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

From: Martin Rubey
Subject: [Axiom-developer] Re: severe (!) bug in normalize
Date: 06 Dec 2006 11:22:44 +0100
User-agent: Gnus/5.09 (Gnus v5.9.0) Emacs/21.4

Dear Waldek,

Waldek Hebisch <address@hidden> writes:

> Have you tried the patch I posted?  

No, I couldn't remember that it was you who posted it, and since it doesn't
contain the word normalize, the search engine didn't find it :-)

> P.S. AFAICS the problem is that the full list of kernel contains both
> transcendental and algebraic kernels. goodCoef is relevant only for
> transcendental kernels and got cofficients as a vector corresponding to
> transcendental kernels. However, the list passed to goodCoef still contain
> algebraic kernels, so goodCoef gets confised, and tries to eliminate wrong
> kernel.

Yes, that's the same what I believe. However, I noticed that goodCoef is called
only in two functions, namely taneval and expeval. 

Here is expeval:

    expeval(f, lk, k, v) ==
      y   := first argument k
      fns := toY lk
      g := y - +/[qelt(v, i) * z for i in minIndex v .. maxIndex v for z in fns]
      (rec := goodCoef(v, lk, "exp"::SY)) case "failed" =>
        expnosimp(f, lk, k, v, fns, exp g)
      v0 := retract(inv qelt(v, rec.index))@Z
      lv := [qelt(v, i) for i in minIndex v .. maxIndex v |
                                                 i ^= rec.index]$List(Q)
      l  := [kk for kk in lk | kk ^= rec.ker]
      h :F := */[exp(z) ** (- retract(a * v0)@Z) for a in lv for z in toY l]
      h := h * exp(-v0 * g) * (k::F) ** v0
      [eval(f, [rec.ker], [h]), [rec.ker], [h]]

What I find a bit surprising is that goodCoef is not called as (roughly)

  goodCoef(v, fns, "exp"::SY)

fns would have to be coerced to the right type, of course. I thought that
(formally), goodCoef

    goodCoef(v, l, s) ==
      for i in minIndex v .. maxIndex v for k in l repeat
        is?(k, s) and
           ((r:=recip(qelt(v,i))) case Q) and
            (retractIfCan(r::Q)@Union(Z, "failed") case Z)
              and gdCoef?(qelt(v, i), v) => return([i, k])

checks whether there is a kernel in l of "type" s, that has a coefficient whose
inverse is an integer, and such that all other coefficients are multiples of
this coefficient. So, v and l should really be of the same length. Looking at

    deprel(ker, k, x) ==
      is?(k, "log"::SY) or is?(k, "exp"::SY) =>
        qdeprel([differentiate(g, x) for g in toY ker],
                 differentiate(ktoY k, x))
      is?(k, "atan"::SY) or is?(k, "tan"::SY) =>
        qdeprel([differentiate(g, x) for g in toU ker],
                 differentiate(ktoU k, x))
      is?(k, NTHR) => rootDep(ker, k)
      comb? and is?(k, "factorial"::SY) =>
        factdeprel([x for x in ker | is?(x,"factorial"::SY) and x^=k],k)

I have the feeling that the coefficients in v really correspond to the lists
toY (for exp) and toU (for tan).

Altogether, it seems to me that the code could need a bit cleaning up. Does
anybody know whether sumit contains equivalent functionality?

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?


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