Re: Solve question

• To: mathgroup at smc.vnet.net
• Subject: [mg48934] Re: Solve question
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Thu, 24 Jun 2004 05:35:52 -0400 (EDT)
• Organization: The University of Western Australia
• References: <cb0u6a\$r36\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```In article <cb0u6a\$r36\$1 at smc.vnet.net>, Arturas Acus <acus at itpa.lt>
wrote:

> Dear group,
>
> Suppose we have a system of linear equations eqns, with more variables,
> than can be solved. The question is. Do the number of solved variables
> can depend on the order of how these variables are listed in second
> Solve argument?
>
> Suppose not.
>
>
> The original problem, why I need to know this, is an attempt
> to eliminate dummy indices in formal sum involving Clebsch Gordan
> coefficients:
> CG[{j1,m1},{j2,m2},{j3,m3}]*CG[{j4,m4},{j3,m3},{j6,m6}]*...
>
> To calculate the sum explicitly. Dummy indices inside CG coefficient
> satisfy well known relations:
> m1+m2==m3, m4+m3==m6,...
>
> Not all indices are dummy, some of them are fixed or numbers. Sum may
> involve other objects, so generally there can be more or, rarely, less
> variables than can be solved. It is of primary
> interest then how Solve will act in these cases, and most important, how
> the solution it provides depends on the variables ordering.

I would avoid using Solve for such problems and instead suggest using
pattern-matching. That is, write the orthogonality conditions or the
contraction summations (e.g. leading to 6-j coefficients), etc., with
general coefficients, as a rule. For example, here is a way to code a
summation identity as a replacement rule:

s1[a_, b_] =
Sum[(-1)^(2k_) (2k_ + 1) SixJSymbol[{a, b, k_}, {a, b, f_}],
{k_, Abs[a - b], a + b}] -> 1

(we want k and f to be generic). Now, to reduce such a sum appearing in
an expression, we apply this rule:

Sum[(-1)^(2l) (2l + 1) SixJSymbol[{c, d, l}, {c, d, g}],
{l, Abs[c - d], c + d}] /. s1[a_, b_]

and get the desired reduction. Note the use of a_ and b_ in the
replacement rule.

Cheers,
Paul

--
Paul Abbott                                   Phone: +61 8 9380 2734
School of Physics, M013                         Fax: +61 8 9380 1014
The University of Western Australia      (CRICOS Provider No 00126G)
35 Stirling Highway
Crawley WA 6009                      mailto:paul at physics.uwa.edu.au
AUSTRALIA                            http://physics.uwa.edu.au/~paul

```

• Prev by Date: Re: XML Importing
• Next by Date: Re: Mathematica can't do this double integral
• Previous by thread: Solve question
• Next by thread: AW: Overlay graphs