![]() ![]() If we allow for any arbitrary function of the coefficients of the polynomials, I was wondering, given a fixed positive integer $k$, what is the minimum dimension of a manifold (or union of manifolds) that are the domain(s) of some generating functions, $h_1,\dots,h_l$, such that, starting from $h_1,\dots,h_l$ and applying recursively algebraic, rational operations as well as compositions, one can eventually find a finite set of functions $f_1,\dots,f_h$ that generate all the roots of all the polynomials of degree equal (or not greater) than $k$, in the sense that I clarify formally below. We know by Galois theory that it is not possible, in general, to solve for the roots of polynomials by extracting radicals. Lattice Makers 2400 x 600mm Mahogany Oriental Lattice (0) 75. Benchmark: 4.1.1.5 Real-World & Mathematical. ![]() I have a question that I have been wondering since always, but I am not aware of any literature about it. To multiply decimals, we multiply them just like whole numbers. For example: 53 × 38 is between 50 × 30 and 60 × 40, or between 15, and 411/73 is between 5 and 6. Its a lot easier than the regular way and its kind of fun too. EDIT: I have realized that there were some problems in some of the definitions, which were not quite what I meant, so I fixed them. One of the most time consuming components for hardware implementations of lattice-based cryptography is currently polynomial multiplication. This is a really cool method for multiplying bigger numbers.
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