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

[Martin Rubey]

Dear William, Dear Waldek,

many thanks for your help!

I guess, the real problem is that

(71) -> ex := 
((-2*t*x*y)+(-2*t*x^2))/(y*(t^2*y^4+((-4*t^2)+(-2*t))*x*y^3+((-6*t^2)+1)*x^2*y^2+((-4*t^2)+(-2*t))*x^3*y+t^2*x^4)^(1/2)+t*y^3+(-x*y^2)+t*x^2*y)

                                                              2
                                               - 2t x y - 2t x
   (71)  
--------------------------------------------------------------------------------------------
           +------------------------------------------------------------------+
           | 2 4        2         3        2      2 2        2       3     2 4  
     3      2      2
         y\|t y  + (- 4t  - 2t)x y  + (- 6t  + 1)x y  + (- 4t  - 2t)x y + t x   
+ t y  - x y  + t x y
                                                                                
                Type: Expression Integer
(72) -> series(ex, t=0)

                      2          3       2     2      3
           - 2x y - 2x       - 2y  - 2x y  - 2x y - 2x   2      3
   (72)  --------------- t + -------------------------- t  + O(t )
           +----+                    +----+
           | 2 2       2           2 | 2 2       3
         y\|x y   - x y           y \|x y   - x y
                                                                   Type: 
UnivariatePuiseuxSeries(Expression Integer,t,0)

is not correct in general, eg., when x*y > 0.  In my case, I consider x and y
in fact as formal power series in t themselves, and I think I also want that
sqrt(x^2)=x.


Martin