Add algorithm Magma to Conic methods

[mstreng]

This patch adds the option algorithm='magma' to (has_)rational_point for conics.

Apply

• attachment: 11455.3.patch
• attachment: 11455-doctests.patch

Depends on #10621
Depends on #11454
Depends on #11456

CC: @sagetrac-florian

Component: algebraic geometry

Keywords: magma conic

Author: Marco Streng

Reviewer: Florian Bouyer

Merged: sage-5.3.beta2

Issue created by migration from https://trac.sagemath.org/ticket/11455

[mstreng]

comment:1

Apparently the Magma interface for number field elements doesn't work the way I thought it would:

sage: L.<s> = QuadraticField(2)
sage: m = magma(s)
sage: m.sage()
NameError: name 's' is not defined

sage: K.<i> = QuadraticField(-1)
sage: m = magma(i).sage(); m
I
sage: m.parent()
Symbolic Ring
sage: K(m)
TypeError: <type 'sage.symbolic.expression.Expression'>

Fraction fields are a problem too:

sage: R.<x> = QQ[]
sage: y=x^2/x; y.parent()
Fraction Field of Univariate Polynomial Ring in x over Rational Field
sage: m = magma(y)
sage: m.sage()
NameError: name 'x' is not defined
sage: (m.Numerator().sage()/m.Denominator().sage())
x

[mstreng]

Work Issues: review tickets on which this depends, and (in a separate ticket) implement magma interface for number field elements

[mstreng]

Changed work issues from review tickets on which this depends, and (in a separate ticket) implement magma interface for number field elements to none

[mstreng]

Changed dependencies from #10621, #11454 to #10621, #11454, #11456

[mstreng]

Attachment: trac_11455_magma_algorithm_conics.patch.gz

use magma to solve conics

[mstreng]

comment:4

Please review #10621, a student will need #11455 for his project in September.

[mstreng]

comment:6

Something is wrong, in 5.0.prealpha1, I get

sage: K.<i> = QuadraticField(-1)
sage: C = Conic(K,[1,1,1])
sage: C.rational_point(algorithm='magma')
NotImplementedError: No correct conversion implemented for converting the Magma point (-i : 1 : 0) on Conic over Number Field with defining polynomial t^2 + 1 over the Rational Field defined by
X^2 + Y^2 + Z^2 to a correct Sage point on self (=Projective Conic Curve over Number Field in i with defining polynomial x^2 + 1 defined by x^2 + y^2 + z^2)

[mstreng]

comment:7

Replying to @mstreng:

Something is wrong

Here's the reason:

sage: K = QuadraticField(-1, 'i')
sage: L = NumberField(x^2+1, 'i')
sage: magma(K.gen()).sage() in K
False
sage: magma(K.gen()).sage() in L
True
sage: magma(L.gen()).sage() in K
False
sage: magma(L.gen()).sage() in L
True
sage: magma(L.gen()).sage() == magma(K.gen()).sage()
True

A field loses its embeddings when converted to Magma and back. A new patch is coming up.

[mstreng]

Attachment: 11455.patch.gz

[mstreng]

comment:10

With this patch on 5.0.prealpha1, all tests pass (except those that already fail on an unpatched 5.0.prealpha1).

[mstreng]

Changed reviewer from florian to Florian Bouyer

[mstreng]

comment:14

Thanks Florian

[jdemeyer]

comment:15

You should use

# optional - magma

instead of

# optional, uses magma

[mstreng]

Attachment: 11455.3.patch.gz

same as previous one, but with corrected "optional - magma" tag

[mstreng]

comment:16

apply 11455.3.patch

[mstreng]

comment:17

oops, with the correct "optional" tag, it turns out a lot of the optional tests fail

[mstreng]

Attachment: 11455-doctests.patch.gz

apply on top of previous, fixes instable doctests

[mstreng]

comment:19

All tests pass! Florian, could you review again?

[mstreng]

comment:20

And thanks Jeroen for catching this!

[sagetrac-florian]

comment:21

I'll review it again, sorry for letting the #optional, uses magma slip by.

[sagetrac-florian]

comment:22

Reviewed it from scratch, everything works.

[jdemeyer]

Merged: sage-5.3.beta2