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