@John May 

It seems as if I was thinking about coeff instead of collect at the moment. You know - if one way doesn't work - trying another one.

I use Maple only for this site postings and since I didn't post here for a while, I didn't use Maple for a while as well. And when you (I mean me) don't use something for a while, such kind of mismatches starts to happen. They both start with co after all... Such things happened before on this site (and I don't even want to comment on what those 2 words started with)...

By the way, strangely enough, coeff works with v^x,

coeff(hh,v^x);
                               2
                            5 x  - 4 x + 4

but doesn't work in the form that I tried to use in collect,

coeff(hh,v,x);
                       x     2               x
                coeff(v  (5 x  - 4 x + 3) + v , v, x)

Alec

@hirnyk 

f:=proc(k,size,h)
local L,U,s;
uses Statistics;
s:=size-1.;
L:= s-10*sqrt(2*s);
U:= s+10*sqrt(2*s);
evalf(Int(Int(CDF(Normal(0, 1), h/sqrt(s*(1/x+1/y)))*
(PDF(ChiSquare(s), x) assuming x>0), x = L .. U, method=_Dexp)^(k-1)*
(PDF(ChiSquare(s), y) assuming y>0), y = L .. U, method=_Dexp))
end:

f(8,100000,3.1);
                             0.9048025818

Also, _NCrule can be used instead of _Dexp,

f:=proc(k,size,h)
local L,U,s;
uses Statistics;
s:=size-1.;
L:= s-10*sqrt(2*s);
U:= s+10*sqrt(2*s);
evalf(Int(Int(CDF(Normal(0, 1), h/sqrt(s*(1/x+1/y)))*
PDF(ChiSquare(s), x), x = L .. U, method=_NCrule)^(k-1)*
PDF(ChiSquare(s), y), y = L .. U, method=_NCrule))
end:

f(8,5000,3.1);

                             0.9046870297

f(8,50000,3.1);

                             0.9047965068

f(8,100000,3.1);

                             0.9048025831

f(8,1000000,3.1);

                             0.9048080531

The last 2 digits should be rounded.

Alec

@hirnyk 

f:=proc(k,size,h)
local L,U,s;
uses Statistics;
s:=size-1.;
L:= s-10*sqrt(2*s);
U:= s+10*sqrt(2*s);
evalf(Int(Int(CDF(Normal(0, 1), h/sqrt(s*(1/x+1/y)))*
(PDF(ChiSquare(s), x) assuming x>0), x = L .. U, method=_Dexp)^(k-1)*
(PDF(ChiSquare(s), y) assuming y>0), y = L .. U, method=_Dexp))
end:

f(8,100000,3.1);
                             0.9048025818

Also, _NCrule can be used instead of _Dexp,

f:=proc(k,size,h)
local L,U,s;
uses Statistics;
s:=size-1.;
L:= s-10*sqrt(2*s);
U:= s+10*sqrt(2*s);
evalf(Int(Int(CDF(Normal(0, 1), h/sqrt(s*(1/x+1/y)))*
PDF(ChiSquare(s), x), x = L .. U, method=_NCrule)^(k-1)*
PDF(ChiSquare(s), y), y = L .. U, method=_NCrule))
end:

f(8,5000,3.1);

                             0.9046870297

f(8,50000,3.1);

                             0.9047965068

f(8,100000,3.1);

                             0.9048025831

f(8,1000000,3.1);

                             0.9048080531

The last 2 digits should be rounded.

Alec

First, that would produce the reversed list, starting with 20 and ending with 2.

Second, a more efficient way of doing that is building a sequence first, avoiding op, and then including it into a list

h:=[][]:
for i to 10 do h:=h,2*i od:
h:=[h];

              h := [2, 4, 6, 8, 10, 12, 14, 16, 18, 20]

Note also that from 1 is not necessary in the loop since it is the default.

_______________
Alec Mihailovs, PhD

First, that would produce the reversed list, starting with 20 and ending with 2.

