You can do:
sage: K.<sqrt2>=QuadraticField(2)
sage: K.register_coercion(K.coerce_map_from(QQ) * QQ.coerce_map_from(ZZ))
For even more speed you can write your own custom Cython coercion from ZZ
to K.
David
On Fri, May 10, 2013 at 12:59 PM, vdelecroix <20100.delecr...@gmail.com>wrote:
> Hi,
>
> Let K be a quadratic number field (let say K = QuadraticField(2)).
> There are "natural morphisms" implemented in Cython from ZZ to QQ and
> from QQ to K. There is also an other way, somewhat more direct, to go
> from ZZ to K. But at the end it is 10 times faster to go the first way
> and Sage does not choose it!
> {{{
> sage: K.<sqrt2>=QuadraticField(2)
> sage: f = K.coerce_map_from(ZZ)
> sage: g = K.coerce_map_from(QQ) * QQ.coerce_map_from(ZZ)
> sage: timeit('f(1)')
> 625 loops, best of 3: 13.8 µs per loop
> sage: timeit('g(1)')
> 625 loops, best of 3: 1.29 µs per loop
> }}}
>
> What can I do to make Sage chooses the undirect way ? In some sense a
> composition of "natural morphisms" (ie mathematically natural and
> Cython implemented) should be prefered to "conversion".
>
> Best,
> Vincent
>
> Note: I get some troubles with #13213 which pops out the natural
> morphism from QQ to K...
>
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