22.03.2012 09:33, Sai Nikhil пишет:
> currently if we are calculating the series for a function ( eg.,
> sin(x).series(x,x0=2,n=6) ) about a point "x0 = a" , where "a != 0" ,
>
> then we are getting the expression of f(x+a) (i.e.,
> sin(x+2).series(x,x0=0,n=6)) about "x0 = 0" , as there is no proper support
> for Order term Arithmetic in sympy .
>
1. Frankly speaking, this is not the whole truth.
Yes, there is a problem in the representing of asymptotic series near
non-zero point, as there is no proper support for Order arithmetic, but
the Order arithmetic depends on the rest expression.
Order term must know (and therefore parse) many things of the rest
expression, and it is not known what arithmetic is easer.
> I want to improve the Order term Arithmetic (around a point that is not '0')
> ...
>
> can you please give me the references for completing this ...
>
>
2. You can see where Order is used now, in simple x==0 case, by
searchiong source lines for the "is_Order" string.
In the main, the code in those lines tests this property of symbolic
expression and deside how to handle with it further. In many places.
The Order expression itself, as described as class and aimed to maintain
common cases (as docstring says) , is placed in the
"sympy/series/order.py" file.
See also "sympy/series/tests/test_order.py" for examples.
3. Another difficulty, that now in SymPy (somehow) not only the power
series are implement, but generalized, e.g.
1 + (log(x)*x) + (log(x)*x)**2 + ...
4. We have the two ways:
* represent assymptotic series as unstructured expression, as it
presents now in SymPy.
In this case we must implement Order term extensively. But it is not
qiet efficient, or even known how to deal with it in common cases.
* represent assymptotic series as expression which has the structure,
like polynomes keep coefficients only.
6. So, as conclusion, I afraid that it is not easy or quick issue.
See also:
https://github.com/sympy/sympy/wiki/UD-series-situation
--
Alexey.
> *-thanks,*
> *Sai Nikhil .T <http://www.tsndiffopera.in>*
>
> *
> *
> *1*
>
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