Mike,
On Sun, Sep 7, 2008 at 4:00 AM, Mike Hansen wrote:
>
> There is a patch up at
> http://trac.sagemath.org/sage_trac/attachment/ticket/4036/trac_4036-2.patch
> which improves conversions between Axiom and Sage. It defaults
> to your unparsed input form if it can't find anything smarter to do.
Excellent. I have applied this patch to
sage-3.1.2.alpha4-sage.math-only-x86_64-Linux and with fricas-1.0.3
installed. I tried a few things and so far it seems to work great!
I'll have more time to test it thoroughly in the next 24 hours and let
you know if I find any problems.
> Bill, if you're interested, this would be one area that would greatly
> benefit from someone who actually knows Axiom. For example,
> a number of questions came up as I was writing this.
>
Yes I am *very* interested. Thank you again for your continuing work
on this interface.
> * Is there only one global precision for floating point numbers or can
> different floating point numbers each have different precisions?
Axiom has several different types of floating point numbers:
DoubleFloat (double precision), MachineFloat (single precision), and
Float (arbitrary precision). The latter is the default. In Axiom Float
values are presumed exact, i.e. they correspond to rational numbers of
the form (mantissa*2^exponent) where the mantissa and exponent are
arbitrary precision integers, but computations involving Float are
carried out in a given globally-set precision and so have a known
possible error.
For a given Float value one can determine the minimum precision
necessary to represent that value by finding the binary length of the
mantissa. E.g.
Create two approximations to pi:
sage: axiom('precision(68)$Float')
68
sage: p=axiom('%pi::Float')
sage: axiom('precision(100)$Float')
68
sage: q=axiom('%pi::Float')
Then determine their precision:
sage: p.mantissa().length()
68
sage: q.mantissa().length()
100
Because of normalization this is the case for most values.
> What happens if you create a number in one precision and then change the
> precision?
>
New computations are carried out in the new precision after the change
but nothing else changes.
> * Given a domain like "Polynomial Integer", how do I get the base ring
> "Integer" programatically? This would be like the base_ring method in
> Sage.
>
There is no direct way in standard Axiom, but you could for example
ask for the type of the value of the leading coefficient:
sage: p=axiom('x+1/2')
sage: p.type()
Polynomial Fraction Integer
sage: p.leadingCoefficient().type()
Fraction Integer
> * Are constructors like "Polynomial" first class objects? I can't
> seem to assign "Polynomial" to a variable -- it always wants it to
> be filled in like "Polynomial Integer".
>
Types are first class objects in Axiom but 'Polynomial' is not a type
- it is a "functor", i.e. it is a constructor that takes an argument.
'Polynomial(Integer)' on the other hand is a type.
Regards,
Bill Page.
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