topics on polynomials
Definitions
 1.
 2.
 3.

4.
polynomial ring over a field
 5.
 6.

7.
$q$ skew polynomial ring
 8.
 9.

10.
length of a polynomial^{}

11.
polynomial growth
Polynomials over $\mathbb{R}$
 1.
 2.
 3.

4.
Sturm’s theorem
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 7.

8.
Abel’s theorem
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 12.
Roots of polynomials
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3.
continuous^{} dependence on coefficients

4.
Tchirnhaus transformations
 5.
 6.

7.
Viete formulas

8.
Descartes’ rule of signs
 9.
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 11.
Polynomials with special properties
 1.

2.
opposite polynomial
 3.
 4.
 5.

6.
all one polynomial

7.
prime factors^{} of ${x}^{n}1$ (http://planetmath.org/PrimeFactorsOfXn1)
 8.
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 14.
Classical orthogonal polynomials
 1.
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 6.
Other polynomial families
 1.
 2.
 3.

4.
http://planetmath.org/node/12200Boubaker polynomials
 5.

6.
Lamé polynomials
Miscellaneous applications
 1.

2.
Characteristic polynomial^{} in linear algebra^{} (see also CayleyHamilton theorem^{})
Related concepts

1.
division algorithm^{} for polynomials

2.
since sets of polynomial are rings, commutative algebra concepts like PID, UFD and Euclidean domains^{} are heavily related

3.
Gröbner basis
Title  topics on polynomials 

Canonical name  TopicsOnPolynomials 
Date of creation  20130322 15:20:57 
Last modified on  20130322 15:20:57 
Owner  matte (1858) 
Last modified by  matte (1858) 
Numerical id  31 
Author  matte (1858) 
Entry type  Topic 
Classification  msc 13P05 
Classification  msc 11C08 
Classification  msc 12E05 
Related topic  PropertiesOfOrthogonalPolynomials 