Obtaining n^th order polynomial combinations in an array
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Hi, I want to obtain an array consisting of all the possible combinations of polynomials upto n^(th) order. For example, for order 2, the array would look like
[1, x(1), x(2), x(3), x(4), x(5), x(6), x(1)*x(1), x(1)*x(2), x(1)*x(3), x(1)*x(4), x(1)*x(5), x(1)*x(6), x(2)*x(2), x(2)*x(3), x(2)*x(4), x(2)*x(5), x(2)*x(6), x(3)*x(3), x(3)*x(4), x(3)*x(5), x(3)*x(6), x(4)*x(4), x(4)*x(5), x(4)*x(6), x(5)*x(5),x(5)*x(6), x(6)*x(6)]
Whereas for order 3, it will look like
[1, x(1), x(2), x(3), x(4), x(5), x(6), x(1)*x(1), x(1)*x(2), x(1)*x(3), x(1)*x(4), x(1)*x(5),
x(1)*x(6), x(2)*x(2), x(2)*x(3), x(2)*x(4), x(2)*x(5), x(2)*x(6), x(3)*x(3), x(3)*x(4),
x(3)*x(5), x(3)*x(6), x(4)*x(4), x(4)*x(5), x(4)*x(6), x(5)*x(5),x(5)*x(6),
x(6)*x(6), x(1)*x(1)*x(1), x(1)*x(1)*x(2), x(1)*x(1)*x(3), x(1)*x(1)*x(4),
x(1)*x(1)*x(5), x(1)*x(1)*x(6), x(1)*x(2)*x(2), x(1)*x(2)*x(3), x(1)*x(2)*x(4),
x(1)*x(2)*x(5), x(1)*x(2)*x(6), x(1)*x(3)*x(3), x(1)*x(3)*x(4), x(1)*x(3)*x(5),
x(1)*x(3)*x(6), x(1)*x(4)*x(4), x(1)*x(4)*x(5), x(1)*x(4)*x(6), x(1)*x(5)*x(5),
x(1)*x(5)*x(6), x(1)*x(6)*x(6), x(2)*x(2)*x(2), x(2)*x(2)*x(3), x(2)*x(2)*x(4),
x(2)*x(2)*x(5), x(2)*x(2)*x(6),x(2)*x(3)*x(3), x(2)*x(3)*x(4), x(2)*x(3)*x(5), x(2)*x(3)*x(6),
x(2)*x(4)*x(4), x(2)*x(4)*x(5), x(2)*x(4)*x(6), x(2)*x(5)*x(5), x(2)*x(5)*x(6), x(2)*x(6)*x(6),
x(3)*x(3)*x(3),x(3)*x(3)*x(4), x(3)*x(3)*x(5), x(3)*x(3)*x(6), x(3)*x(4)*x(4), x(3)*x(4)*x(5),
x(3)*x(4)*x(6), x(3)*x(5)*x(5), x(3)*x(5)*x(6), x(3)*x(6)*x(6), x(4)*x(4)*x(4), x(4)*x(4)*x(5),
x(4)*x(4)*x(6), x(4)*x(5)*x(5),x(4)*x(5)*x(6), x(4)*x(6)*x(6), x(5)*x(5)*x(5), x(5)*x(5)*x(6),
x(5)*x(6)*x(6), x(6)*x(6)*x(6)]
So far, I am manually defining such arrays, but as you can see, it is very tedious. Is there a way to code this for any random order n? Thank you for all the help!
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