Mike,
Before I reply to your email, let me ask a simple question about sage
as installed on sage.math. When I try the axiom interface there I get:
[EMAIL PROTECTED]:~$ sage
----------------------------------------------------------------------
| SAGE Version 3.1, Release Date: 2008-08-16 |
| Type notebook() for the GUI, and license() for information. |
----------------------------------------------------------------------
sage: axiom('1+1')
sage: axiom('1+1')
sage: axiom('1+1')
Type: PositiveInteger
sage: exit
Exiting SAGE (CPU time 0m0.06s, Wall time 0m33.20s).
Exiting spawned Axiom process.
[EMAIL PROTECTED]:~$ which sage
/usr/local/bin/sage
--------
This result is typical of the failure due to readline/clisp
synchronization problems on some platforms. The only solution I have
for this involves calling FriCAS in such a way as to defeat readline
in './devel/sage-main/sage/interfaces/axiom.py' as follows:
Expect.__init__(self,
name = 'axiom',
prompt = '\([0-9]+\) -> ',
command = "sh -c 'axiom -nox -noclef | cat'",
Although it generates more processes than should be required to do the
job, perhaps this change should be included in the next release?
On Sun, Aug 31, 2008 at 11:11 PM, Mike Hansen wrote:
> ...
> I don't think the interfaces are as much "magic" as you make them
> out to be.
Magic is only science that we don't understand, right? :-) I did not
mean to give the impression that I thought it was magic - only that I
felt some basic documentation in this area was missing. To this end
your comments below are very helpful.
> If you're interested in converting object from Sage to Axiom/FriCAS,
> then there are really only two methods you need to worry about --
> _axiom_ and _axiom_init_. _axiom_init_ method just returns a
> string used to construct self in Axiom. For example, say we have
>
> class Foo(SageObject):
> def __init__(self, n):
> self.n = int(n)
> def _axiom_init_(self):
> return str(self.n)
>
> Then I can do
>
> sage: a = Foo(2); a
> <class '__main__.Foo'>
> sage: axiom(a)
> 2
> sage: axiom(a).type()
> PositiveInteger
>
Thanks! So the point is that we can obtain the string representation
of some Sage object by calling 'str' and often this string can be
passed directly to the Axiom interpreter. I think that is a good
thing, but of course whether or not this works will depend on the type
inferences done by the interpreter. For example:
sage: K = FiniteField(2)
sage: k=K(1)
sage: k.parent()
Finite Field of size 2
sage: k+1
0
sage: k_ax = axiom(k)
sage: k_ax.type()
PositiveInteger
sage: k_ax+1
2
Something is wrong here! In Axiom we do have an appropriate type:
sage: k_ax2=axiom('1$FiniteField(2,1)')
sage: k_ax2.type()
FiniteField(2,1)
sage: k+1
0
Obviously the default conversion from a string is not correct. How can
we make the conversion from Sage to Axiom smarter in this case? Does
it mean that we need to override the _axiom_init_ method with
something more appropriate in some more specific class in Sage? I see
that:
sage: k?
Type: IntegerMod_int
Base Class: <type 'sage.rings.integer_mod.IntegerMod_int'>
String Form: 1
Namespace: Interactive
Docstring:
Elements of Z/nZ for n small enough to be operated on in 32 bits
AUTHORS:
-- Robert Bradshaw (2006-08-24)
So should we add _axiom_init_ to IntegerMod_int class? Something like this?
def _axiom_init_(self):
return str(self.n)+'::FiniteField(%d,1)'%n
where do I get a value for n?
But I notice that:
sage: k=IntegerModRing(2)(1)
sage: k.parent()
Ring of integers modulo 2
sage: k?
Type: IntegerMod_int
Base Class: <type 'sage.rings.integer_mod.IntegerMod_int'>
String Form: 1
Namespace: Interactive
Docstring:
Elements of Z/nZ for n small enough to be operated on in 32 bits
AUTHORS:
-- Robert Bradshaw (2006-08-24)
and also that in Axiom we have 'IntegerMod(2)' as distinct from
"FiniteField(2,1)'. Both Sage and Axiom distinguish between the ring
and the field, so maybe IntegerMod_int is not the right place for
_axiom_init_ since that would make it a field in all cases.
Maybe _axiom_init_ has to come from the Sage parent? How do I do that?
This is the kind of thing that still seems a little mysterious to me ...
> For more complicated things, the _axiom_ method takes in an Axiom
> interface object and returns self constructed in Axiom.
>
> class Foo(SageObject):
> def __init__(self, n):
> self.n = int(n)
> def _axiom_(self, axiom):
> return axiom(str(self.n))
>
> This behaves the same as above.
>
This form seems obscure to me. What is an "Axiom interface object"?
Why/How does this code behave the same way as the first example?
> The Macualay2 interface in sage/interfaces/macaulay2.py has some
> good examples of moving objects back and forth between systems.
>
> Anyway, I did some work on the Axiom interface today such as
> doctesting it, removing broken code, adding tab completion, etc.
> You can see my changes at
> http://trac.sagemath.org/sage_trac/ticket/4028
Great. I have applied these changes to my test version of axiom interface.
> Things like the online help didn't work with either the fricas spkg
> or just on a local copy, but I'd be more than happy to help adding
> that functionality (as well as anything else).
>
Thanks for your work! I hope it will attract more developers
interested in the Axiom interface in Sage.
Regards,
Bill Page.
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