#12269: coercion and conversion for absolute_field
-----------------------------+----------------------------------------------
Reporter: mstreng | Owner: davidloeffler
Type: defect | Status: new
Priority: major | Milestone: sage-5.0
Component: number fields | Keywords: coercion conversion
absolute_field number field structure relative absolute
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
-----------------------------+----------------------------------------------
Description changed by mstreng:
Old description:
> {{{
> sage: x = var('x')
> sage: K1.<a1> = CyclotomicField(11)
> sage: K2.<a2> = K1.extension(x^2 - 3)
> sage: K3.<a3> = K2.extension(x^2 + 1) # Let's make a big relative number
> field
> sage: t=a1+6*a2+a3*a1 # with a complicated element.
> sage: L = K3.absolute_field('b')
> sage: L(t)
> # The code at #11869 takes 12 seconds to compute roots of a
> # polynomial, and then doesn't use them.
> # TypeError: No compatible natural embeddings found for Number Field in b
> with .... and Complex Lazy Field
> sage: L.structure() # However, the correct conversion
> map is available and works almost instantly
> #(Isomorphism map:... , Isomorphism map: ...)
> sage: L.structure()[1](t)
> # big output
> sage: L.gen() + t # It would be good if one of the
> structure maps is a coercion, but they aren't at the moment
> # TypeError: unsupported operand parent(s) for '+': ....
> sage: K3(L.gen()) # There are similar problems in the
> other direction
> # TypeError: Cannot coerce element into this number field
> sage: L.structure()[0](L.gen()) # for which the structure maps also
> work.
> # a3 - a2 + a1
> }}}
>
> So to do:
>
> * make both structure maps into conversions
> * make one of the structure maps into a coercion
> * move the "compatible embedding" code of #12186 to the beginning of the
> method, to avoid unnecessary root-finding
>
> I guess the third item is unrelated to the first two, so could be a
> separate ticket.
New description:
{{{
sage: x = var('x')
sage: K1.<a1> = CyclotomicField(11)
sage: K2.<a2> = K1.extension(x^2 - 3)
sage: K3.<a3> = K2.extension(x^2 + 1) # Let's make a big relative number
field
sage: t=a1+6*a2+a3*a1 # with a complicated element.
sage: L = K3.absolute_field('b')
sage: L(t)
# The code at #11800 takes 12 seconds to compute roots of a
# polynomial, and then doesn't use them.
# TypeError: No compatible natural embeddings found for Number Field in b
with .... and Complex Lazy Field
sage: L.structure() # However, the correct conversion
map is available and works almost instantly
#(Isomorphism map:... , Isomorphism map: ...)
sage: L.structure()[1](t)
# big output
sage: L.gen() + t # It would be good if one of the
structure maps is a coercion, but they aren't at the moment
# TypeError: unsupported operand parent(s) for '+': ....
sage: K3(L.gen()) # There are similar problems in the
other direction
# TypeError: Cannot coerce element into this number field
sage: L.structure()[0](L.gen()) # for which the structure maps also
work.
# a3 - a2 + a1
}}}
So to do:
* make both structure maps into conversions
* make one of the structure maps into a coercion
* move the "compatible embedding" code of #11800 to the beginning of the
method, to avoid unnecessary root-finding
I guess the third item is unrelated to the first two, so could be a
separate ticket.
--
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12269#comment:1>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To post to this group, send email to [email protected].
To unsubscribe from this group, send email to
[email protected].
For more options, visit this group at
http://groups.google.com/group/sage-trac?hl=en.
