[Axiom-developer] RE: More AxiomUI

[Martin Rubey]

Dear Bill,

in fact, I "knew" that what you describe below can be done. The sole purpose of
my mail was to try to get things organised. I have the feeling that it is not
at all clear what "we" want, and in fact, there are several different "we"s,
since some of us are doing math research, some want to use axiom for teaching,
others to use axiom as a platform to try out new ideas, ...

Even the group that does research will very probably have several different,
possibly conflicting "ideals".

Concerning regression testing: I would use the domain specific equality
function of Axiom. After all, Axiom's philosophy is that "simplifications" are
done by user interaction, Axiom itself coerces the stuff only into the domains
representation.

Martin

Page, Bill writes:
 > Martin,
 > 
 > As you know, on MathAction we can write a pseudo-environment
 > 
 > \begin{axiom}
 > guess([1,1+q,1+q+q^2])
 > $GUESS(n,FRAC POLY INT,i+->q^i,FRAC POLY INT, EXPR INT, i+->i, i+->i)
 > \end{axiom}
 > 
 > to achieve the kind of output you describe below.
 > 
 > It would not be difficult at all to achieve this same result with
 > Axiom documentation written in pamphlet format. The command
 > 
 >   $ noweave guess.pamphlet
 > 
 > just creates the LaTeX output from the pamphlet file. This file can
 > contain the same Axiom pseudo-environments as on MathAction. But
 > before it can be processed by the latex command it would first have
 > to be pre-processed by Axiom to convert the \begin{axiom} sections
 > to actual latex. The process would be like this:
 > 
 >   $ noweave example.pamphlet > example.axiom
 >   $ runaxiom < example.axiom > example.tex
 >   $ latex example.tex
 > 
 > This could be make part of the existing `document' script.
 > 
 > Your example file would then look like this:
 > 
 > % ------------------------ example.pamphlet -------------------------
 > 
 > The exported function takes a list of elements of [[F]] and returns a
 > list of expressions over [[R]] that seem to fit the data. For example,
 > 
 > <<inputfile>>=
 > guess([1,1+q,1+q+q^2])
 > $GUESS(n,FRAC POLY INT,i+->q^i,FRAC POLY INT, EXPR INT, i+->i, i+->i)
 > @
 > 
 > returns
 > 
 > \begin{axiom}
 > <<inputfile>>
 > \end{axiom}
 > 
 > % ---------------------------end of example --------------------------
 > 
 > If this is really of interest to you, I can provide the `runaxiom'
 > script based on a simplified version of the Python code that we
 > use on MathAction.
 > 
 > Having it "compare Axiom's output with a given result and raise a
 > warning if the two differ" is certainly possible. This is often
 > called regression testing. Tim Daly has discussed it several times
 > before on this list (see CATS computer algebra test suite). There
 > already some provision for this in the current Axiom makefiles but
 > it is not yet fully functional.
 > 
 > Implementing this properly still requires a bit more design of how
 > to document the expected results and how to perform the comparison.
 > For example: should the comparison be based on the LaTeX generated
 > or just on text output? Is a simple `diff' of the output and expected
 > result adequate?
 > 
 > Regards,
 > Bill Page.
 > 
 > On Tuesday, June 21, 2005 5:39 AM you wrote:
 > 
 > > ...
 > > I think that the pamphlet file syntax we currently have is not too
 > > bad (as "external representation"), but I wouldn't mind if it were
 > > replaced by something else.
 > >
 > > One thing I dislike about it is the following: Currently I have to
 > > write:
 > >
 > > % --------------------------------- example -------------------------
 > >
 > > The exported function takes a list of elements of [[F]] and returns a
 > > list of expressions over [[R]] that seem to fit the data. For example,
 > >
 > > <<inputfile>>=
 > > guess([1,1+q,1+q+q^2])
 > > $GUESS(n,FRAC POLY INT,i+->q^i,FRAC POLY INT, EXPR INT, i+->i, i+->i)
 > > @
 > >
 > > returns
 > >
 > > [[      n 
 > >       q  - 1
 > > (1)  [------]                                      
 > >        q - 1                                       
 > >             Type: List Expression Integer 
 > >]]
 > >
 > > % ---------------------------end of example --------------------------
 > >
 > > However, I'd really like to have axiom compute the result. The best
 > > thing would be, if axiom computes the result and, if present, it
 > > compares it with the given result and raises a warning if the two differ.
 >