Improve conversion of GAP objects into sage objects.

[sagetrac-jlopez]

As of now, certain kinds of sage objects can be converted into GAP objects, but the resulting GAP objects cannot be converted back to sage objects.

Examples of this are matrices over finite fields:

sage: g = matrix(GF(5),2,[1,2, -1, 1])
sage: gg = g._gap_()
sage: gg.sage()
---------------------------------------------------------------------------
NotImplementedError

sage: a = gap('E(9)')
sage: a
-E(9)^4-E(9)^7
sage: a.sage()
---------------------------------------------------------------------------
NotImplementedError  

Being able to translate gap field elements into sage ones would help accesing GAP character tables, and a good conversion of matrices would allow many methods to be available for matrix groups.

See this thread at sage devel for more details:
http://groups.google.com/group/sage-devel/browse_thread/thread/a04006e5da578bd

Component: interfaces

Author: Javier López Peña

Issue created by migration from https://trac.sagemath.org/ticket/7890

[sagetrac-jlopez]

Added a _sage_ method in GapElement class (gap.py) that tries to convert matrices into sage matrices. This only work if the coefficient ring can be converted into a sage ring. Also, modified _matrix_ in the same class so that it tries to find a ring if none is given.

[sagetrac-jlopez]

comment:1

Attachment: 13590.patch.gz

[sagetrac-jlopez]

Author: Javier López Peña

[sagetrac-jlopez]

Conversion for finite and cyclotomic fields and their elements.

[sagetrac-jlopez]

comment:2

Attachment: 13591.patch.gz

The patches should be applied in order.
This provides conversion of finite fields, cyclotomic fields and their elements, as well as gap matrices.

[sagetrac-jlopez]

Simplification of one of the previous functions

[sagetrac-jlopez]

Attachment: 13592.patch.gz

Further simplifications and merging. Apply only this patch.

[wdjoyner]

comment:3

Attachment: gap_to_sage.patch.gz

Last patch applied fine to sage-4.3.a0 on a 64bit ubuntu machine, but the following tests failed:

The following tests failed:


        sage -t  "devel/sage/sage/groups/perm_gps/permgroup.py"
        sage -t  "devel/sage/sage/structure/parent.pyx"
        sage -t  "devel/sage/sage/structure/parent_old.pyx"
        sage -t  "devel/sage/sage/misc/sagedoc.py"
        sage -t  "devel/sage/sage/misc/sage_eval.py"

[williamstein]

comment:4

Hi Javier,

What are your intentions regarding #7890
It seems to have got dropped over two years ago. Now none of the patches apply to recent
versions of Sage. I wonder if you're planning to clean this up and finish it?

-- William

[sagetrac-jlopez]

comment:5

Hi William,

yeah, sorry about that. I changed jobs in 2010 and my whole work plan went south.
I would like to get this thing working eventually, but I don't believe the approach I was trying is a good one. The lack of types in GAP creates some ambiguity in gap elements that can have different parents and where a choice needs to be made.

Probably a better approach would be to provide an optional argument sage_parent to the _sage_ function in GapElement, and then put the heavy lift into the sage parent where an ad-hoc gap-to-sage function can be defined, something like this:

def _sage_(self, sage_parent = None):
    if sage_parent is not None:
        return sage_parent._call_from_gap(self)
    else:
        .... # The function as it used to work

In this way, anyone creating a sage structure could implement their own "take an element from gap here" function rather than mess up with the interface. How does that sound?

In any case it might make sense to wait a little bit and get GAP 4.5 working first, as it seems the representation of some objects has changed.

[videlec]

comment:6

Hello,

With #18152, it works fine for cyclotomic elements (because I introduced a function E in the global namespace)

sage: a = gap('E(9)')
sage: a.sage()
-E(9)^4 - E(9)^7

Vincent

[videlec]

comment:7

Note that with the new libgap the conversion works almost fine for matrices (it is converted into a list of lists instead of a matrix)

sage: m = matrix(GF(5), 2, [1,2,-1,1])
sage: a = m._libgap_().sage()
sage: a
[[1, 2], [4, 1]]
sage: matrix(a) == m
True