Please read the extensive documentation at
http://doc.sagemath.org/html/en/thematic_tutorials/coercion_and_categories.html#coercion-and-categories
Concerning your code, you need at least to:
1 - remove the attribute _parent and the method parent in
ParametricRealFieldElement
2 - remove the __call__ in ParametricRealField
3 - call the constructor of FieldElement as in
class ParametricRealFieldElement(FieldElement):
def __init__(self, value, parent=None):
...
...
FieldElement.__init__(self, parent)
4 - call the constructor of Field as in
class ParametricRealField(Field):
def __init__(self, values=[], names=()):
...
...
Field.__init__(self)
On 13/07/16 08:55, Yuan ZHOU wrote:
Hi,
I wish to construct a new class ParametricRealField. I implemented it as
follows.
class ParametricRealFieldElement(FieldElement):
def __init__(self, value, parent=None):
FieldElement.__init__(self, parent) ## this is so that
canonical_coercion works.
self._val = value
self._parent = parent ## this is so that .parent() works.
def parent(self):
return self._parent
def __hash__(self):
return hash(self._val)
class ParametricRealField(Field):
def __init__(self, values=[], names=()):
NumberField.__init__(self)
self._element_class = ParametricRealFieldElement
self._zero_element = ParametricRealFieldElement(0, parent=self)
self._one_element = ParametricRealFieldElement(1, parent=self)
self._gens = [ ParametricRealFieldElement(value, parent=self) for
value in values ]
def _an_element_impl(self):
return ParametricRealFieldElement(1, parent=self)
def _coerce_map_from_(self, S):
return CallableConvertMap(S, self, lambda s:
ParametricRealFieldElement(s, parent=self), parent_as_first_arg=False)
def __call__(self, elt):
if parent(elt) == self:
return elt
return ParametricRealFieldElement(elt, parent=self)
def _coerce_impl(self, x):
return self(x)
Then I got an error when running the following code.
sage: K.<a,b> = ParametricRealField([2, 1])
sage: K.is_commutative()
True
sage: K.is_ring()
True
sage: K in CommutativeRings()
False
sage: R = PolynomialRing(K, 'x')
---------------------------------------------------------------------------
TypeError: Base ring <class '__main__.ParametricRealField'> must be a
commutative ring.
How can I make K commutative?
Thanks,
Yuan
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