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refresh the doc about coercion and test the given example #36919

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Dec 26, 2023
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refresh the doc about coercion and test the given example #36919

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04a860b
refresh the doc about coercion and test the given example
fchapoton Dec 19, 2023
457a121
remove one doctest, fix the other
fchapoton Dec 21, 2023
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183 changes: 97 additions & 86 deletions src/doc/en/reference/coercion/index.rst
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Original file line number Diff line number Diff line change
Expand Up @@ -386,87 +386,97 @@ but that would obscure the main points being made here.)

::

class Localization(Ring):
def __init__(self, primes):
"""
Localization of `\ZZ` away from primes.
"""
Ring.__init__(self, base=ZZ)
self._primes = primes
self._populate_coercion_lists_()

def _repr_(self):
"""
How to print self.
"""
return "%s localized at %s" % (self.base(), self._primes)

def _element_constructor_(self, x):
"""
Make sure x is a valid member of self, and return the constructed element.
"""
if isinstance(x, LocalizationElement):
x = x._value
else:
x = QQ(x)
for p, e in x.denominator().factor():
if p not in self._primes:
raise ValueError("Not integral at %s" % p)
return LocalizationElement(self, x)

def _coerce_map_from_(self, S):
"""
The only things that coerce into this ring are:

- the integer ring

- other localizations away from fewer primes
"""
if S is ZZ:
return True
elif isinstance(S, Localization):
return all(p in self._primes for p in S._primes)


class LocalizationElement(RingElement):

def __init__(self, parent, x):
RingElement.__init__(self, parent)
self._value = x


# We're just printing out this way to make it easy to see what's going on in the examples.

def _repr_(self):
return "LocalElt(%s)" % self._value

# Now define addition, subtraction, and multiplication of elements.
# Note that left and right always have the same parent.

def _add_(left, right):
return LocalizationElement(left.parent(), left._value + right._value)

def _sub_(left, right):
return LocalizationElement(left.parent(), left._value - right._value)

def _mul_(left, right):
return LocalizationElement(left.parent(), left._value * right._value)

# The basering was set to ZZ, so c is guaranteed to be in ZZ

def _rmul_(self, c):
return LocalizationElement(self.parent(), c * self._value)

def _lmul_(self, c):
return LocalizationElement(self.parent(), self._value * c)
sage: from sage.structure.richcmp import richcmp
sage: from sage.structure.element import Element

sage: class MyLocalization(Parent):
....: def __init__(self, primes):
....: r"""
....: Localization of `\ZZ` away from primes.
....: """
....: Parent.__init__(self, base=ZZ, category=Rings().Commutative())
....: self._primes = primes
....: self._populate_coercion_lists_()
....:
....: def _repr_(self) -> str:
....: """
....: How to print ``self``.
....: """
....: return "%s localized at %s" % (self.base(), self._primes)
....:
....: def _element_constructor_(self, x):
....: """
....: Make sure ``x`` is a valid member of ``self``, and return the constructed element.
....: """
....: if isinstance(x, MyLocalizationElement):
....: x = x._value
....: else:
....: x = QQ(x)
....: for p, e in x.denominator().factor():
....: if p not in self._primes:
....: raise ValueError("not integral at %s" % p)
....: return self.element_class(self, x)
....:
....: def _an_element_(self):
....: return self.element_class(self, 6)
....:
....: def _coerce_map_from_(self, S):
....: """
....: The only things that coerce into this ring are:
....:
....: - the integer ring
....:
....: - other localizations away from fewer primes
....: """
....: if S is ZZ:
....: return True
....: if isinstance(S, MyLocalization):
....: return all(p in self._primes for p in S._primes)

sage: class MyLocalizationElement(Element):
....:
....: def __init__(self, parent, x):
....: Element.__init__(self, parent)
....: self._value = x
....:
....: # We are just printing out this way to make it easy to see what's going on in the examples.
....:
....: def _repr_(self) -> str:
....: return f"LocalElt({self._value})"
....:
....: # Now define addition, subtraction and multiplication of elements.
....: # Note that self and right always have the same parent.
....:
....: def _add_(self, right):
....: return self.parent()(self._value + right._value)
....:
....: def _sub_(self, right):
....: return self.parent()(self._value - right._value)
....:
....: def _mul_(self, right):
....: return self.parent()(self._value * right._value)
....:
....: # The basering was set to ZZ, so c is guaranteed to be in ZZ
....:
....: def _rmul_(self, c):
....: return self.parent()(c * self._value)
....:
....: def _lmul_(self, c):
....: return self.parent()(self._value * c)
....:
....: def _richcmp_(self, other, op):
....: return richcmp(self._value, other._value, op)

sage: MyLocalization.element_class = MyLocalizationElement

That's all there is to it. Now we can test it out:

.. skip
.. link

::

sage: R = Localization([2]); R
sage: TestSuite(R).run(skip="_test_pickling")
sage: R = MyLocalization([2]); R
Integer Ring localized at [2]
sage: R(1)
LocalElt(1)
Expand All @@ -475,12 +485,12 @@ That's all there is to it. Now we can test it out:
sage: R(1/3)
Traceback (most recent call last):
...
ValueError: Not integral at 3
ValueError: not integral at 3

sage: R.coerce(1)
LocalElt(1)
sage: R.coerce(1/4)
Traceback (click to the left for traceback)
Traceback (most recent call last):
...
TypeError: no canonical coercion from Rational Field to Integer Ring localized at [2]

Expand All @@ -497,25 +507,26 @@ That's all there is to it. Now we can test it out:
sage: R(3/4) * 7
LocalElt(21/4)

sage: R.get_action(ZZ)
Right scalar multiplication by Integer Ring on Integer Ring localized at [2]
sage: cm = sage.structure.element.get_coercion_model()
sage: cm.explain(R, ZZ, operator.add)
Coercion on right operand via
Conversion map:
Coercion map:
From: Integer Ring
To: Integer Ring localized at [2]
Arithmetic performed after coercions.
Result lives in Integer Ring localized at [2]
Integer Ring localized at [2]

sage: cm.explain(R, ZZ, operator.mul)
Action discovered.
Right scalar multiplication by Integer Ring on Integer Ring localized at [2]
Coercion on right operand via
Coercion map:
From: Integer Ring
To: Integer Ring localized at [2]
Arithmetic performed after coercions.
Result lives in Integer Ring localized at [2]
Integer Ring localized at [2]

sage: R6 = Localization([2,3]); R6
sage: R6 = MyLocalization([2,3]); R6
Integer Ring localized at [2, 3]
sage: R6(1/3) - R(1/2)
LocalElt(-1/6)
Expand All @@ -525,12 +536,12 @@ That's all there is to it. Now we can test it out:
sage: R.has_coerce_map_from(ZZ)
True
sage: R.coerce_map_from(ZZ)
Conversion map:
Coercion map:
From: Integer Ring
To: Integer Ring localized at [2]

sage: R6.coerce_map_from(R)
Conversion map:
Coercion map:
From: Integer Ring localized at [2]
To: Integer Ring localized at [2, 3]

Expand All @@ -539,7 +550,7 @@ That's all there is to it. Now we can test it out:

sage: cm.explain(R, R6, operator.mul)
Coercion on left operand via
Conversion map:
Coercion map:
From: Integer Ring localized at [2]
To: Integer Ring localized at [2, 3]
Arithmetic performed after coercions.
Expand Down
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