As to your first question:

epostma — Thu, 26 Jan 2012 09:23:15 Z

You can't really define w as both a bivariate function w(ξ,s) and a univariate function w(ξ). I'd suggest using notation like

w2 := (ξ,s) -> N(s) . w1(ξ);

where w2 is the bivariate and w1 the univariate function. Note that I wrote the function definition in the non-ambiguous arrow notation; writing it as

w2(ξ,s) := N(s) . w1(ξ);

may work, depending on your settings, but the former always does. Note also the use of the period (.) for matrix and vector multiplication.

If you show us a little more of what you're trying to achieve, I bet we'll find out that it's even better to not define w2 itself, but just a definition equation

w2def := w2 = (ξ,s) -> N(s) . w1(ξ);

and then use eval(something, w2def) in some well-chosen spots. This way, you can control when Maple applies this definition of w2; otherwise, it is always applied immediately when Maple encounters the function w2 and you will never get a result that involves w2.

As to your other question: this is not always easy. We would need to see a bit more of the problem you're trying to solve in order to answer it. By the way, it may or may not work to use the same symbol s for the index of x and its argument; if you substitute a value like 2 or 5 for s, you would get x₂(2) and x₅(5), not x_s(2) or x_s(5). It might be better to write this as xs(s) - Maple will never break up a single "word" like that. (There are other solutions involving things called "inert identifiers" - but I'd advise to do that only if it's really worth the added complexity.)

Hope this helps,

Erik Postma
Maplesoft.

MaplePrimes - answers and comments on Question, Multivariable function in matrix form

As to your first question: