Re: comparison operators and %pi

"Sumant S.R. Oemrawsingh" <[email protected]> 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