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...
okay i found out it is not okay, but can you explain me why not? i thought the decomposition theorem for group homomorphisms sais it should be correct?
ps: i assume you meant f(8)=9
Hey thanks for the stated reasoning. Now, I'm asking if it is also correct to just take the inverse of all the couples I get from the relation k->2^k, but then I get a different mapping from yours: f={(1,0),(2,1),(3,4),(4,2),(5,9),(6,5),(7,11),(8,3),(9,8),(10,10),(11,7),(12,6)}
Okay I'm sorry, the title is wrong, I'm looking for a isomorphism. (In the end I'm looking for a homomorphism from the integers under multiplication mod13 to the complex numbers length 1.)
I have now, but actually now I'm even doubting the isomorphism at itself. The only thing i can think of is something with a logarithm, base 2 cause that converts a 2 into 1 and a product into a sum. But i can't verify it cause it doesn't invert the mapping of the power of class 2.
I'm looking for a formula isomorphism from the set of integers under multiplication mod 13 to the set of integers under addition mod 12. I know the other way around it's easily expressed as a power of class 2. But this way I have no idea if its expressible as a formula.