On 03/17/2011 10:19 AM, Yrogirg wrote:
> I failed to find the answer in axiom books (at least in first few). It
> is only said that "The type Expression Integer (abbreviated EXPR INT)
> is used to represent general symbolic expressions in Axiom".
>
> What is the underlying theory (I guess the one that underlies all
> CAS's)? Is there a technique to avoid this general type? Or why it
> should not be avoided?
Wow! What a question. Browsing through the history of the mailing
archive, you'll find that I also don't like "Expression" very much.
The answer for whether "EXPR INT" represents a general expression is
true and false in some sense.
True, because it is the way to take general input of a user (which is
usually an expression -- actually even only a string of characters) and
transforming that into some typed FriCAS object. Since there some
guessing is involved and it doesn't succeed all the time, there must be
some fallback. EXPR INT is such a fallback. It is somehow a necessary
evil for the interpreter. When it however comes to library programming,
I am very much for avoiding EXPR altogether.
The answer is false, because, the implementation of EXPR INT is not what
perhaps other CAS do or how one would imagine an ordinary expression
tree. FriCAS tries to figure out what the smallest units of the
expressions are. Such "smallest units" are known by the term "kernel"
(see Kernel as the corresponding domain). And then FriCAS tries to
represent the expresssion as a rational function with coefficients being
from INT (the argument of EXPR) and "variables" being these kernels.
If you look more carefully through the implementation of EXPR, then you
find that there is not even just one internal representation.
>grep '^ *Rep' expr.spad.pamphlet
Rep := Fraction MP
Rep := MP
Rep := FreeAbelianGroup K
Rep := K
Rep := RF
I hope that helps a bit.
Ralf
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