The multiplication sign is missing in front of the last expression in parentheses.

Alec

q := ((2+sqrt(a))/(a+2*sqrt(a)+1)-(sqrt(a)-2)/(a-1))*(1+1/sqrt(a));

radnormal(q);

                                  2
                                -----
                                a - 1

Alec

Oh, yes. I see what is happening. If that can be simply fixed, I'll post that in my blog.

Yhank you very much for pointing that out.

Alec

Oh, yes. I see what is happening. If that can be simply fixed, I'll post that in my blog.

Yhank you very much for pointing that out.

Alec

Making corresponding adjustmest (to the new picture in my mind), my suggested above algorithm can be modified as follows:

1st step> LeastSquares(A,b);

2nd step> replace the out of range values in the solution to the closest to them ends of the given ranges.

3rd step> construct new Matrix A1 consisting of the columns of A corresponding to the remaining variables (which are inside the given ranges), and replace b with b1 = b - A.(vector with the ends of the ranges selected in step 2 for out of range variables and 0s for other variables.

4th step> LeastSquares(A1,b1)

If the solutions are inside the given ranges, we are done, otherwise go to step 2 above etc.

The number of columns decreases after steps 1-3, so this process is finite.

In the example discussed above, that works as follows,

A1:=LinearAlgebra:-SubMatrix(A,1..-1,2);

                                    [-2]
                                    [  ]
                              A1 := [ 0]
                                    [  ]
                                    [ 2]

b1:=b-A.<2,0>;

                                    [0]
                                    [ ]
                              b1 := [0]
                                    [ ]
                                    [1]

LinearAlgebra:-LeastSquares(A1,b1);

                                [1/4]

Alec

Making corresponding adjustmest (to the new picture in my mind), my suggested above algorithm can be modified as follows:

1st step> LeastSquares(A,b);

2nd step> replace the out of range values in the solution to the closest to them ends of the given ranges.

3rd step> construct new Matrix A1 consisting of the columns of A corresponding to the remaining variables (which are inside the given ranges), and replace b with b1 = b - A.(vector with the ends of the ranges selected in step 2 for out of range variables and 0s for other variables.

4th step> LeastSquares(A1,b1)

If the solutions are inside the given ranges, we are done, otherwise go to step 2 above etc.

The number of columns decreases after steps 1-3, so this process is finite.

In the example discussed above, that works as follows,

A1:=LinearAlgebra:-SubMatrix(A,1..-1,2);

                                    [-2]
                                    [  ]
                              A1 := [ 0]
                                    [  ]
                                    [ 2]

b1:=b-A.<2,0>;

                                    [0]
                                    [ ]
                              b1 := [0]
                                    [ ]
                                    [1]

LinearAlgebra:-LeastSquares(A1,b1);

                                [1/4]

Alec

Yes, I drew a wrong picture (in my mind). LSSolve's answer in this example is better. I wonder what formulas are used in it. The LeastSquares is using

(A^%T.A)^(-1).A^%T.b;
                                [7/3 ]
                                [    ]
                                [5/12]

The optimal solution is such point <x,y> in the square [0,2]×[0,2] that A.<x,y> is the closest point to A.<7/3,5/12> in the parallelogram A.(the square [0,2]×[0,2]), and not the closest point to <7/3,5/12> in the square [0,2]×[0,2] as I thought.

Alec

Yes, I drew a wrong picture (in my mind). LSSolve's answer in this example is better. I wonder what formulas are used in it. The LeastSquares is using

(A^%T.A)^(-1).A^%T.b;
                                [7/3 ]
                                [    ]
                                [5/12]

The optimal solution is such point <x,y> in the square [0,2]×[0,2] that A.<x,y> is the closest point to A.<7/3,5/12> in the parallelogram A.(the square [0,2]×[0,2]), and not the closest point to <7/3,5/12> in the square [0,2]×[0,2] as I thought.

Alec

Joe,

I've just played a little bit with it and it works simply great!

Thank you very much for writing it and making it available here!

Alec

Jacques,

Perhaps, it is just aging? You know... Getting older... Mid-life crisis... Things that interested you earlier, don't interest you anymore...

I am trying to provide some entertainment (from time to time), at least for myself.

For me, this site is about the same except your posts are missing. With you posting more often it was more interesting,

Alec

That's what I usually get during last couple of weeks. I've already learned the username "druprimes" by heart (and I can guess the password :)

We are not talking about 99.9% here. At least 30% or 40% would be nice. All the weekends are usually out and most of the nights, too. In the middle of a day, it is usually less than 50% chance to get connected.

It was better earlier - not quite 99.9%, but still more than 50%.. Is that new pattern related to that announced "upcoming development'?

Alec

That's not that simple as it may seem. What about functions with domain, say (-infinity, -10^1000), (10^10000, infinity). Which range would you suggest and how it could possibly be found?

For any suggestion, it is easy to construct an example when it doesn't work.

It's not just Maple. Such things are not implemented anywhere, because it is impossible.

Note that Maple doesn't have a command for a domain (or a range) of a function, because that is also impossible to find except very simple cases (I posted some procedures for that 5 or 6 years ago in the Maple newsgroup, and I think, the "usual suspects" (using Thomas Unger's term),  Robert Israel, Joe Riel, and Carl Devore also posted a few procedures working for usual Calculus problems, but I don't have the exact reference). 

Alec

For most people, job is one thing and hobby is something different. If they coincide - it is great - you do what you like and you get paid for that.

This is a situation for many people working at Wolfram Research. They post a lot in the Mathematica newsgroup and other forums.

For people working at Maplesoft, the situation seems to be more typical - they are bored by their work, don't have time to post here when they are working and are trying to forget anything Maple related when they are out of work.

2 people assigned by Maplesoft to work on this site, Will and Tim Vrablik, with Will being quite proficient in web development, ant Tim also, probably, proficient in something, know very little about Maple, and what they know seems to come from other people's posts on this site.

Customer service people post here something like: "I've got an email from a user having a problem with Maple installation on the latest Fedora. Can somebody please help him (and me)?" And you want them to post more?

Alec

Now, how can Maple do that? Do you have any code suggestion?

The problem with that is that different people have different needs - somebody might want ro see the graph of sqrt(x-12) from x=12 to x=13, and somebody might want to see it from x=0 to x=100. There is no the "best" choice. That's why Maple is leaving that to users - everybody can enter the range that he or she would like.

Frankly, I can't suggest a better default range than Maple has already. If my plot looks good with it (for constants, for instance), I use it - otherwise (usually), I enter the range that I like.

Alec

I have some opinions on that, but I don't think that anybody would be interested in them. That should be answered by Maplesoft developers, and they are practically unnoticable on this site (except Dr. Paulina Chin doing a really great job answering plotting related questions).

I really appreciate Maplesoft people posting here - especially such stars as Dave Linder, Paul DeMarco, and Laurent Bernardin. I've learned a lot from their posts as well as from Alex Potapchik's, Jan Bakus's, John P. May's, Erik Postma's, Darin Ohashi's and other Maplesoft developers' posts. It would be great if they posted more.

Joe Riel's posts are always interesting - but I consider him being a Maple expert (i.e. on our side) rather than a Maplesoft employee.

Alec