Symmetric polynomials in Maple?

[mrbohn1]

Does anyone know if it possible to generate elementary symmetric polynomials in Maple (I am using version 12), and if so, how?

I have scoured all the help files, and indeed the whole internet, but the only thing I have found is a reference to a command "symmpoly", which was apparently included in earlier versions, but does not seem to be available now.

Why would they delete this capability? Surely there must be a way to do this...any help much appreciated!

 

[g_edgar]

symmpoly is not what you want. It was introduced in 4.0, and removed in 4.3. Currently that feature is PolynomialTools[IsSelfReciprocal] ... since "self-reciprocal" is a better term than "symmetric" to describe polynomials like 2*x^3-4*x^2-4*x+2 . But it is not about elementary symmetric functions.

Why didn't they include it? I don't know. Maybe because it is easy to do yourself...

(-1)^k*coeff(expand((X-a)*(X-b)*(X-c)*(X-d)),X,4-k):

for example

(-1)^3*coeff(expand((X-a)*(X-b)*(X-c)*(X-d)),X,4-3);
b c d + a c d + a b d + a b c

 

[mrbohn1]

Thanks for the reply. I disagree it is easier to do it yourself than use a pre-programmed routine! However you're right that it is easy...I was just being lazy. In the end I gave up looking and did it like this (for elementary symmetric polynomials in the variables y_i)

symmpoly:=proc(m,n);
S:={};
for i from 1 to m do
S:=S union {y};
od;
for k from 1 to n do
Tk:=choose(S,k);
s[k]:=sum(product(Tk[j],j=1..k),i=1..nops(Tk));
od;
end proc;

A bit more complicated than your version! I hadn't thought of utilizing the neat factorization.

Anyway, this was a good lesson for me: often it is much quicker to do something for yourself than to search for a quick a fix on google...

 

[LCKurtz]

Here's mine

P := proc (n, k)

(-1)^(n+k)*coeff(collect(expand(product(x-a, i = 1 .. n)), x), x, k)

end proc;

This gives the symmetric polynomials for degree n, k = 0 .. n-1

 

[blue_raver22]

I understand your frustration in trying to find a solution for generating elementary symmetric polynomials in Maple. Unfortunately, it seems that the "symmpoly" command was removed in version 12 and there is no direct replacement for it. However, there are still some workarounds that you can try.

One option is to use the "symmetricpolynomial" function in Maple, which allows you to specify the variables and the degree of the polynomial. Another option is to use the "symmetrize" command, which can be used to generate symmetric polynomials from a given set of variables.

Additionally, there are also packages and libraries available in Maple that can help with generating symmetric polynomials. You may want to explore the "symmetric" package or the "symmetricpolynomials" library, which can provide more advanced tools for working with symmetric polynomials.

It is unclear why the "symmpoly" command was removed in later versions of Maple, but it could be due to updates and improvements in the software. Regardless, I hope these alternatives can help you achieve your goals in generating symmetric polynomials.