Testing low-degree polynomials over prime fields

2009 ◽  
Vol 35 (2) ◽  
pp. 163-193 ◽  
Author(s):  
Charanjit S. Jutla ◽  
Anindya C. Patthak ◽  
Atri Rudra ◽  
David Zuckerman
Keyword(s):  
Low Degree ◽  
Prime Fields ◽  
Low Degree Polynomials

scholarly journals Hard Functions for Low-Degree Polynomials over Prime Fields

2013 ◽  
Vol 5 (2) ◽  
pp. 1-15
Author(s):  
Andrej Bogdanov ◽  
Akinori Kawachi ◽  
Hidetoki Tanaka
Keyword(s):  
Low Degree ◽  
Prime Fields ◽  
Low Degree Polynomials

scholarly journals Irreducible skew polynomials over domains

2021 ◽  
Vol 29 (3) ◽  
pp. 75-89
Author(s):  
C. Brown ◽  
S. Pumplün
Keyword(s):  
Polynomial Ring ◽  
Skew Polynomial Ring ◽  
Weyl Algebras ◽  
Skew Polynomials ◽  
Low Degree ◽  
Skew Polynomial ◽  
Low Degree Polynomials ◽  
Injective Endomorphism

Abstract Let S be a domain and R = S[t; σ, δ] a skew polynomial ring, where σ is an injective endomorphism of S and δ a left σ -derivation. We give criteria for skew polynomials f ∈ R of degree less or equal to four to be irreducible. We apply them to low degree polynomials in quantized Weyl algebras and the quantum planes. We also consider f(t) = tm − a ∈ R.

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