Hi Nicolas,
On 2013-09-04, Nicolas Borie <nicolas.bo...@univ-mlv.fr> wrote:
> This way works ! But it overwrite the scalar multiplication for the
> other usuals ring.
Just an idea: _get_action_ could try to determine whether the usual
action (that relies on _rmul_/_lmul_) is available. If it is available
then probably it is faster (because of Cython implementation).
But hang on, I just see that you do something along these lines:
> + def _get_action_(self, S, op=operator.mul, self_on_left=True):
> + r"""
> + """
> + if self.has_coerce_map_from(self.base_ring()):
> + return None
> + if S == self.base_ring():
> + return ActionFromBaseRing(self.base_ring(), self)
> + return None
Hence, if the category is properly initialised, such that there is a
coercion from the base ring by virtue of __init_extra__, then the
default action will still be used with your patch (which is a good
thing), isn't it?
> +from sage.categories.action import Action
> +
> +class ActionFromBaseRing(Action):
> + r"""
> + """
> + def _call_(self, elem, mat):
> + r"""
> + """
> + P = mat.parent()
> + return P.diagonal_matrix(elem)*mat
I guess creating a diagonal matrix and doing a matrix multiplication is
very inefficient. I wonder if perhaps it would (after all) be a better
idea to simply imitate what is done in _lmul_/_rmul_. As much as I
understand, the main problem is that _lmul_/_rmul_ expects wrong types,
hence, you could do in _call_ the same trickery with .set_unsafe() and
and so on, but simply without expecting that the method argument is of a
specific type sage.structure.element....
> I have now a scalar multiplication which is *really more* generic ( but
> ok, I should multiply each entries by the right scalar after having
> generated a copy ).
+1 (see above...)
> AttributeError: 'FreeAlgebra_with_category' object has no attribute
> 'is_field'
That's why I'd somehow like to see 'R.is_field()' replaced with
'R in Fields()'.
If I recall correctly, the problem is that there are still many fields
that are not (or can not be) properly initialised as fields, because the
test whether it is a field or just a ring is expensive. Hence,
Fields.__contains__ is a lot more complicated than Rings.__contains__.
And while "R in Rings()" is about as fast as calling a non-cached Python
method "R.is_field()" returning the constant "True" or "False", the test
"R in Fields()" would be slower than "R.is_field()".
Hence, for time critical applications, "R.is_field()" might be a good
idea...
That said, I believe Rings() should provide a (cached?) parent method
Rings.ParentMethods.is_field() returning False by default. For properly
initialised fields, this would be overridden by
Fields.ParentMethods.is_field(), and sage.rings.field.Field.is_field()
is available too, for fields that use the arithmetic base classes.
> ***************************************************************
>
> Schur functions :
> ***************************************************************
> sage: Id = identity_matrix(SF, 2);
> sage: Id.adjoint()
> ---------------------------------------------------------------------------
> TypeError Traceback (most recent call last)
><ipython-input-41-8ec4e1fe1f2c> in <module>()
> ----> 1 Id.adjoint()
>
> /home/nborie/sage/local/lib/python2.7/site-packages/sage/matrix/matrix2.so
> in sage.matrix.matrix2.Matrix.adjoint (sage/matrix/matrix2.c:40809)()
>
> /home/nborie/sage/local/lib/python2.7/site-packages/sage/matrix/matrix2.so
> in sage.matrix.matrix2.Matrix._adjoint (sage/matrix/matrix2.c:41159)()
>
> /home/nborie/sage/local/lib/python2.7/site-packages/sage/matrix/matrix0.so
> in sage.matrix.matrix0.Matrix.__neg__ (sage/matrix/matrix0.c:26187)()
>
> TypeError: Cannot convert
> SymmetricFunctionAlgebra_schur_with_category.element_class to
> sage.structure.element.RingElement
> ***************************************************************
This is because _lmul_ is called, which expects this type.
Perhaps it makes sense to implement a cdef _lmul_unsafe_ in
sage.matrix.matrix0 and use this both in the new action and in __neg__
and in other places that are currently calling _rmul_ and _lmul_?
> TypeError: unsupported operand parent(s) for '/': 'Univariate Polynomial
> Ring in z over An example of an algebra with basis: the free algebra on
> the generators ('a', 'b', 'c') over Rational Field' and 'Univariate
> Polynomial Ring in z over An example of an algebra with basis: the free
> algebra on the generators ('a', 'b', 'c') over Rational Field'
Why is this?? Can the fration field of this polynomial ring be
constructed? Where is the problem?
> Here come questions :
>
> - Does all rings should have a *is_field* method and if yes, where
> should we place it ? (I guess in parent method of the category Rings()
> .... )
They currently don't have, but I think they *should* have!
See above.
That said, if I recall correctly, some people where strongly opposed to
this idea. But frankly I found the counter arguments not convincing and
forgot what they were like...
> If not, what should be the new test ? ( I guess something like
> Fields() in self.base_ring().category().all_super_categories() ... )
Nonono, this would be very slow, and moreover it might not work on
fields whose category isn't properly initialised!
'R in Fields()' would be the way to go, *unless* it is time-critical (see
above), in which case it would be better to have a method 'R.is_field()'.
This is why I suggested to have 'Rings.ParentMethos.is_field()'.
Alternatively one could catch an attribute error, argueing that an
object without an is_field() method is certainly no field:
try:
if R.is_field():
do something
else:
do something else
except AttributeError:
do something else
> - What is the best way to generically invert element ? I don't know
> between ~, .inverse(), .__invert__(), 1/...
If I recall correctly, one implements ~ by means of __invert__, or by
means of _div_ together whith establishing a coercion from ZZ to the
ring, because then Sage can use a default implementation of __invert__
relying on 1/...
Best regards,
Simon
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