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Re: Bug in Series with NonCommutativeProduct?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg122198] Re: Bug in Series with NonCommutativeProduct?
*From*: D J G C <dundjoh at googlemail.com>
*Date*: Thu, 20 Oct 2011 07:43:50 -0400 (EDT)
*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com
*References*: <201110130748.DAA02390@smc.vnet.net> <j79160$i4b$1@smc.vnet.net>
On Oct 14, 11:59 am, Daniel Lichtblau <d... at wolfram.com> wrote:
> On 10/13/2011 02:48 AM, D J G C wrote:
>
> >>Series[(A h) ** (B h), {h, 0, 2}]
>
> > ... + A B h^2+O[h]^3
>
> > The problem is the appearance of a commutative product A B. It should
> > instead be A ** B
>
> > However applying the D gives the correct answer:
>
> >> D[(A h ) ** (B h), {h, 2}]
>
> > 0**(B h)+2 A**B+(A h)**0
>
> It's just doing a "blind" Taylor expansion. One can see this by
> replacing NonCommutativeMultiply with some (undefined) function f:
>
> In[242]:=Series[f[(A h), (B h)], {h, 0, 2}]
>
> Out[242]= SeriesData[h, 0, {
> f[0, 0], B Derivative[0, 1][f][0, 0] + A Derivative[1, 0][f][0, 0],
> Rational[1, 2] (
> B^2 Derivative[0, 2][f][0, 0] + 2 A B Derivative[1, 1][f][
> 0, 0] + A^2 Derivative[2, 0][f][0, 0])}, 0, 3, 1]
>
> Daniel Lichtblau
> Wolfram Research
A series always is a "blind" Taylor expansion.
The bug is, that in this "blind" expansion it gets the second
derivative wrong, by ignoring the possibility for a non-commutative
product.
The D[] is aware of this. Why not use its result in the expansion
(which by the way is the definition of a series)?
This is a bug, as Mathematica is a mathematical software, offering the
(a) non-commutative product, which part of it does not handle. At
least the user has to be warned.
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