Re: Bug in Series with NonCommutativeProduct?

*To*: mathgroup at smc.vnet.net*Subject*: [mg122111] Re: Bug in Series with NonCommutativeProduct?*From*: Daniel Lichtblau <danl at wolfram.com>*Date*: Fri, 14 Oct 2011 05:54:40 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201110130748.DAA02390@smc.vnet.net>

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

**References**:**Bug in Series with NonCommutativeProduct?***From:*D J G C <dundjoh@googlemail.com>