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Question: Get homogenous expressions from symmetric polynomial

Question:Get homogenous expressions from symmetric polynomial

nguyenhuyenag 90 Maple
polynomial
March 17 2017
0

How to get homogenous expressions from symmetric polynomial.

Example. Let P = (a^2 + 2)(b^2 + 2)(c^2 + 2), we have deg(P) = 6. I want to get polynomials of degree n on A[n] with n = 0, 1, ..., 6. Specific

P = a^2b^2c^2 + 2(a^2b^2 + b^2c^2 + c^2a^2) + 4(a^2 + b^2 + c^2) + 8.

And

A[0] = 8

A[1] = 0

A[2] = 4(a^2 + b^2 + c^2)

A[3] = 0

A[4] = 2(a^2b^2 + b^2c^2 + c^2a^2)

A[5] = 0

A[6] = a^2b^2c^2

Thank you very much.
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