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[Axiom-developer] [AxiomOutputFormatting]

From: kratt6
Subject: [Axiom-developer] [AxiomOutputFormatting]
Date: Fri, 17 Feb 2006 02:35:07 -0600


-From kratt6 Fri Dec 9 06:09:28 -0600 2005
-From: kratt6
-Date: Fri, 09 Dec 2005 06:09:28 -0600
-Message-ID: <address@hidden>
-You have to say
In this particular case you have to say


Here are some more detailed explanations:

How can I affect the way Axiom displays its results?

    Whenever Axiom needs to write an element of a domain, i.e., an expression 
'Expression Integer', a number from 'PrimeField 5', a factored polynomial from
'Factored Polynomial Fraction Integer', etc., to the screen, it calls the
operation with the signature 'coerce: % -> OutputForm' from that domain.

For example, to output a polynomial in factored form, the "real" way to do it
is to coerce it into the domain Factored Polynomial Integer:

(x^2-y^2)::Factored Polynomial Integer

Thus, philosophically, the way things are output depends only on the domain,
and if we want to implement a different way, we need to implement a new
domain. This is very easy, see SandBoxDistributedExpression.

How does this work in 'Polynomial Integer', 'Expression Integer'?

    The domain 'EXPR INT' contains expressions in the form p/q where p and q are
polynomials -- with the variables being the "kernels" -- and the polynomials
are displayed in the same form as in 'POLY INT', which is unfortunately slightly
confusing. Roughly: "larger" variables are factored out:


since "z" is "larger" than "a". Of course, "larger" is simply a rather
arbitrary, but fortunately fixed internal order of the variables. For
Expressions, this order is not even fixed, I think, but I might be wrong here.
In fact, this ordering is the thing about axiom that I hate most, I don't
really want it to say:

tan x > sin x
tan x > sin y

although I got used to it...

Can I make Axiom display $(xy+x+1)/(y+1)$ as $x+1/(y+1)$?

    As follows from the above, this currently cannot be done within the domain 
'EXPR INT'. I think that there are several possibilities, which I will explain 
on an
old example, the problem of displaying expressions in "fully expanded" form:

* one can write a domain which only overrides the output functionality, and
  applies the simplifications every time the element is written on the
  screen. That's what I have done for DistributedExpression. This is the quick
  and dirty way.

* one writes a new domain with a new representation. For
  'DistributedExpression' I failed to do so, since the proper representation
  would be 'DMP', but this only accepts a 'List Symbol' as variables, for
  expressions I need to allow an arbitrary 'OrderedSet' however.

* one abstracts the form and writes a new functor, as for example
  'Factored'. I'm not quite sure, but it may be that a functor 'Distributed'
  would be the best solution. I would have to look why the original developers
  chose to implement 'DistributedMultivariatePolynomials' instead.

So, the conclusion is that you might want to write a function first that takes
- for example - an expression and returns a list of expressions. It would be
easy to make this into a new domain "MyExpression". I vaguely recall that
Maxima has such a function.

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