Re: [Axiom-mail] Failure to simplify trig functions of simple rational multiples of %pi

[Martin Rubey]

Dan Hatton <address@hidden> writes:

> Further to the earlier bits of this thread, I'd been hoping to be able
> to produce the answer "1" with something like
>
> l:Union(Variable l,Integer)
> simplify(cos(2*%pi*l))

> but instead I just get the cosine expression quoted back at me - is
> there some other function I should use instead of simplify() for this,
> please?

The short answer is, unfortunately, "no".  Axiom (FriCAS, OpenAxiom)
currently does not support "assumptions" like "assume that l is an
integer".

The declaration

(1) ->  l:Union(Variable l,Integer)

                                                                   Type: Void

demonstrates a frequent misunderstanding of axiom's types: what you
really tell axiom here is that the type of l is 

    Union(Variable l,Integer)

which means that l can hold either the variable "l", or a *concrete*
integer:

(2) -> l := -42

   (2)  - 42
                                                     Type: Union(Integer,...)
(3) -> l := 'l

   (3)  l
                                                 Type: Union(Variable(l),...)

There is (currently) no such type as "symbolic integer".

There has been a lot of discussion on how to implement what you want,
but as far as I know, nobody is working on it.  Would you be interested?

Martin