Symbolic expression to number fields

[videlec]

The ticket stands to improve the AlgebraicConverter in sage.symbolic.expression_converters and make it works with number fields.

As mentioned on ask the following fails

sage: K = QuadraticField(3)
sage: K(sqrt(3))
Traceback (most recent call last):
...
TypeError: ...

The following gives an answer with a wrong parent

sage: x = K(3)**(1/2); x
sqrt(3)
sage: a.parent()
Symbolic Ring

while it is possible to do

sage: y = K(3).sqrt(); y
a
sage: y == K.gen()
True

Finally, we hopefully have

sage: K.gen() == sqrt(3)
sqrt(3) == sqrt(3)
sage: bool(K.gen() == sqrt(3))
True

CC: @videlec @mkoeppe

Component: number fields

Author: Dave Morris

Branch/Commit: a5fc9f9

Reviewer: Vincent Delecroix

Issue created by migration from https://trac.sagemath.org/ticket/14602

[fchapoton]

comment:7

everything seems to work fine now (sage 8.9.b7)

[videlec]

comment:8

Indeed. The situation improved.

[kevinywlui]

comment:9

Yep.

Every example in the ticket text now works!

[fchapoton]

comment:10

Is this doctested somewhere ?

[kevinywlui]

comment:11

Replying to @fchapoton:

Is this doctested somewhere ?

Not as far as I can tell. Good point. Forgot to check that.

[DaveWitteMorris]

Branch: public/14602

[DaveWitteMorris]

comment:13

The PR adds doctests. Note that we still have

sage: (K(3)^(1/2)).parent()                                                  
Symbolic Ring

That seems ok to me, but if the parent should be K, then I think another ticket should be opened. (The parent of sqrt(K(3)) is K, and is one of the new doctests.)

---

New commits:

ac5aa6a

doctests for trac 14602

[DaveWitteMorris]

Commit: ac5aa6a

[DaveWitteMorris]

Author: Dave Morris

[videlec]

comment:15

Could you also doctest the other embedding

sage: L = QuadraticField(3, embedding=-AA(3).sqrt())
sage: bool(L.gen() == -sqrt(3))
True

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

a5fc9f9

additional doctest

[sagetrac-git]

Changed commit from ac5aa6a to a5fc9f9

[DaveWitteMorris]

comment:17

Thanks for the suggestion. I added this doctest.

[videlec]

Reviewer: Vincent Delecroix

[videlec]

comment:18

Thanks. Good to me. Waiting for the patchbot.

[DaveWitteMorris]

comment:20

Thanks!

[vbraun]

Changed branch from public/14602 to a5fc9f9