Maybe an error in sage tutorial

[lainme]

In the section, "A Guided Tour"->"Basic Algebra and Calculus"-
>"Euler’s Method for Systems of Differential Equations", I found that
the answer of the example is z(1)≈0.75, which seems to be wrong.

The calculation is
------------------------------------------------------------------------
sage: t,x,y = PolynomialRing(RealField(10),3,"txy").gens()
sage: f = y; g = -x - y * t
sage: eulers_method_2x2(f,g, 0, 1, 0, 1/4, 1)
t x h*f(t,x,y) y
h*g(t,x,y)
0 1 0.00
0 -0.25
1/4 1.0 -0.062
-0.25 -0.23
1/2 0.94 -0.12
-0.48 -0.17
3/4 0.82 -0.16
-0.66 -0.081
1 0.65 -0.18
-0.74 0.02
------------------------------------------------------------------------

So I think the right answer should be z(1)≈0.65

[kcrisman]

On Feb 11, 10:53 pm, Minh Nguyen <nguyenmi...@gmail.com> wrote:
> Hi,
>
> On Fri, Feb 12, 2010 at 2:15 PM, lainme <lainme...@gmail.com> wrote:
>
> <SNIP>

>
> > So I think the right answer should be z(1)≈0.65
>

> Thank you very much for the bug report. This issue is now tracked at
> ticket #8245:
>
> http://trac.sagemath.org/sage_trac/ticket/8245

And one should also point out that we probably don't need
PolynomialRing in it anymore. I wish I had time to update the
tutorial for the "modern world" of Sage... sigh.

- kcrisman