Alex Smith

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17 years, 17 days

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These are replies submitted by Alex Smith

Yes, this seems to work. But how do I save the change so that the "fixed" format is the default when Maple is launched?

I'm not following what you are saying about cores and threads, but maybe you should be looking for more efficient ways to construct matrices. The do loop construction is slow. If you try

M := Array( 1 .. 30000000,1..1, (i,j)->i);

then within a minute, Maple constructs M.

 

 

No, it does not refute his claim. It reinforces it.

 

When I evalf the solution from 9.5, I get

t=(0.2979758039e-32-2.244632116*I)*h/tau

so this looks like t=-2.244632116*I*h/tau...imaginary.

Substituting this back into the equation, it looks like a solution.

Another solution is

t=-0.568808526*I*h/tau

No, it does not refute his claim. It reinforces it.

 

When I evalf the solution from 9.5, I get

t=(0.2979758039e-32-2.244632116*I)*h/tau

so this looks like t=-2.244632116*I*h/tau...imaginary.

Substituting this back into the equation, it looks like a solution.

Another solution is

t=-0.568808526*I*h/tau

I think I follow Acer's example, but I'm not sure.

For this case:

 f:=x->-cos(1/x)/x^2;
 a:=1/10000;
  evalf(int(f(x),x=evalf(a)..2/Pi));

I would expect Maple to use the antiderivatve sin(1/x). But instead it hauls off into quadrature, without much success. So in this case, evalf(int.. is acting like evalf(Int...

This is to be contrasted with my recollection  that dsolve typically converts all of the floating point coefficients and initial conditions in a diffeq to rationals before attempting to solve:

dsolve({diff(g(x),x)=f(x),g(evalf(a))=0}); 

returns sin(1/x)-sin(1000) instead of something with floats.
 

 

 

The workaround that John May and Alec propose is productive. When I ran it, Maple 12 returned 92 solutions, whereas Maple 9.5 returned 128 solutions, but we will check theory, etc. to see if the discrepancy is real.

I suppose that my colleagues and I could figure this next step out on our own ("exercise for the reader"!), but John May and Alec seemed primed to do this four orders of magnitude faster:

How can we take the returned solutions that contain variables such as a_1_1 and efficiently convert the solutions to variables such as a[1,1]? 

Thanks!

Maple 9.5 and Maple 10 can solve the following system of equations found at this link Download 2448_system.mws


in about 5 or 10 minutes. They both properly come up with 128 solutions.

Maple 11, and now Maple 12, cannot solve the system.

The workaround given by jpmay does not work since it only returns 1 of the 128 solutions.

It is disappointing that this tracked bug was not fixed before Maple12 was released

In this case, you can  extend the domain of f to include (0,0) and then define partial deriviatives directly using limit, and then things seem to work properly:

f:=proc(x,y) ;
   x*y*(x^2-y^2)/(x^2+y^2);
end;

 f(0,0):=0;

 d2:=proc(x,y);
     limit((f(x,y+h)-f(x,y))/h,h=0);
  end;
 
d1:=proc(x,y);
      limit((f(x+h,y)-f(x,y))/h,h=0);
  end;

d1(0,0); d2(0,0); d1(x,y);

etc.


 It's too bad you have to directly define d1 and d2. You would think that D[1] and D[2] would have this built in.

Are you trying to typeset something like this?

or are you trying to do something else?

Are you trying to typeset something like this?

or are you trying to do something else?

You could try something like this:

with(numtheory):

p:=nextprime(5*10^199);

q:=nextprime(p);


 N:=p*q;

I think N has 400 digits.
 

Yes, I know Maple can handle an integration range like t=t..0.  But calculus instructors cannot, and something like this sends up a red flag. Clearly this is a weakness in Maple that is not worth fixing. 

Maple's plot cannot handle it either. Try

plot(t^2, t=0..t);

Using syntax like t=t..0 should not be encouraged or condoned.

Yes, I know Maple can handle an integration range like t=t..0.  But calculus instructors cannot, and something like this sends up a red flag. Clearly this is a weakness in Maple that is not worth fixing. 

Maple's plot cannot handle it either. Try

plot(t^2, t=0..t);

Using syntax like t=t..0 should not be encouraged or condoned.

In general, finding W=(phi@@(-1))(V) explicitly is very difficult. It almost seems like an algorithm that could do this would be an algorithm that endows a computer with "visualization" powers.

 

Think about Matthias Kawski's intdraw3d package for Maple...the first page of this preprint might be relevant to this discussion:

http://math.la.asu.edu/~kawski/preprints/97mapletech.ps

This reminds me of the challange encountered in a complex variables course, where one tries to find an explict one-to-one analytic map from the unit disk to a simply connected proper domain of C (Riemann mapping theorem). In general it is impossible to explicitly compute the map. For certain domains, there are nice techniques.

 

 

Something like A:={a,b} is a set, and we know {a,b}={b,a} because order does not matter in a set.

Something like L:=[a,b] is a list, which is like an ordered set, and L[1] will certainly be "a".

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