Consider the space of all polynomials in n variables of degree at most d. The dimension of that space is C(n+d,d). How do I calculate the dimension of that same space when I restrict the domain of the polynomials to the unit ball? In that case all the polynomials (sum(i=1..n) x_i^2)^p with p a natural number are identical to the polynomial 1. One professor agrees with me that you have to subtract the cardinality of the set {(sum(i=1..n) x_i^2)^p | p in N} from C(n+d,d). But in my course text (written by another professor) sais that the correct formula is C(n+d,d)-C(n+d-2,d-2)(adsbygoogle = window.adsbygoogle || []).push({});

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# Dimension of a multivariate polynomial space

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