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

 From: Martin Rubey Subject: [Axiom-developer] Re: [fricas-devel] Re: possible bug Date: 30 Apr 2008 14:10:43 +0200 User-agent: Gnus/5.09 (Gnus v5.9.0) Emacs/21.4

```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

```

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