Re: Full expansion with a mixture of Times and NonCommutativeMultiply
- To: mathgroup at smc.vnet.net
- Subject: [mg103527] Re: Full expansion with a mixture of Times and NonCommutativeMultiply
- From: Szabolcs Horvát <szhorvat at gmail.com>
- Date: Sun, 27 Sep 2009 07:29:37 -0400 (EDT)
- References: <h9kpqa$n0g$1@smc.vnet.net>
On 2009.09.26. 13:18, ChrisL wrote:
> Dear all,
> I am using a non-associative, non-commutative product **
> (NonCommutativeMultiply[]). I have a procedure which builds long
> polynomials that use ** and the usual Times. What I need eventually is
> to extract each of the mononials (parts of the final expression that
> do not contain any Plus[]) for some further processing.
> I defined NonCommutativeMultiply[] very simply like this:
> Unprotect[NonCommutativeMultiply];
> ClearAttributes[NonCommutativeMultiply, Flat]; (* forcing non-
> associativity *)
> 0 ** x_ := 0;
> x_ ** 0 := 0;
> 1 ** x_ := x;
> x_ ** 1 := x;
> (m_Integer*x_) ** y_ := m*(x ** y);
> x_ ** (m_Integer*y_) := m (x ** y);
> Protect[NonCommutativeMultiply];
>
> And getting the full expansion seems to work fine:
> Distribute[2 (3 a1) ** (5 a2)]
> Distribute[a1 ** (2 a2 + a3 ** a4)]
> yields
> 30 a1 ** a2
> 2 a1 ** a2 + a1 ** (a3 ** a4)
> This is great: I can pick up each mononial with Table[expr[[i]],
> {i,Length[expr]}]
>
> Unfortunately, the expansion seems to stop at the second level. Thus:
> Distribute[((2 a2 + a3 ** a4 ) ** a6) ** a7]
> Distribute[(2 a2 + a3 ** a4 ) ** (3 a6)]
> yields
> ((2 a2 + a3 ** a4) ** a6) ** a7
> 3 (2 a2 + a3 ** a4) ** a6
>
> when I need:
> 2 (a2**a6)**a7 + ((a3**a4)**a6)**a7
> and
> 6 a2**a6 + 3 (a3**a4)**a6
>
> Is there any way achieve this? Or do I need to write the full
> expansion algorithm myself? Note that the final expression will be
> much longer - about 30'000 mononials.
>
There will most likely be better answers, but you can use this as a
starting point:
e = ((2 a2 + a3 ** a4 ) ** a6) ** a7
e //. expr : ((_ ** Plus[_, __]) | (Plus[_, __] ** _)) :>
Distribute[expr]
One warning though:
Removing Flat from NonCommutativeMultiply might not be such a good idea
because a ** b ** c is still parsed as NonCommutativeMultiply[a,b,c].
Since parens are required around every operand pair, having an operator
notation (**) isn't a big advantage anyway.