Talk:Display a linear combination

Wat?

There's a variety of ways of implementing linear combinations, and this particular task is requiring a representation which will not be executable in many languages. So it would be good to add some motivation to the task description. Why would someone want to do this? --Rdm (talk) 16:15, 13 October 2015 (UTC)

I was working on my Perl 6 Geometric Algebra library and I needed some way of displaying a multivector. By default I had an output like this one:

MultiVector.new(blades => (my Real %{UInt} = 0 => 1, 4 => 1, 10 => 3))

Which is the output from $1+e(2)+3*e(1)*e(3)$, and it is clearly not satisfying. I wanted an output that looks like the input. The more I thought about it the more I was annoyed by the idea that in order to have something that looks good I would have to make sure I don't display the scalars if they are 1, and that I use a subtraction where appropriate. It was looking like quite a hassle,so I thought: « why not make a rosetta task so that I can steal the solution from others? »  :-)

As a matter of fact soon after I created the task I realized I could get a simple solution by using string substitutions on the output, so I was actually able to write the first solution in Perl 6.

I still think it's a useful task, as it can be used for instance to display complex numbers or quaternions. In perl 6 for instance the output for complex numbers is not perfect. i is displayed as '0+1i;', which to me is acceptable but not so great. With Math::Quaternions it's much worse and arguably not acceptable.

--Grondilu (talk) 22:09, 13 October 2015 (UTC)

Sure, it's useful, but the syntactic constraints are also tailored towards perl6 - so that should at minimum be mentioned in the task description (and ideally would also have been in the page name). --Rdm (talk) 23:17, 13 October 2015 (UTC)

Is it really [targeted at Perl]? It looks like something a functional language or Lisp would be pretty good at and the Tcl solution is nice. --CraigD (talk) 23:30, 13 October 2015 (UTC)

Here's how the -1, -2, 0, -3 example might look if it rendered to lisp: (+ (- (e 1)) (* -2 (e 2)) (* -3 (e 4))). Here's how it might look if it rendered to forth: 1 e 0- 2 e -2 * + 4 e -3 * +, and there are a good variety of other possible renderings also. --Rdm (talk) 23:42, 13 October 2015 (UTC)

I'm not sure what you mean when you say that the syntactic constraints are tailored towards perl6. An expression like $a+b-2c$ is not language specific. It's how you write a linear combination in standard math. Let me remind you that this task is about output, not input. If I'm not mistaken your predilection language, J, as an elaborate syntax and I'm sure there are plenty of ways to create a linear combination, but a human friendly, and mathematically conventional way of displaying such linear combination is quite universal. In fact in Perl 6 we could use any syntax we want since we could create a slang or something. I've just picked one that corresponds to the way we write algebraic expressions in maths, regardless of the programming language.--Grondilu (talk) 23:54, 13 October 2015 (UTC)

Ok, so that's what it is. In that case, the spec should still be documented in the task description - it's just not perl6 lik I thought it was. Of course, you are hindered by the fact that "Standard Math" isn't very standard - it was created just a few years ago, and is a rather slippery collection of concepts also. I tried finding a definitive definition, and the best I found was an inexact common core document with a 2015 copyright on it. So most older math texts won't be using it, for example and it's difficult to talk about.

Still... do the best you can. --Rdm (talk) 00:41, 14 October 2015 (UTC)