The expected running time is O(n^{3/2}). But we think it is possible to do it in O(n) time.

]]>For example, (x1 + x2 + x3 + . . . + xd)r ?

Or did you mean summing all the variables raised to the rth power from linear polynomials in d variables?

But if they are linear, then how can there be an rth powered variable?

• With or without coefficients?

With, you can fudge an equality.

So, you want either to add something raised to the rth power or sum over some things raised to the rth power with a

non-determined number of monomials of a homogeneous polynomial which somehow is suppose to equal a symmetric polynomial, yes?

An example of a symmetric polynomial given in Wikipedia is a counter-example to what you suspect.

A full proof either way requires Galois Theory which is beyond my pay grade.

Curious, this connexion of models for your learning process is just for you only, right?

]]>For example, (x1 + x2 + x3 + . . . + xd)^r ?

Or did you mean summing all the variables raised to the rth power from linear polynomials in d variables?

But if they are linear, then how there be an rth

powered variable?

• With or without coefficients?

With, you can fudge an equality.

So, you want either to add something raised to the rth power or sum over some things raised to the rth power with a

non-determined number of monomials from a homogeneous polynomial which somehow is suppose to equal a symmetric polynomial, yes?

An example of a symmetric polynomial given in Wikipedia is a counter-example to what you suspect.

A full proof either way requires Galois Theory which is beyond my pay grade.

Curious, this connexion of models for your learning process is just for you only, right?

]]>