Compute all third degree monomials out of a given vector

Suppose you are given a vector

How can one effieciently construct a vector containing all third degree monomials of the vector entries? That is a vector of dimension containing the entries .

[darova]

What is your question?

[Mohamed Abdalmoaty]

See the edited question.

[Matt J]

I don't see how you get . There are nchoosek(n,2) pairings of the u(i) and 4 mononomials per pairing, so I get .

[Mohamed Abdalmoaty]

Are you counting and as two different monomials? (or and ) ...These count as 1 for me.

[Matt J]

For me too.

Answer 1

[Matt J]

p=eps(u);  
p(u<0)=-p(u<0);

logresult = nchoosek(log(u+p),2)*[3 2 1 0 ; 0 1 2 3];

result= real(exp(logresult))