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MAT1001, Fall 2011 Oblig 1
MAT1001, Fall 2011 Oblig 1

Review/Outline Frobenius automorphisms Other roots of equations Counting irreducibles
Review/Outline Frobenius automorphisms Other roots of equations Counting irreducibles

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Section A.6 Notes Page 1 A.6 Solving Equations

... Notice that numbers are large on this one. We must see if there is a common factor first. We find that each number is divisible by 2, so we can factor out a 2: 2(2 x 2 − 19 x + 35) = 0 Now we can factor what is inside the parenthesis. This doesn’t ask for an intercept, but just to solve for x. ...
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On the Relation between Polynomial Identity Testing and Finding

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lecture notes as PDF

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... is continuous and differentiable, with derivative f 0 (x) = nxn−1 . Since f (0) = 0 and limx→+∞ f (x) = +∞, the intermediate value theorem tells us that the graph of f crosses the line y = r somewhere, say at the point (s, r). This means f (s) = r, or in other words sn = r. But now we ask: “Why does ...
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A Quadratic Formula for Finding the Root of an Equation where P = f

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arXiv:math/9802122v1 [math.CO] 27 Feb 1998

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Parallel lines: Application for a multiphase flow

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Factoring in Skew-Polynomial Rings over Finite Fields

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High School – Number and Quantity

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FFT - Personal Web Pages

... Find the (2n-1)-degree polynomial that goes through the points {(x0,p(x0)q(x0)), (x1,p(x1)q(x1)), …, (x2n-1,p(x2n-1)q(x2n-1))}. ...
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FFT - Department of Computer Science

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Integral Calculus Notes

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Bridge of Don Academy – Department of Mathematics Advanced

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Math 161 Notes 1.2

< 1 ... 53 54 55 56 57 58 59 60 61 ... 97 >

Eisenstein's criterion

In mathematics, Eisenstein's criterion gives a sufficient condition for a polynomial with integer coefficients to be irreducible over the rational numbers—that is, for it to be unfactorable into the product of non-constant polynomials with rational coefficients.This criterion is not applicable to all polynomials with integer coefficients that are irreducible over the rational numbers, but it does allow in certain important cases to prove irreducibility with very little effort. It may apply either directly or after transformation of the original polynomial.This criterion is named after Gotthold Eisenstein. In the early 20th century, it was also known as the Schönemann–Eisenstein theorem because Theodor Schönemann was the first to publish it.
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