Hi,

> The error message is uniformative, but given that
> 'get_rational_solutions2' is not visible here _some_ error is
> expected. 

Oh right, I can not call "get_rational_solutions2" because
it is not exported by the domain. And importing does does
not change that fact. (It indeed was too late.)

The aldor compiler would have told me that by
an informative message:

[L43 C5] #1 (Error) There are no suitable meanings for the operator ...


Well, then I need to write a package first for computing
rational roots of polynomials. I hoped that a System like
Axiom already had such a functionality.

I tried to extract the function from 'ElementaryRischDEX' and
put the new package here:

  https://github.com/raoulb/fricas_code/tree/master/ratroots

At the moment it compiles, I consider this already a small success.
But the exported functions are not really what I think the should be.

The simplest function should maybe have a signature like:

  rationalRoots: (Poly(R), Symbol) -> List(Frac(R))

Or maybe not. I have no idea what a the perfect and
appropriately generalized function should look like.


Without such a functionality, I can not continue :-/


> > > Maximal root is well defined only if coefficients are numbers.
> > 
> > The polynomial is univariate f.e over Q, so my coefficients
> > are indeed numbers.
> 
> Even that is tricky: your extension has multiple embeddings into
> complex numbers.  The set of real root and maximal real root
> depends on the embedding of coefficient field.  So if you really
> need maximal root, you need to fix the embedding.

Uhm, ok.

> Yes, it ATM it is internal -- I needed rational roots for computing
> integrals and apparently there was no usable function in sight,
> so I wrote it.  Current version is specialized for expressions
> (I wrote exactly what was needed for integration), but the method
> works as long as 'reducedSystem' works, that is base ring must
> satisfy 'LinearlyExplicitRingOver(Integer)' (alas, for
> RealClosure(Fraction(Integer)) 'reducedSystem' is unimplemented).

Then the main purpose of "LinearlyExplicitRingOver" is to
provide "reducedSystem", I see.


Importing the RationalRoots package at least makes my other
code compile. 

Thanks so far.

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