Generate Polynomial Expansion Orders as a matrix

Hi,

I have to create a polynomial, lets say, with dimensions =4 (x1,x2,x3,x4) and order =2.

Then the expansion becomes:

f= 1+a1*x1+a2*x2+a3*x3+a4*x4+a5*x1^2+a6*x1*x2+a7*x1*x3+a8*x1*x4+a9*x2^2+a10*x2*x3+......so on.

I want these monomial orders in the format such as :

[0,0,0,0;

1,0,0,0;

0,1,0,0;

0,0,1,0;

0,0,0,1;

2,0,0,0;

1,1,0,0;

1,0,1,0,

1,0,0,1;

0,2,0,0;

0,1,1,0;

...... so on]

I am not able to figure out how to get that.

Therefore, requesting your help.

Answer 1

[Bruno Luong]

You can use this FEX (also attached)

allVL1(4,2,'<=')

ans = 15×4

0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 2 0 0 1 1 0 0 2 0 0 1 0 1 0 1 1 0

[Aksh Chordia]

Thanks a lot!

[Aksh Chordia]

Thanks a lot bruno.

But, I need the coefficients, in the specific order mentioned in the question.

Could you provide information on how to change that?

[Bruno Luong]

Do you want like this?

A=sortrows(allVL1(4,2,'<='),'descend');
[~,is]=sort(sum(A,2));
A=A(is,:)

A = 15×4

0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 2 0 0 0 1 1 0 0 1 0 1 0 1 0 0 1 0 2 0 0

[Aksh Chordia]

Thanks a lot. It really helps :)