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Re:可以解释一下吗?In Reply To:Re:可以解释一下吗? Posted by:atlas_of_rruucc at 2004-12-01 11:41:40 转换成z=x+iy和z'=x-iy的多项式就可以理解了
> 令F={f(x,y)},f(x,y)=(x^i)*(y^j),i+j<=d
> 它们是线形无关的当且仅当i,j互不相等
>
> 所以Invariant Polynomials组成的the vector space的dimension等于 |F|
> 且在F中有限定条件: f (x cos α - y sin α, x sin α + y cos α) = f (x, y)
>
> 然后利用极坐标或者复数的性质可以证明:
> f (x cos α - y sin α, x sin α + y cos α) = f (x, y) <=> n| i-j
>
> 所以|F| = number of (i, j) s.t. i+j<=d and n|i-j
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