@rlopez 

I posted a similar picture for another identity earlier on this site (there is a link to it instead now, which is not working, but the plot can be restored from the Maple commands), and Robert Israel posted there branch cuts calculations for that identity and the proof that the difference between the lhs and the rhs of it is a piecewise constant (with connected regions being the pieces).

A similar proof works here for the ratio of the rhs and the lhs (which can be either 1 or -1 for z≠±I because the squares of the lhs and the rhs are equal),

simplify(diff(sqrt(z^2+1)/sqrt(z+I)/sqrt(z-I),z));

                                  0

with the picture being constructed as

z:=x+I*y:plots:-densityplot(Re(sqrt(z^2+1)/sqrt(z+I)/sqrt(z-I)),
x=-4..4,y=-4..4,color=red,style=patchnogrid,axes=box,grid=[100,100]);

which is not that colorful though.

Alec

@Istarion 

Depending on what you need, there are some other useful commands, ?Sqrfree and ?Berlekamp , for instance.

Also ?DistDeg , ?Divide , ?Factors , ?Gcd , ?Power , ?Powmod , ?Quo , ?Rem etc.

Alec

@Istarion 

Depending on what you need, there are some other useful commands, ?Sqrfree and ?Berlekamp , for instance.

Also ?DistDeg , ?Divide , ?Factors , ?Gcd , ?Power , ?Powmod , ?Quo , ?Rem etc.

Alec

@Scimann 

The convergence can be checked directly through

MultiSeries:-asympt(k*p*Beta(k,p+1),k,0) assuming p>1;

                                     p
                              O((1/k) )

The exact value is a different story.

Alec

@Scimann 

The convergence can be checked directly through

MultiSeries:-asympt(k*p*Beta(k,p+1),k,0) assuming p>1;

                                     p
                              O((1/k) )

The exact value is a different story.

Alec

@Alejandro Jakubi 

Yes, and it is not that easy to write a good matching pattern (I mean the second and the third parameter values in evalindets), except for very simple cases.

Your approach with applyrule seems to beat everything else in this thread (in this gem).

Alec

@Alejandro Jakubi 

It works better with 2 lines,

f:=exp(x)*(sin(u+v)+sin(u-v)):
eval(f=expand(f),solve({u+v=x,u-v=y},{u,v}));

 exp(x) (sin(x) + sin(y)) = 2 exp(x) sin(y/2 + x/2) cos(- y/2 + x/2)

That's how the corresponding procedure implemented through evalindets would work. I didn't mean that that has to be done manually.

Alec

Probably, I'll get an access to Maple 15 either in late August, or in September. Then I'll be able to play with it.

Are there plans to add Maple packages for symmetric functions (and other algebraic combinatorics), and for finite group representations (character tables etc.)?

Alec

The first way there doesn't work for polynomials - just for specific values of them. Domains module was a great idea which had been left unfinished. In present form it gives just a skeleton in this case which has to be filled with body and blood (and that's a lot of work) to make it working.

Alec

The first way there doesn't work for polynomials - just for specific values of them. Domains module was a great idea which had been left unfinished. In present form it gives just a skeleton in this case which has to be filled with body and blood (and that's a lot of work) to make it working.

Alec

As far as I can tell, nowadays in the USA in Introductory Algebra courses, only the case with a=1 is trained. Optionally - with c=1 or small prime a or c (usually 2, 3, or 5) in which cases it is quite easy and useful. Saves a lot of time doing that with, say x²−5x+6 instead of using the quadratic formula.

Alec

That can be written in 2 lines,

f:=sin(u+v)+sin(u-v):
eval(f=expand(f),solve({u+v=x,u-v=y},{u,v}));

          sin(x) + sin(y) = 2 sin(x/2 + y/2) cos(x/2 - y/2)

Alec

@Axel Vogt 

My guess, abraham voted it down.

Alec

It is a Maple V release 3 notebook with .ms extension. It opens in Maple 14 with changing the file selector to "All files". Then after changing * to &* in evalm in assignments of alpha, delta, and P in the loop it works.

However, as far as I understand, it doesn't contain the "full code" of the method - it is a small example, with some fixed parameters, of how this method doesn't work in some cases.

Alec

It is a Maple V release 3 notebook with .ms extension. It opens in Maple 14 with changing the file selector to "All files". Then after changing * to &* in evalm in assignments of alpha, delta, and P in the loop it works.

However, as far as I understand, it doesn't contain the "full code" of the method - it is a small example, with some fixed parameters, of how this method doesn't work in some cases.

Alec