## Alec Mihailovs

Dr. Aleksandrs Mihailovs

## 4470 Reputation

19 years, 353 days
Mihailovs, Inc.
Owner, President, and CEO
Tyngsboro, Massachusetts, United States

## Social Networks and Content at Maplesoft.com

I received my Ph.D. from the University of Pennsylvania in 1998 and I have been teaching since then at SUNY Oneonta for 1 year, at Shepherd University for 5 years, at Tennessee Tech for 2 years, at Lane College for 1 year, and this year I taught at the University of Massachusetts Lowell. My research interests include Representation Theory and Combinatorics.

## Another identity...

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

## Sqrfree and Berlekamp...

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

## Sqrfree and Berlekamp...

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

## convergence...

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

## convergence...

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

## Yes...

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

## It's better with 2 lines...

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

## Plans for finite groups...

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

## there and Domains...

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

## there and Domains...

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

## Gem 14...

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

## abraham...

My guess, abraham voted it down.

Alec

## But...

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

## But...

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

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