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nhigham.com | ||
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xorshammer.com
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| | | | | There are a number of applications of logic to ordinary mathematics, with the most coming from (I believe) model theory. One of the easiest and most striking that I know is called Ax's Theorem. Ax's Theorem: For all polynomial functions $latex f\colon \mathbb{C}^n\to \mathbb{C}^n$, if $latex f$ is injective, then $latex f$ is surjective. Very... | |
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pfzhang.wordpress.com
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| | | | | Consider a monic polynomial with integer coefficients: $latex p(x)=x^d + a_1 x^{d-1} + \cdots + a_{d-1}x + a_d$, $latex a_j \in \mathbb{Z}$.The complex roots of such polynomials are called algebraic integers. For example, integers and the roots of integers are algebraic integers. Note that the Galois conjugates of an algebraic integer are also algebraic integers.... | |
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hbfs.wordpress.com
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| | | | | Evaluating polynomials is not a thing I do very often. When I do, it's for interpolation and splines; and traditionally those are done with relatively low degree polynomials-cubic at most. There are a few rather simple tricks you can use to evaluate them efficiently, and we'll have a look at them. A polynomial is an... | |
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thisandthatthenextpart.wordpress.com
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