Second, a more efficient way of doing that is building a sequence first, avoiding op, and then including it into a list

h:=[][]:
for i to 10 do h:=h,2*i od:
h:=[h];

              h := [2, 4, 6, 8, 10, 12, 14, 16, 18, 20]

Note also that from 1 is not necessary in the loop since it is the default.

_______________
Alec Mihailovs, PhD

@Will 

Still hasn't been fixed.

Alec

By the way, there is also the folowing interesting result,

collect(hh,v,x);
                        x     2               x
                     x(v  (5 x  - 4 x + 3) + v )

Alec

While the idea is correct, the last 2 vertices and the Jacobian are calculated wrong.

Alec

While the idea is correct, the last 2 vertices and the Jacobian are calculated wrong.

Alec

@Pseudomodo 

Thank you very much!

That was very useful!

Alec

@Dave L 

Thank you!

Alec

@Christopher2222 

The problems with using Maple in teaching in the US are not related to Maple being Canadian or Japanese, I think. Some schools are using it traditionally - Tennessee Tech, for instance.

I don't think that many of us think that Canadians live in igloos. There is an old joke

"- Do you know what Americans think about Canadians?

- They don't."

The word "Americans" here means the USA citizens.

What is better for teaching, Maple or Mathematica, generally, depends mostly on the instructor preference. Some people prefer Mathematica, others - Maple. I don't have a statistics showing which is used more. In some cases it may be a department's chair preference.

In my case - Wolfram Research sent me a complimentary copy of Mathematica, and Maplesoft didn't send me (or offered a download link to) complimentary copies of Maple 13, 14, 15, so the last Maple version that I used in teaching was Maple 12, which I received complimentary from Maplesoft.

Alec

@pvrbik 

Agree. It's a bad design causing a lot of problems, especially in plot and sum commands. Could be called "a bug in design", perhaps.

To change that in, say, Maple 16, one (or more than one - I mean developers) has to work out the backward compatibility issues - so that the worksheets created in earlier Maple versions worked properly opened in the newest Maple version.

It's not such a big deal, actually, and could be done just by adding something like with(Maple8); at the beginning of a worksheet created in Maple 8, but that (making a backward incompatible change) hasn't been done in Maple for a long time - perhaps, since Maple 6.

Alec

@pvrbik 

Agree. It's a bad design causing a lot of problems, especially in plot and sum commands. Could be called "a bug in design", perhaps.

To change that in, say, Maple 16, one (or more than one - I mean developers) has to work out the backward compatibility issues - so that the worksheets created in earlier Maple versions worked properly opened in the newest Maple version.

It's not such a big deal, actually, and could be done just by adding something like with(Maple8); at the beginning of a worksheet created in Maple 8, but that (making a backward incompatible change) hasn't been done in Maple for a long time - perhaps, since Maple 6.

Alec

It is interesting that some of UK schools still use Maple. In my Engineering Differential Equations course last year, with 3 regular hours and 1 lab/week at the University of Massachusetts Lowell, I used Matlab (which was required) and Mathematica. In addition to the regular homework (handwritten), it had 3 midterms and the final also handwritten and done in a regular classroom and 3 small projects and 1 large project done "at home" (actually, in the computer lab, but not in our class time) using Matlab and Mathematica. I couldn't use Maple even if I wanted to because it was not installed there.

It would be interesting to teach a course of "mathematician's tools" covering LaTeX, some basic Linux including shell programming and awk, Python and Sage, and a survey of Matlab, Mathematica, and Maple, plus optionally some HTML, Javascript, C, and assembly if time permits (I'd certainly like to include some other stuff, too - such as Visual Studio and C#, but it would require more time than 3 or 4 hours/week).  It would be hard, probably, to do usual midterms and the final in it though, because they couldn't be done in a regular classroom, without computers, and couldn't be done in a lab because some of the best students may be slow and won't be able to finish in time.

_______________
Alec Mihailovs, PhD