Re: [Axiom-mail] comparison operators and %pi

[Sumant S.R. Oemrawsingh]

Hi,

Thank you for your answer! Apparently I fell immediately into a hairy bit
there...

I just find this very strange:
(1) -> %e

   (1)  %e
                                                     Type: Expression Integer
(2) -> %pi

   (2)  %pi
                                                                     Type: Pi

Why is %e of type Expression Integer, while %pi is of type Pi? Is there some
deeper reason why Pi is its own type?

Anyway, your answer was very helpful, and so was Themos': numeric(%pi) works
equally well.

Thanks again!

Sumant



On Thu, May 24, 2007 at 06:06:33PM +0200, Martin Rubey wrote:
> "Sumant S.R. Oemrawsingh" <address@hidden> writes:
> 
> > I just tried axiom today for the first time, since it appears quite
> > powerful. This of course means I'm a total newbie, so I've tried searching
> > for the problem that I have through the archives, without luck.
> 
> welcome, and do not hesitate to ask!  I highly recommend the axiom book by
> Jenks and Sutor as first reading, by the way.  What
> 
> > I'm trying to define a piecewise function, and I didn't manage. I could 
> > track
> > the problem down to this expression in the predicate: x < %pi.
> 
> Note that (unfortunately) if you are dealing with things like trigonometry 
> %pi,
> you are often confined to the domain "Expression Integer", which is currently
> not very powerful in axiom.
> 
> Most importantly:
> 
>  the operation "<" does not use the "mathematical" ordering in Expression
>  Integer!  In fact, it wouldn't make sense anyway, think of "cos x < 0", and
>  currently we do not have a domain for "constant" expressions, I believe. (But
>  we certainly should).  In particular, in Expression Integer, you have "%pi <
>  %e" evaluate to true:
> 
> (1) -> %pi < %e
> 
>    (1)  true
>                                                                 Type: Boolean
>  What you want is to compare numerically:
> 
> (2) -> %pi::Float < %e
> 
>    (2)  false
> 
> (3) -> 1::Float < %pi
> 
>    (3)  true
>                                                                 Type: Boolean
> (4) -> 1.0 < %pi
> 
>    (4)  true
>                                                                 Type: Boolean
> 
> > However, Float (1.1 < %pi) and AlgebraicNumber (sqrt(2) < %pi) work
> > properly. Nevertheless, I want to evaluate the function at any point and get
> > a symbolic answer instead of Float->Float. What can I do?
> 
> maybe you want something like
> 
> (9) ->   less(a, b) == a::Expression Float::Float < b::Expression Float::Float
>    Compiled code for less has been cleared.
>    1 old definition(s) deleted for function or rule less 
>                                                                    Type: Void
> (10) -> less(sin %e, %pi)
>    Compiling function less with type (Expression Integer,Pi) -> Boolean
>       
>    (10)  true
>                                                                 Type: Boolean
> 
> ?
> 
> (The additional coercion to Expression Float is necessary, since the
> interpreter is too stupid to convert %e directly to float, unfortunately.)
> 
> 
> Martin
>