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[Axiom-developer] [#269 some issues with the 'Factored' domain] (nouveau

 From: kratt6 Subject: [Axiom-developer] [#269 some issues with the 'Factored' domain] (nouveau) Date: Fri, 17 Feb 2006 04:35:41 -0600

Changes http://wiki.axiom-developer.org/269SomeIssuesWithTheFactoredDomain/diff
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Consider the following:
\begin{axiom}
q:FR POLY INT := (x-1)*(x^2+1)
p:FR POLY INT := (x-1)*(2*x)
p+q
)tr MULTFACT )ma
factor(p+q)
\end{axiom}

The documentation says:

Others, like addition require somewhat more work, and unless the argument
domain provides a factor function, the result may not be completely factored.

which is not true, as shown by the result of $p+q$ above.

Furthermore, applying 'factor' to $p+q$ should probably not first expand the
expression and then factor it again. It should rather map over the already
known factors.

I'm not sure whether 'FR' should always try to factor the result of an
addition, at least, I don't think that this was the intention of the original
author.

Another issue is raised by the documentation to 'expand: % -> R':

'expand(f)' multiplies the unit and factors together, yielding an "unfactored"
object. Note: this is purposely not called 'coerce' which would cause the
interpreter to do this automatically.

I tested this and found it not to be true. Note that the domain was written
already in 1985, so it might well be that the interpreters behaviour has
changed in this respect.

Martin

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