Thanks a lot for the instructions. I revised my code as follows.
from sage.structure.coerce_maps import CallableConvertMap
class ParametricRealFieldElement(FieldElement):
def __init__(self, value, parent=None):
FieldElement.__init__(self, parent)
self._val = value
def __hash__(self):
return hash(self._val)
class ParametricRealField(Field):
def __init__(self, values=[], names=()):
Field.__init__(self, 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 _coerce_impl(self, x):
return self(x)
Now I have
sage: K.<a,b> = ParametricRealField([2, 1])
sage: K in CommutativeRings()
True
However, sage: R.<x,y> = PolynomialRing(K) raises NotImplementedError.
I suspect that the _element_constructor_ method of the class
ParametricRealField needs to be provided.
I tried the following in class ParametricRealField(Field):
def _element_constructor_(self, elt):
if elt.parent() == self:
return elt
return ParametricRealFieldElement(elt, parent=self)
This allows me to construct K and R, but I'm not able to get the generators
of R.
sage: K.<a,b> = ParametricRealField([2, 1])
sage: R.<x,y> = PolynomialRing(K)
sage: x
---------------------------------------------------------------------------
TypeError: unsupported operand parent(s) for '*': '<class
'__main__.ParametricRealField_with_category'>' and '<class
'__main__.ParametricRealField_with_category'>'
On Wednesday, July 13, 2016 at 6:57:56 PM UTC+1, vdelecroix wrote:
>
> 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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