Re: The audience for Mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg102182] Re: The audience for Mathematica
- From: David Bailey <dave at removedbailey.co.uk>
- Date: Fri, 31 Jul 2009 05:58:53 -0400 (EDT)
- References: <h4rq53$m3b$1@smc.vnet.net>
Alexei Boulbitch wrote: > Dear Community, > > This question seems to be an important one, if to judge by the number of comments. > I would like to look at this problem from a little bit different perspective. > > I belong to the group #3 according to AES classification cited below. And as such, I see great > advantages of Mathematica for me and for people like myself, as well as lacks of some properties > that Mathematica might, but does not have. > Therefore, it may be a constructive idea to make a list of such desired features classified according to > classes of Mathematica users like the ones cited below. This may help the developers in their great and difficult > work. > > Here I start from myself and invite you to do the same, if you would like to. > > What I badly need are instruments that would enable one to easily bring an expression to a desired form > when making analytical transformations. Let me explain this in more details. Operations like > Simplify, Apart, Factor etc. make a great job. However, when the answer is lengthily it often helps, > if one can group terms in the answer, factorize some parts of those terms separately from one another. > Here it is important that transformation should go not automatically (like it goes now when say, Simplify is applied). > What I have in mind is a complete control of the transformation applied on different levels of the expression by the user > together with a possibility to apply simultaneously different operations on different levels and to different > parts of the same level. > > To give an example, (just the first that that I could think of) here is a simple algebraic expression which is grouped > and factorized in different ways: > > expr = -a^2 b^2 c^2 + 4 a^3 c^3 + 4 a^2 b^3 d - 18 a^3 b c d + > 27 a^4 d^2 = > > =a^2 (b^2 (-c^2 + 4 b d) + 27 a^2 d^2) + 2 a^3 c (2 c^2 - 9 b d) = > > =a^3 (4 c^3 + 27 a d^2) - 2 a^2 b (-2 b^2 + 9 a c) d - a^2 b^2 c^2 > > Such transformations may result in a further simplification that is not most simple according to the Mathematica > criterion, but is most simple from the user point of view. It may also help in understanding of relative contributions of > terms and may enable one to neglect some and thus, to further simplify the whole expression and so on. > > That is how we worked during the pre-Mathematica era, and it often brought a success. I know people (and many of them) > who made important contributions just because they zealously rewrote and rewrote long expressions > many times in many different forms until they have found advantageous ones. > > At present sometimes it is also possible to do so on-screen (e.g. without going to the paper as an intermediate step), > but (i) not in all cases, (ii) this requires > programming which is not always evident and (iii) because of this it draws one away from his primary subject > to a secondary one (e.g. to programming). > > Please understand me correctly: what already exists is already great. I do not propose to refuse of it (or of any its part). > What I would like to, is to have an additional tool, to be applied when necessary by those who need it. > > Therefore, it would be great, if in say, next Mathematica version some tools would be introduced helping to fulfill > such tasks. > > Many years ago, I did indeed introduce a package to do some of this. It worked by letting the user colour certain parts of an expression, and then specify operations that related only to subexpressions of a particular colour, and was fairly feature-rich. Although a few people remember this fondly, it didn't generate much interest, and I didn't update it to work with later versions of Mathematica. David Bailey http://www.dbaileyconsultancy.co.uk