations())(f_Long_to_Sage)
# Tried:
# Hom(LongIntegers, SageIntegers, Rings().Realizations())(f_Long_to_Sage)
# Hom(LongIntegers, SageIntegers, category)(f_Long_to_Sage)
Sage_to_Long.register_as_coercion()
Long_to_Sage.register_as_coercion()
class Notations(Category_realization_of_parent):
r"""
The category of the realizations of the integer ring
"""
def super_categories(self):
return [Rings().Realizations()]
class LongIntegers(Parent, UniqueRepresentation, BindableClass):
r"""
The integer ring, using strings
INPUT:
- ``A`` -- a parent with realization in :class:`RingOfIntegers`
EXAMPLES::
sage: A = RingOfIntegers()
sage: LongIntegers = A.LongIntegers(); LongIntegers
Integer Ring (redone) in the realization LongIntegers
"""
def __init__(self, A):
r"""
EXAMPLES::
sage: A = RingOfIntegers()
sage: LongIntegers = A.LongIntegers(); LongIntegers
Integer Ring (redone) in the realization LongIntegers
sage: x = LongIntegers.an_element()
sage: y = LongIntegers.an_element()
sage: x
'7'
sage: x+y # broken
"""
Parent.__init__(self, category = A.Notations())
def an_element(self):
return self("7")
class Element(ElementWrapper):
wrapped_class = str
# Because I don't want to change Integer directly, yet want to use the Notations category. There is certainly some better way to do this:
class SageIntegers(Parent, UniqueRepresentation, BindableClass):
r"""
The integer ring, using sage integers
INPUT:
- ``A`` -- a parent with realization in :class:`RingOfIntegers`
EXAMPLES::
sage: A = RingOfIntegers()
sage: SageIntegers = A.SageIntegers(); SageIntegers
Integer Ring (redone) in the realization SageIntegers
TESTS:
The product in this basis is computed by converting to the fundamental
basis, computing the product there, and then converting back::
sage: A = RingOfIntegers()
sage: SageIntegers = A.SageIntegers(); SageIntegers
Integer Ring (redone) in the realization SageIntegers
sage: x = SageIntegers.an_element()
sage: y = SageIntegers.an_element()
sage: SageIntegers.product
<bound method RingOfIntegers.SageIntegers_with_category.product of Integer Ring (redone) in the realization SageIntegers>
sage: x*y
36
sage: SageIntegers.product(x, y)
36
sage: SageIntegers.summation
<bound method RingOfIntegers.SageIntegers_with_category.summation of Integer Ring (redone) in the realization SageIntegers>
sage: x+y
12
"""
def product(self, x, y):
return self(x.value*y.value)
def summation(self, x, y):
return self(x.value+y.value)
def __init__(self, A):
r"""
EXAMPLES::
sage: A = RingOfIntegers()
sage: SageIntegers = A.SageIntegers(); SageIntegers
Integer Ring (redone) in the realization SageIntegers
sage: TestSuite(SageIntegers).run()
"""
Parent.__init__(self, category = A.Notations())
def an_element(self):
"""
sage: SageIntegers.an_element()
6
"""
return self(Integer(6))
def one(self):
return self(Integer(1))
def zero(self):
return self(Integer(0))
class Element(ElementWrapper):
wrapped_class = Integer