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[Axiom-developer] [#99 x^1 abc[y] should be a syntax error] annoying

From: Bill Page
Subject: [Axiom-developer] [#99 x^1 abc[y] should be a syntax error] annoying
Date: Thu, 17 Feb 2005 15:05:54 -0600

First, I find it rather annoying that the **Status** was changed
by an anonymous user to 'closed' without further discussion. Maybe
I would agree with a status of 'pending' but I think it would 
at least be courteous to identify oneself by clicking 'preferences'
before changing a status. That way at least I know who to blame. ;)
Maybe we should make it so that a user id must be specified in order
to click the 'Change' button?

Second, it was clear from the original description that it is
'not a syntax error'. The bug report said: **should be** a syntax
error. So maybe you mean 'should not be a syntax error'?

Third most of your "explanation" is quite easy to find in the Axiom
book (see page 818)

"Univariate polynomials can also be used as if they were functions."

but the fact that abd[y] when appearing in a Type is displayed as
'*01abc y' is not described anywhere. This notation is especially
odd since it is not a valid input form. So perhaps you might have
proposed to change the category of this issue to 'Axiom Documentation'
and leave the status 'Open'?

But I am not at all convinced that Axiom should behave in this
strange manner. The idea that::

  1 x[k]

is the unit of the domain of univariate polynomials over the
variable x[k] is extraordinarily obscure and does not seem to
have any obvious application to me. Further the fact that::

  1 x

is not defined (because the type of x is of type **Variable x* and
not **Symbol** and for some reason the interpreter does not consider
the obvious coercion of x to **Symbol** while something more complicated
like 'x[k]' is of type *Symbol* by defautl) is at best very awkward
and bordering on the bizarre.

I am not sure whether to blame the interpreter (which is apparently
only following a fairly well defined search strategy) or perhaps better
to blame the implementation of UnivariatePolynomial for allowing this
form of abbreviated 'composition' of polynomials (which I think should
be seen as at best idiosyncratic) as something so ubiquitous in Axiom
as 'function application'. I think there are very good reasons to
distinguish polynomials and expressions in general from functions
(i.e. the lambda abstraction).

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