Dear Olfa,

On Tue, Dec 30, 2008 at 5:30 AM, olfa <[email protected]> wrote:
>
> Hi Mr Ondrej,
>>Do you know an algorithm for calculating the thing you want? If so, let's 
>>implement that in sympy.
> No, unfortunately I don't know.
>
>>So for example you can compare lists with something
> like:
> In [2]: m = [x, y, z+z]
> In [3]: l = [x, y, 2*z]
> In [6]: m == l
> Out[6]: True
>
> In your example here, you specify concretely the elements of your
> lists, but what I want is to deal with symbolically with lists (by
> symbolic I mean without specifying the concrete contents or the length
> of the list)!So how to do that?

You will have to write a function that does that.

>
> Is sympy able to solve something like this: when i have j<N and i==j+1
> the result would be  i==N .

Currently our solver can't do that, but it is on our todo list, see here:

http://code.google.com/p/sympy/issues/detail?id=1047

>
> Could sympy solve this system of equations: xP = 1 + a/yP  and |yP-xP|
> <= epsilon, without fixing the value of epsilon.

You can specify the conditions:

In [1]: var("xP a yP epsilon")
Out[1]: (xP, a, yP, ε)

In [2]: Eq(xP, 1+a/yP)
Out[2]:
         a
xP = 1 + ──
         yP

In [3]: Le(abs(yP-xP), epsilon)
Out[3]: │yP - xP│ ≤ ε

But our solver is not yet intelligent enough to handle absolute values
in inequalities. I created an issue for that:

http://code.google.com/p/sympy/issues/detail?id=1253

Ondrej

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