[Axiom-developer] Re: [fricas-devel] possible bug

[Waldek Hebisch]

Martin Rubey wrote:
> 
> I'd be very grateful if somebody could look at the input file below. (Don't be
> afraid, most of the definitions are not needed)
> 
> I would have thought that bug() would yield twice the same thing.  It may be a
> mistake on my side, of course, but note that
> 
> * axiom does not compute 
> 
>   map(c +-> sqrtrule c, series(first Phi Psi Phi [x,y,Z.2], t=0)::ULS(EXPR 
> INT, t, 0))
> 

Using FriCAS I get errors.  I would prefer clearer error message, but
as William Sit noted, this can not really work due to zero denominators.

> * neither axiom nor fricas can compute
> 
>   map(c +-> sqrtrule c, series(first Phi Psi Phi [x,y,Z.2], t=0)::ULS(EXPR 
> INT, t, 0))-first Phi Psi Phi [x,y,Z2]
> 
> 
> since this is actual work, I'd be extremely grateful for help!
> 
> Martin
> 
> -------------------------------------------------------------------------------
> K := ((t*y+t*x)*z*z+(t*y*y+(-x*y)+t*x*x)*z+t*x*y*y+t*x*x*y)
> Z := zerosOf(K, z)
> 
> sqrtrule := rule sqrt(a^2*?b) == a*sqrt b
> Z1 := map(c +-> sqrtrule c, series(Z.1, t=0)::ULS(EXPR INT, t, 0))::ULS(FRAC 
> POLY INT, t, 0)
> Z2 := map(c +-> sqrtrule c, series(Z.2, t=0)::ULS(EXPR INT, t, 0))::ULS(FRAC 
> POLY INT, t, 0)
> 
> Phi l == [l.2 * l.3/ l.1, l.2, l.3]
> 
> Psi l == [l.1, l.1 * l.3/l.2, l.3]
> 
> -- I guess the following is a bug:
> -- I cannot even subtract the two!
> bug() == 
>     output map(c +-> sqrtrule c, series(first Phi Psi Phi [x,y,Z.2], 
> t=0)::ULS(EXPR INT, t, 0))
>     output first Phi Psi Phi [x,y,Z2]
> 

You may consider alternative way of doing computation:

sd := x*y*sqrt(argument (kernels(numer(Z.1)::Expression Integer + t*y^2_
-x*y + t*x^2).1).1/(x^2*y^2))
ZZ1 := (sd - (t*y^2 -x*y + t*x^2))/(2*t*(x+y))
ZZ2 := (-sd - (t*y^2 -x*y + t*x^2))/(2*t*(x+y))

then

series(first Phi Psi Phi [x,y,ZZ2], t=0)::ULS(EXPR INT, t, 0)_
 - first Phi Psi Phi [x,y,Z2]

gives me 0.

-- 
                              Waldek Hebisch
address@hidden