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

[kratt6]

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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