[Axiom-developer] Re: severe (!) bug in normalize

[Martin Rubey]

Waldek Hebisch <address@hidden> writes:

> > I have the feeling that the coefficients in v really correspond to the
> > lists toY (for exp) and toU (for tan).
> >
> 
> Yes, exactly.  But toY (and toU) transform kernels while goodCoef needs to
> look at original (untransformed) kernel, so we would have to produce a
> separate list.

OK, very good. We agree on the way things work.

> > I must admit that I do not understand your patch. I assume that it also 
> > fixes
> > the correspondence between the vector of coefficients v and the list of 
> > kernels
> > l. Why doesn't it fix that rather in expeval and taneval?
> > 
> 
> I really do not "fix the correspondence": I detect when there is a
> possible mismatch and return "failed" in this case.  The
> 
>      not (h = (maxIndex(v) - minIndex(v) + 1)) => "failed"
> 
> line is doing that.

OK.

> Please understand that the patch is a compromise.  There are other bugs when
> using EFSTRUC but at least one problem really affect most of algebra.
> Namely, rischNormalize can get into infinite loop:

Yes, I found such situations, too.

> rischNormalize (using Risch strucute theorem) can detect that some kernels
> are algebraically dependent and forms an expression which is a constant.  But
> simplifier is unable to see that the expression is constant.  You have
> written that simplifing is undecidable, but that happens even for "easily
> decidable" classes.  The problem really is that various part of Axiom use
> inconsistent conventions.  rischNormalize is sound _only_ when
> sqrt(6)=sqrt(2)sqrt(3).  But simplifier refuses to do such simplifications
> (they are invalid using default "real" convention) and things which
> matematically are fields turn into rings with zero divisors.

Yes. This *really* needs cleaning up. In fact, I think we should consider to
redesign the algebra to make use of axioms like canonicalUnitNormal and the
like. Maybe Francois is heading in the right direction, too, when he tries to
choose consistent simplification rules for EXPR. However, I think that he will
need some help.

I guess that the main problem with EXPR and friends is, that it is not clear
what the variables are. Do you know the assumptions needed for RischNormalize?

I wonder whether SumIt is a similar mess.
 

Martin