5 seems to be rather far from infinity though.

5 seems to be rather far from infinity though.

Last Maple version that I used (few years ago) was Maple 10. In that version, if I remember correctly, VectorCalculus:-int provided just a shorthand notation for a repeated integral. Many things could change since then. Especially, as Joe Riel mentioned, in new DifferentialGeometry package. It would be interesting if more general multidimensional integrals were introduced.

The standard terminology for 2-dimensional case is Type I if it's "y-axis convex", and Type II if it is "x-axis convex".

Alec

One simple case is when the domain is given by an inequality or a system of inequalities. Something like f(x,y,z)<=0. In this case, if the change of variables is given by formulas x=X(u,v,w), y=Y(u,v,w), and z=Z(u,v,w), then the new domain is defined by an inequality f(X(u,v,w),Y(u,v,w),Z(u,v,w))<=0 in this example. One thing that still has to be checked in addition to that is that the transformation is bijective.

Not talking that multidimensional integrals are not defined in Maple though - except the case of repeated 1-dimensional integrals.

Alec

Alejandro,

As usual, you are right. I should say: "It's great to live in the United States and be a student nowadays."

Alec

The Student version is much cheaper - I am just being jealous :) 

I guess, I should register for some courses - and then I would be able to get not only cheap student versions of Maple, Mathematica, and Matlab, but also MSOffice and free VS2008.

It's great to be a student nowadays.

Alec

PS It would be fun if I could register for my own courses :) -Alec

That seems to be consistent with Document mode in Maple - spaces are interpreted as product signs. In this particular example, a(b+c) is a value of a function and a (b+c) is a product. That, certainly, is easier to implement than the type checking.

A (slightly) negative side of that is that the existing LaTeX code should be revised before entering in the system, with manual adding of missed spaces (or deleting some of them for an opposite interpretation.) Still, that would be a significant progress comparing to the current necessity of rewriting the LaTeX code completely for entering it in a Maple session.

In Maple, that could be distinguished by checking the type of a. Except, maybe, the cases where function f(a,b,c) is defined as a(b+c) and it is not clear from the definition whether a is a function or a variable. Still, that could be parsed as a conditional expression - if a is a function, then it is the value of that function at b+c, otherwise - the product.

As far as I recall, Maple was treating numbers as functions though, so, say, if a=3, then a(b+c) = 3. That could be avoided, perhaps, by checking also whether a is a number as well (in addition to checking whether it is an operator.)

In general, an actual implementation of such things in Maple would, propably, require the revision of the existing type system (resulting in breaking some backward compatibility which seems to be a "no-no".)

I would, probably, post more if I had Maple installed.

Alec

I would, probably, post more if I had Maple installed.

Alec

Congratulations, Axel,

And I completely agree with Georgios that it was well deserved. As well as all the previous Maple Mentor Awards. Whoever chose them, did a very good job, too.

Alec

In Ubuntu 8.04 with Firefox 3.0b5 the central mapleprimes page gave only one warning,

Warning: Expected ',' or '{' but found '0'. Ruleset ignored due to bad selector. Source File: http://www.mapleprimes.com/themes/mapleprimes/style.css Line: 1141

The user account page gave the same warning and the error message that I mentioned in the original post in this thread,

Error: unterminated string literal
Source File: http://www.mapleprimes.com/user/thomasunger
Line: 281, Column: 12
Source Code:
 s.pageName="MP:User:Thomas

Previewing this post produced a bunch of warning messages that I also mentioned above.

Alec

It may be useful on other pages - it just doesn't seem to be useful on this particular one.

About error messages - I just checked them in Firefox 2.0.0.14 on Windows Vista SP1 by clicking Tools (in the menu) and then Error Console. Going to the page http://www.mapleprimes.com gives 3 warnings in the Error Console,

Warning: Error in parsing value for property 'display'.  Declaration dropped.
Source File: http://www.mapleprimes.com/modules/system/defaults.css
Line: 43

Warning: Unknown property '_width'.  Declaration dropped.
Source File: http://www.mapleprimes.com/themes/mapleprimes/style.css
Line: 167

Warning: Expected ',' or '{' but found '0'.  Ruleset ignored due to bad selector.
Source File: http://www.mapleprimes.com/themes/mapleprimes/style.css
Line: 1141

Going to the user account page that I mentioned in the original post, adds to them another 3 warnings and 1 error message - that I posted in the original post.

I didn't try that in Linux. After posting that, I am going to check that in Ubuntu 8.04 with Firefox 3 beta 5 (that is installed there by default.)

Alec

The error console was opened when I posted that, and I saw that the posting created series of new warnings:

Warning: Unknown property 'filter'.  Declaration dropped.

and so on - the same warning message but for different lines and different properties filled several pages in the error console.

Alec