Generate Polynomial Expansion Orders as a matrix

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Aksh Chordia
Aksh Chordia 2022-4-17
评论： Aksh Chordia 2022-4-19
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.

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Bruno Luong
Bruno Luong 2022-4-17
编辑：Bruno Luong 2022-4-17
Ran in:
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
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Bruno Luong
Bruno Luong 2022-4-18
编辑：Bruno Luong 2022-4-19
Ran in:
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

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