Reducibility of polynomials of the form f(x)-g(y)
A. Schinzel (1967)
Colloquium Mathematicae
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Displaying similar documents to “Minimal polynomials of algebraic numbers with rational parameters”
Reducibility of polynomials of the form f(x)-g(y)
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A new rational and continuous solution for Hilbert's 17th problem.
Charles N. Delzell, Laureano González-Vega, Henri Lombardi (1992)
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In this note it is presented a new rational and continuous solution for Hilbert's 17th problem, which asks if an everywhere positive polynomial can be expressed as a sum of squares of rational functions. This solution (Theorem 1) improves the results in [2] in the sense that our parametrized solution is continuous and depends in a rational way on the coefficients of the problem (what is not the case in the solution presented in [2]). Moreover our method simplifies the proof and it is...
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Smith normal form of a matrix of generalized polynomials with rational exponents
Miroslav Kureš, Ladislav Skula (2008)
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It is proved that generalized polynomials with rational exponents over a commutative field form an elementary divisor ring; an algorithm for computing the Smith normal form is derived and implemented.
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DoYong Kwon (2007)
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Andrzej Schinzel (1995)
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Multiplication formulas for q-Appell polynomials and the multiple q-power sums
Thomas Ernst (2016)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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In the first article on q-analogues of two Appell polynomials, the generalized Apostol-Bernoulli and Apostol-Euler polynomials, focus was on generalizations, symmetries, and complementary argument theorems. In this second article, we focus on a recent paper by Luo, and one paper on power sums by Wang and Wang. Most of the proofs are made by using generating functions, and the (multiple) q-addition plays a fundamental role. The introduction of the q-rational numbers in formulas with...
Polynomials dividing infinitely many quadrinomials or quintinomials
L. Hajdu, R. Tijdeman (2003)
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